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Behaviour and reliability of wood tension members exposed to elevated temperatures Lau, Peter Wing Cheong 1996

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BEHAVIOUR A N D RELIABILITY OF W O O D TENSION M E M B E R S EXPOSED TO ELEVATED TEMPERATURES By PETER W I N G C H E O N G L A U B.Sc.E, The University of Toronto, 1977 M.Sc.E, The University of Toronto, 1980 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in T H E FACULTY OF GRADUATE STUDIES Department of Wood Science We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH C O L U M B I A October 1996 © Peter Wing Cheong Lau, 1996 in presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or Her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of ^Jo°h $ CZ^t The University of British Columbia Vancouver, Canada D A T E A ^ v e ^ ^ e r - 2^o DE-6 (2788) ABSTRACT The merit of approaching fire safety design from the standpoint of rehability is the impetus of this thesis. Reliability, a direct function of time to failure, is a measure of performance which falls naturally under a performance-based code. The objectives of this study focus on advancing our understanding of the structural behaviour of light-frame wood members subject to tension and elevated temperatures, on actual strengths of brittle materials and how these strengths are affected by time at elevated temperatures, and on the time to failure under a given stress-and-temperature history. A model based on linear damage accumulation theory was developed to predict the time to failure. This model is based on a kinetic theory for strength loss as a function of temperature and stress histories, coupled with a kinetic term, to express the pyrolytic process as a form of damage. The model has four independent parameters and requires the short-term strength of the member as an input. This model fits well to experimental data on nominal 2x4 structural lumber tested at three different rates of loading under tension, and at four temperatures, 150, 200 and 250°C, and room temperature. The model also predicts, with reasonable accuracy, the behaviour of lumber under constant load at 250°C. In analyzing the rate-of-loading effect on lumber at elevated temperatures and the reliability as affected by lumber grade, the model predicts that the rate-of-loading effect becomes increasingly significant as temperature is increased. It also predicts that lower-grade material, when subject to a constant tension stress, has a lower reliability index at elevated temperatures up to 250°C. The differences, however, are expected to be msignificant based on current design practices. Temperature effects on strength are approximately linear at temperatures up to 150°C. Above 150°C durations becomes as dominant a factor as temperature. Based on a comparison with existing data, lumber at 9-11% moisture content is more adversely affected by temperature than small, dry, clear specimens. i i Table of Contents Abstract ii Table of Contents iii List of Figures vii List of Tables x Acknowledgements xi 1.0 INTRODUCTION 1 1.1 Merits of Reliability-Based Design 2 1.2 Fire Safety Engineering of Wood-Based Structural Systems 3 2.0 OBJECTIVES 5 3.0 PROBLEM ANALYSIS AND LITERATURE REVIEW 6 3.1 Probabilistic Design 6 3.1.1 Reliability Analysis 6 3.1.2 Performance Function 9 3.2 Strength of Solids 11 3.2.1 Actual Strength 13 3.3 Behaviour of Wood Material at Elevated Temperatures 18 3.3.1 Short-term Strength Properties 18 3.3.2 Creep 22 3.4 Resistance of Lumber Exposed to Fire 24 3.4.1 Strength Models 26 3.4.2 Experimental Data 30 3.4.3 Factors Affecting Strength Distribution 31 3.4.4 Rate of Charring 38 iii 3.5 Time-Dependent Lumber Strength Models 45 3.5.1 Damage Accumulation Approach 45 3.5.2 Fracture Mechanics Approach 47 3.5.3 Kinetic Energy Barrier Approach 49 3.5.4 Statistical Theory of Absolute Reaction Rate Approach 51 3.5.5 Strain Energy Density Approach 52 4.0 RELIABILITY ANALYSIS OF M E M B E R S EXPOSED TO FIRE 53 4.1 Performance Function 53 4.2 Governing Equation for Failure in Tension 54 4.3 Probability of Failure 57 4.4 Treatment of Variables 58 4.4.1 Fire Exposure 58 4.4.2 Temperature 59 4.4.3 Rate of Charring 60 4.4.4 Initial Load 61 4.4.5 Short-term Strength (grade effect) 62 5.0 EXPERIMENTAL W O R K 65 5.1 Scope and Assumptions 65 5.2 Experimental Design 66 5.2.1 Equipment for Exposure to Elevated Temperatures 67 5.2.2 Sampling Methods . 67 5.3.3 Material Sampling 70 5.3.4 Test Procedures 71 5.3.5 Temperature Distribution 72 5.3.6 Other Physical Data 73 iv 6.0 TENSION TEST RESULTS 74 6.1 General Observations 74 6.2 Failures outside Exposed Region 76 6.3 Temperature Variations 78 6.3.1 Lengthwise Variations witiun Specimen 78 6.3.2 Transverse Variations within Specimen 80 6.4 Moisture Content Distribution 84 6.5 Relative Density Distribution 84 6.6 Strength Distribution — Room Temperature 86 6.6.1 Expected versus Observed 86 6.6.2 Weibull Probability Plots 91 6.6.3 Effect of Rate of Loading 91 6.7 Strength Distributions — 150°, 200° and 250°C 92 7.0 TIME TO FAILURE MODELLING 95 7.1 Model Development 95 7.1.1 Key Model Characteristics 98 7.2 Approach to Model Fitting 99 7.2.1 Single-Valued versus Randomly-Valued Coefficients 99 7.2.2 Model Consistency w.r.t. Input Parameter o0 100 7.2.3 Methods and Procedures 104 7.2.4 Modelling Temperature Histories 105 7.2.5 Experimental^ Data 109 7.3 Results of Model Fitting 110 7.3.1 Discussion 112 7.4 Model Evaluation and Testing 112 7.4.1 Relevance with Published Data 113 7.4.2 Model Predictions for Verification Data 115 v 8.0 M O D E L PREDICTIONS 119 8.1 Short-term Strength of Lumber 119 8.1.1 Constant Uniform Material Temperature 120 8.1.2 Constant Surface Temperature 122 8.2 Rate-of-Loading Effect 125 8.3 Reliability Analysis 126 8.3.1 Grade Effect 127 8.3.2 Temperature Effect 129 8.3.3 Stress Effect 131 9.0 SUMMARY, CONCLUSIONS A N D RECOMMENDATIONS 135 9.1 Summary 135 9.2 Conclusions 138 9.3 Recommendations 139 9.4 Final Remarks 141 Nomenclature 143 Bibliography 146 APPENDIX I 155 APPENDIX II 156 APPENDIX III 174 APPENDIX IV 196 vi List of Figures 3.1 Reliability and probability density functions 7 3.2 Basic reliability problem given in terms of probability density function of resistance and load 8 3.3 Relationship between quasi-elastic force and inter-particle distance 12 3.4 Propagation of cracks in acetate cellulose under various loads 14 3.5 Effects of temperature on strength and modulus of elasticity of spruce in tension parallel to grain 19 3.6 Effect of duration of heating on modulus of elasticity and maximum strength in tension perpendicular to grain 21 3.7 Behaviour of wood exposed to elevated temperature 24 3.8 The failure process in structural wood members in fires 25 3.9 Modelling of tf data of Noren (1988) by Weibull distribution 30 3.10 Duration-of-load effect in 2x6 No.2 & Better hemlock lumber 36 3.11 Effect of temperature on duration-of-load effect as affected by grade 36 5.1 Cross-section (a) and longitudinal-section (b) views of the heating apparatus and the test specimen 68 5.2 Sampling errors (standard errors) as affected by sample size and percentile in the sample 70 5.3 Schematic diagram of a typical heating and loading sequence of the experiments 71 5.4 Test set-up for temperature distribution in the lengthwise direction of specimens 73 5.5 Test set-up for temperature distribution near the platen end in lengthwise direction of specimens 73 vii 5.6 Test set-up for temperature distribution in the transverse direction of specimens 73 6.1 Cell-wall degradation as a function of exposure temperature 75 6.2 The effect of censoring on cumulative frequency distribution of sample containing outside failures 77 6.3 Temperature distribution along the longitudinal axis within the exposed region 79 6.4 Temperature distribution in the direction of heat-flow (thickness direction) at an exposure temperature of 150°C 81 6.5 Temperature distribution in the direction of heat-flow (thickness direction)at an exposure temperature of 200°C 82 6.6 Temperature distribution in the direction of heat-flow (thickness direction)at an exposure temperature of 250°C 83 6.7 Cumulative frequency distribution of relative density 84 6.8 Strength distribution at room temperature, 150, 200, and 250°C for a rate of loading of 1.85 kN/s 87 6.9 Strength distribution at room temperature, 150°, 200° and 250°C for a rate of loading of 0.2 kN/s 88 6.10 Strength distribution at room temperature, 150°, 200° and 250°C for a rate of loading of 0.067 kN/s 89 6.11 Comparison between observed and expected distribution G(x) 90 6.12 Approximation of the expected strength distribution G(x) by Weibull distribution 92 7.1 A typical damage rate function at room temperature for a loading rate of 1.85 kN/s 99 viii 7.2 Comparison of the value of the dependent variable o* calculated from Eqn [7.24] and the numerical solution of Eqn [7.23] 103 7.3 Temperature history predicted — theoretical approach (assumptions: one-dimension heat-transfer; no mass transfer) 108 7.4 Temperature history predicted — empirical approach Eqn [7.30] 108 7.5 Fitting of the model (parameters listed in Table 7.3) to experimental data . . . I l l 7.6 Verification I — predicted t{ values and test data 117 7.7 Verification II — predicted Rvalues and test data 118 8.1 Effect of temperature on the short-term strength as predicted using the damage accumulation model 121 8.2 Temperature model in accordance with Eqn [8.2] and Eqn [8.3] 124 8.3 Short-term strength as a function of temperature and duration of exposure . . 124 8.4 Effect of rate of loading on the short-term strength as a function of wood temperature and for a duration of 1800 s 126 8.5 Reliability indexes of structural lumber as a function of material temperature and duration for the M S R grade of 2400f-2.0E and 1650f-1.5E 128 8.6 Effect of temperature variability on rekability indexes of structural lumber (a) 2400f-2.0E and (b) 1650f-1.5E 132 8.7 Effect of stress variability on reliability indexes of structural lumber (a) 2400f-2.0Eand(b) 1650f-1.5E 134 ix List of Tables 3.1 Typical values of coefficients in Eqn [3.13] 16 3.2 Values of U0 and y for several materials 17 3.3 Charring rates of some common wood species 40 3.4 Empirical charring models for some common softwood wood species 44 3.5 Damage accumulation models for duration of load effect in wood 46 4.1 Procedures to analyze the effect of grade on the reliability of members exposed to fire 64 5.1 Experimental design and sample size of each different combinations of variables 66 6.1 Means and standard deviations of initial and final moisture contents of specimens tabulated by sample 85 6.2 Parameters of Weibull distribution 90 6.3 Means and standard deviations of tension strengths computed by samples . . . 94 6.4 Weibull distribution parameters for the tension strength 94 7.1 Procedures to determine the best-fit values of the model parameters 104 7.2 Lognormal distribution parameters (6=threshold, ^ l oca t ion , o=scale) of the experimental tf distributions 110 7.3 Model parameters as determined using PARAFIT 110 7.4 Conditions of Verification Test I and II conducted on samples whose data have not been exercised in the modelling 116 8.1 Procedures for analyzing the effect of temperature on short-term strength . . . 120 8.2 Procedures for analyzing the effect of temperature on rate-of-loading effect . . 125 8.3 Procedures to determine the reliability indexes of different grades of structural lumber 127 8.4 Procedures to determine the reliability indexes as affected by variability of temperature 130 x Procedures to determine the reliability indexes as affected by variability of stress xi Acknowledgement The author is gratefully indebted to many people, directly or indirectly, involved in this thesis work. Particularly, the author acknowledges the members of the thesis committee: Dr. Starvos Avramidis for his helpful comments, Dr. Dave Barrett for his support and advice as thesis supervisor, Dr. Richardo Foschi for his seemingly inexhaustible guidance, and Dr. Jim Mehaffey for his passionate interest in the project and direction concerning fire safety issues. The author acknowledges Forintek Canada Corp., who, through its alliance with Natural Resources Canada, provided much of the financial and technical support without which a project of this scale would not be possible. In particular, the author would like to mention: Dr. Jim Dangerfield who approved the project, Mr. J.-C. Havard who suggested the research area and supported the author and the work; Dr. Don Onysko whose encouragement over many coffee-breaks were invaluable; Mr. Les Richardson for his review of this manuscript; Mr. Conroy Lum for his caring interest in the project and countless hours of critical discussions; Link Olson and Ken Love for their inputs to the development and fabrication of the heating apparatus, Roy Abbott for grading the test material, Tony Thomas for assembling the data acquisition system, and Len Stroh for carrying out some of the experimental work. Thanks also go to Miguel Batista, Gilles Chauret, Henley Fraser, Doreen Liberty, Barber Holder, Jean Cook, and Howard Gribble. The author is grateful to Dr. Carson Woo and his wife, Ellen, for their wiJJingness to accommodate the author, and for their encouragement and friendship, during the author's residency in Vancouver. The author thanks his wife, Elaine, for her encouragement, tolerance, support, and understanding. xii 1.0 I N T R O D U C T I O N Modern engineered wood structural systems are often assembled from light-framing lumber which may rely on metal-plate connectors or structural adhesives to transmit loads between members or systems of members. Under Canadian and US grading rules, the lumber employed in these systems is normally classified as Light Framing or Structural Light Framing - a class of dimension lumber typically 38 mm thick, and 89 to 286 mm wide. Our understanding of their structural performance, and particularly their composite behaviour and load-sharing between elements, has been steadily advanced. The design of these systems to perform under normal operating conditions has become very efficient. W i t h respect to fire exposure, the design for life safety has remained relatively unchanged and in the form of prescriptive regulations and standards developed decades ago. In other words, fire safety design has not kept pace with advances in structural design. While the performance of light-frame engineered wood systems has been proven under normal conditions, their ability to carry loads under fire conditions has been questioned (Brannigan 1992). It is well known that traditional heavy-timber construction can endure attack by fire for "relatively" long periods of time because their designs are conservative and the char layer formed actually retards those pyrolytic processes normally associated with fire exposure. However, there is a general lack of knowledge about how light-frame wood systems perform in fire, therefore in these applications wood — as a structural material — is treated conservatively by code authorities. Fire safety engineering and design must evolve — through introduction of probabilistic design principles — as we prepare for the implementation of an objective-based building code1 for the National Building Code of Canada (NBCC) by the year 2001. 1 A n objective-based (performance-based) code w i l l establish the fire safety goals for various bui ld ing occupancies, develop relevant performance objectives and criteria, recommend a suitable solution, and develop guidelines to assess a proposed solution. A key feature is that the approach w i l l specify some form of "performance measure" and permit the use of any solution that demonstrates compliance. 1 1.0 Introduction 2 Generally, target reliability is an input parameter to any probabilistic design procedure, and reliability analysis is used to assure that the target reliability is achieved in modern design codes. In Canada, structural design codes for steel, concrete, and wood have been completely converted from a deterministic format to a reliability-based format since 1989. The reliability theory will provide the needed analytical framework for risk assessment of fire-rated structures. Risk assessment is increasingly recognized as an effective tool to quantify performance and performance expectation. This thesis is intended to advance knowledge of the reliability of structural wood systems during fire exposure and the short-term effects of exposing such systems to elevated temperatures up to 250°C. Specifically, it focuses on the reliability of structural tension members. The motivations which relate to the wood industry are elaborated in the remaining sections of this chapter. 1.1 Merits of Reliability-Based Design The adoption of a performance-base code approach will, inevitably, demand more advanced knowledge of material behaviour, particularly property variability, in order to assess the risk of not meeting the design objectives. Currently, analytical methods are used to bridge the gap between limited experimental data and information required for design. Such analyses, however, have invariably been performed under the assumption that relevant design parameters, with the exception of material strength, are single-valued. The assumption, while simplifying the design process considerably, is generally invalid since most design parameters are actually random in nature. Traditionally, this variability problem is "nullified" by applying a safety factor in deriving the design material properties. The safety factor is usually selected on the basis of consequence of failure, practical experience, and economic considerations. This deterministic approach, adopted in "working stress" design, is generally insensitive to the variability of the parameters constituting the 1.0 Introduction 1.1 Merits of Probabilistic Design 3 design equation. However, the actual level of safety, or conversely the risk, is not formally considered in selecting safety factors for working stress design codes. In reliability-based design, nonperformance is measured in terms of the probability of failure which is a direct measure of safety. Target reliability levels can be an input to risk assessment. In this context, reliability is a form of performance measurement. Reliability-based design is therefore an equitable design approach within which different designs can actually be compared. Canada is not alone in switching to a performance-based building code. New Zealand adopted a performance-based code format through legislation (Buchanan 1994). Australia is in the midst of developing its own performance-based code (Beck 1994). Britain and Japan have long been permitting alternative designs for fire safety on the basis of equivalence in performance. 1.2 Fire Safety Engineering of Wood-Based Structural Systems The North American Wood Products Fire Research Consortium2 (NAWPFRC) was established to coordinate fire safety engineering research needed to make performance-based design of wood buildings possible. The Consortium recognizes that fire safety design must take an engineering approach, much the same way as for structural safety, and that it should be based on analytical models for the prediction of fire loadings, heat transfer, thermal degradation, structural damage, and ultimately, the probability of failure of wood members exposed to fire. This approach is consistent with recommendations of international organizations such as ISO (International Standard Organization). One critical link, which is lacking or inadequate, is knowledge of the structural behaviour of lumber 2 T h e N o r t h A m e r i c a n W o o d Products Fire Research Consor t ium is composed of Canadian W o o d Counc i l , Forintek Canada Corp., American Forest and Paper Association, Forest Products Laboratory of the U n i t e d States Department of Agriculture, and A P A - The Engineered Wood Association. 1.0 Introduction 1.2 Fire Safety Engineering of Wood-Based Structural Systems 4 exposed to elevated temperatures, up to the charring temperature of wood (~288°C). Hay (1988) commented that "for lighter-weight elements with greater efficiency in exploiting the structural advantages of high strength wood fibres, it is very doubtful that much reliance can be placed on the information currently available about the point at which there starts to be significant loss of strength, due to heat damage." Knowledge of the behaviour of wood elements exposed to fire must be advanced to permit valid reliability assessments. The steel and concrete industries have been able to provide relevant data with which fire safety designs in their materials can be "engineered". WitJhin an engineered wood system, multiple failure modes can occur in the event of fire. Engineering systems, in general, may introduce large interconnected concealed spaces in which wide spread fire attack on the structural members can occur. Because of the interdependence between different elements in the system, failure at any one location may quickly spread to other locations, leading to sudden collapse. Since the tension strength of lumber often governs designs, the behaviour of wood members in tension during fire exposure is critical to the overall performance of structural systems. Tension rupture occurs with little warning because of wood's brittle nature. 2.0 OBJECTIVES The work upon which this thesis was based was part of a comprehensive research program3 focused on developing (1) the required theoretical and experimental bases with which reliability of structural light-frame wood members during fire exposure can be assessed and related to variables such as the initial short-term strength of the members, and (2) a framework based on reliability concepts by which the effect of variables such as wood quality can be quantified given known temperature and stress histories. Specifically, the objectives of the thesis are: • to identify the research needs required to relate the time-to-failure of structural wood members exposed to fire to the initial load, the initial member size, the charring rate of wood, and the temperature and the short-term strength4 of the members; • to establish, on the basis of appropriate experimental testing, the effect of temperature on the short-term strength of structural members taking into account the effect of duration of exposure; • to develop a mathematical model to predict the time-to-failure of structural members under tension loads and temperatures up to 250°C; • to formulate the reliability-based performance function for fire safety design of structural members; • to apply the model to analyze the reliability of nominal 2x4 lumber subject to tension and elevated temperatures for various appropriate durations and initial short-term strength distributions. Fire endurance research by various members of N A W P F R C . The short-term strength of lumber is normally established i n testing under ramp loading at a constant loading rate such that maximum load is achieved i n approximately 10 minutes but not less than 5 nor more than 20 minutes ( A S T M D 198). 5 3.0 P R O B L E M ANALYSIS A N D L I T E R A T U R E R E V I E W The literature related to the stated objectives is examined in this chapter. The general concepts of probabilistic design and reliability analysis are discussed in Section 3.1. Section 3.2 reviews the theoretical strengths of brittle solids. The effects of temperature on clear wood specimens and on lumber are documented in Section 3.3 and Section 3.4, respectively. The state-of-art modelling approaches of time-dependent wood strength behaviour are reviewed in the final section. 3.1 Probabilistic Design Generally, probabilistic design accounts for uncertainties present in the design performance function while, at the same time, recognizing that no design providing absolute safety can be afforded. Thus, each design results in a certain probability of failure, P f , or conversely a reliability, R, which is equal to 1 - P f . On the basis of these probabilities, a design requirement with respect to either ultimate strength or serviceability may be formulated. In this context, a more satisfactory structure is one with a lower probability of failure or a higher reliability. Design methods, using reliability concepts, allow different materials to be used so long as the same level of reliability is achieved. There will be cases where several performance functions are considered in design, each with a different reliability requirement. The final design may also be influenced by cost, environmental impact, and availability of materials. 3.1.1 Reliability Analysis 6 3.1 Probabilistic Design 3.1.1 Reliability Analysis 7 Target reliability is a design input in the probabilistic design process. The reliability of a structural system is the probability that it will successfully perform a specific task under a given set of operating conditions for a specified duration. This specified duration is called the design service life of the system. Loosely speaking, a reliability statement about a structural system in design "reflects" the proportion of a "large" sample of statistically similar systems which remains intact and functional over the design service life. w z LU Q >-CO < m o cc Q. m < UI a. The technique by which the probability of survival (or failure) is calculated is called reliability analysis. There are two principal approaches by which the specified problem can be tackled. The survival (or failure) rates at any given operating time may be estimated from a life-length model. The other approach is to infer the probability of survival from the statistical distributions of the load and resistance effects in the service life. In structural analysis, this approach is referred to as the load-resistance design method. L IFE-LENGTH (HOURS) Figure 3 .1: Reliability and probability density functions Life-length Model. A life-length model of a component is developed through actual observations of the variable time-to-failure (tf) of a sample of the component operating under the specified end-use conditions. It is normally presented as a probability density distribution of the variable tf. Figure 3.1 shows a schematic life-length model probability density function f(t{) and the corresponding reliability function. As indicated, failure probabilities are calculated from the area under the probability density function as follows: 3.1 Probabilistic Design 3.1.1 Reliability Analysis 8 [3.1] OVERLAPPING REGION Load-Resistance Design. Sometimes the life-length of a component or a system of components is simply too long to be determined experimentally, or it is required to operate under very complex conditions which can not be duplicated experimentally. In this situation, the reliability analysis may be performed if the probability density distributions of both the load effect (fs) and the resistance effect (fR) can be determined. Many of the analyses then involve deriving the corresponding probability density distribution functions for the load (s) and resistance (r) effects. Assuming that the probability density distributions of both these effects are known, as shown in Figure 3.2, then the probability of failure is given by Figure 3.2: Basic reliability problem given in terms of probability density function of resistance and load Js ~o Jr = o [3.2] Although the integral is evaluated over the entire domain of r and s, its value really depends only on the "overlapping region" of the two distribution functions (Figure 3.2). Most structural reliability problems are of this kind. The greatest difficulty encountered in applying this approach has been in the proper modelling of/ R and/ s . For example, in buUding design,/s is the distribution of the maximum load effect over the design service life of the building. Such data are difficult to obtain. Similarly, the distribution of member resistance^(r) can be difficult to evaluate, particularly in wood materials because strength properties vary with moisture content, temperature, and load history. In the case of a 3.1 Probabilistic Design 3.1.1 Reliability Analysis 9 structure exposed to a fire, the resistance effect will need to be modified "continuously" during the course of the fire, as resistance changes under the effect of heat. 3.1.2 Performance Function The design performance function (G) may be generalized in the form of: where S represents the resistance (or supply) and D represents the loads (or demand), and the limit state is given by G = 0. The probability of the event G < 0, that is, the probability that supply is less than the demand, denotes the failure probability of the performance function. The complement of this probability, that is, the probability of the event G z 0, represents the reliability of the member. In reliability-based design, this probability is aimed toward a prescribed value. Both S and D can be given as a function of some other parameters such that S=S(x{..Jcn) andD=D(j1...jn) where the parameter sets xx...xn andy1...yn may consist of variables such as size and geometry of individual components or the systems, load and stress distribution, and material properties. Furthermore, S andD may also be provided as an output from an analytical model. In design, the performance function will need to be described analytically since it will not be possible to test every possible design. If the distribution functions of the variables in the performance function are known, and if values of the variables are randomly drawn from their respective distributions to compute a value for G (a realization in G), then, the probability of failure (Pf) can be estimated as follows: G = S - D [ 3 . 3 ] N G<0 [ 3 . 4 ] N 3.1 Probabilistic Design 3.1.2 Performance Function 10 where N is the total number of realizations attempted and i V G < 0 is the number of occurrences of G < 0. The reliability is 1- P f . This evaluation process is known as Monte Carlo simulation. The reliability index p is defined as where <&~l(-) is the inverse of standard cumulative Normal distribution function. Alternatively, a more efficient method may be used (Ang and Tang 1990), which approximates the probability of failure on the basis of "equivalent" independent normal distributions of the variables in the performance function. In summary, reliability of a member (or system) is governed by the distributional characteristics of the load and resistance effects. These effects — often expressed in terms of appropriate probability density functions — may be functions of several random variables. From these functions, sample values can be generated using Monte Carlo simulation. The sample values of S and D are used to establish the probability of failure of the member or system. In this way, uncertainties in the design parameters may be accounted for in probabilistic design. In the cases where the true distributional characteristics are not known, except for the first two moments (i.e. mean and standard deviation), then the second-moment reliability method may be applied as a rough approximation (Ang and Tang 1990). In reliability studies, the distributional characteristics of a variable may be intentionally varied to study its effect on the calculated reliability. This is known as sensitivity analysis. Such studies provide guidance as to which variables are most important in determining reliability. [3.5] 3.2 Strength of Solids 11 Other variables which do not appear explicitly in the performance function may be evaluated through their effects on those variables comprising the performance function. 3.2 Strength of Solids The strength of solids is their capacity to resist rupture. Brittle and ductile modes of failure are possible within a single material, but which one will occur depends critically on the temperature of the material. Since the complete account of these phenomena is beyond the scope of this literature review, the discussion will focus mainly on fracture strength of brittle materials as affected by temperature. A brittle solid is one whose strength is characterized by the lack of "ductile" deformation prior to fracture. Wood behaves in a brittle manner under tension loading. The calculation of the theoretical strength of solids normally begins with inter-particle forces of attraction between the constituents of solids whether they be molecules, atoms or ions. However, the exact solution depends on the nature of the forces of interaction and on the molecular structure which can be quite complicated. For a simple structure such as rock salt, an ideal monocrystal5, the cleavage force or quasi-elastic force6 required to separate two particles depends on the potential energy of the interactions between the particles. The potential energy (17) is a function of the distance between the particles, the structure of the crystal lattice, whether the bonding between the particles is ionic, covalent or metallic, and the type of applied stress. Using different approaches, Orowan and Kobeko (Bartenev and Zuyev 1968, p. 5) arrived at approximately the same expression relating the theoretical strength of brittle materials to the modulus of elasticity of the materials. In Orowan's case, which is a semi-empirical approach, he assumed that the 5 The basic bui ld ing block of a crystal lattice. 6 The quasi-elastic force is equal to -dU/dx where U is the potential energy of interaction, calculated for a single particle and x is the distance between particles i n the direction of tension. The value of the maximum quasi-elastic force, mult ipl ied by the number of atoms or ions, situated on a single plane of the solid body i n the unstressed condit ion at right angles to the directions of tension, is equal to the theoretical strength. 3.2 Strength of Solids 12 quasi-elastic force o' was a sine function of the inter-particle distance x as shown in Figure 3.3. That is, a' — o sin m — (* " XQ) [3.6] where o m is the maximum of the quasi-elastic force (theoretical strength), x0 the distance between two particles at equilibrium, a0 is twice the maximum bond elongation (that is twice the distance from the position of equilibrium to the position corresponding to Figure 3.3: Relationship between quasi-elastic force and inter-particle distance om). The expression Eqn [3.6] was simplified for small displacements from the position of equilibrium: a 7t o — (x - xn ) m v 0 ' [3.7] According to Hooke's law, which is valid for small displacements, a = E ( \ x - V [3.8] where E is the modulus of elasticity of solid. Equating the two expressions Eqn [3.7] and Eqn [3.8], dr. a — m [3.9] where o m is expressed as a fraction % of E. Since maximum quasi-elastic strength is usually reached at 10-20% elongation of bonds, that is, a0/2 = 0.1-0.2 x0, the constant % has a range from 0.07 to 0.13 depending on the type of chemical bond in the solid. Kobeko arrived at the same range of values for x based on Morse formula: 3.2 Strength of Solids 13 U = _£>/e-b0(*-*o) (2 - g-W'-'o')) [3.10] where D ' is the energy of dissociation per single particle, b0 = (co/D')' / 2l/A0, co is the frequency of oscillation of particles, and A0 is the amplitude. On average, the theoretical strength of brittle solids is approximately 10% of the modulus of elasticity of the solids. 3.2.1 Actual Strength The actual strength of brittle solids is usually much less than the derived theoretical strength due to inherent flaws, in the form of cracks at the microscopic level. Within a given volume of material, the actual strength decreases with increasing length of these micro defects in the material. This phenomenon was explained by Griffith (1921) in what is generally known as fracture mechanics theory. The natural variation in strength, on the other hand, occurs due to the natural phenomenon that no two samples of the "same" material have identical distributions of flaws. As a result of this natural variability in internal flaws, actual strength may decrease with increasing volume of material under consideration. This "volume" effect — particularly evident in brittle materials — was first explained by Weibull (1939) and others using probability theory. In the literature, this effect is referred to as the statistical strength theory for materials or the "weakest link theory". Fracture Mechanics Theory. Griffith (1921) explained the discrepancy between theoretical and actual strengths by a "fracture mechanics theory" for materials containing micro cracks. When such a material is subjected to a load, stresses in the material will grow gradually toward the edges of the micro cracks, to a maximum significantly higher than the average stress in the material. Griffith called this phenomenon a stress concentration effect. When the stress concentration exceeds the so-called theoretical strength of the material, the micro crack grows catastrophically. 3.2 Strength of Solids 3.2.1 Actual Strength 14 Griffith further assumed that the change in elastic energy during the growth of the crack equals the surface energy of newly formed free surfaces. For a thin strip7 containing a crack of length C , Griffith's assumption led to the well-known expression: 4 a E [3.11] K \| 71 C where oK is the actual strength, C ' is the length of the micro crack, and KS is the surface energy. The value oK-(7tC')' /2=(4as-£)1/2 is a material constant which was verified by Griffith in experiments with glass. The experimentally obtained value of the constant is called the fracture toughness of the material. It can be interpreted from Eqn [3.11] that the magnitude of the stress concentration is a function of the length of the crack: the longer the crack, the higher is the amplifications of the stress, and consequently the lower is the actual strength oK required for unstable crack propagation. Failures also occur at stress levels less than oK as a result of crack growth under the effect of the applied stress. This is a loading time phenomenon in that the actual strength of the material gradually decreases as C increases. Zhurkov and Tomashevskii (Bartenevand Zuyev 1968, p. 23) observed the propagation of cracks in cellulose acetate under various loads and found that near failure the rate of crack growth increased very suddenly (Figure 3.4). Such data suggest that the internal damage in the material, also grows in a similar manner. 1 \ i i i i > * t i % — « 0 4 8 12 16 TIME(104s) Figure 3.4: Propagation of cracks in cellulose acetate under various loads It is assumed that the in i t ia l length of the crack is small relative to the width of the t h in strip. 3.2 Strength of Solids 3.2.1 Actual Strength 15 Statistical Strength Theory. The general concept of statistical strength theory stems from the model that a solid body contains a variety of different defects and that these defects are randomly distributed over the volume and surface of the material. The strength of the specimen is determined primarily by the most critical defect. The fundamental arguments on which the statistical theory of strength is based are (1) specimens obtained by identical methods can have defects of different criticality, (2) the strength of the sample is determined by the most critical defect within the sample, and (3) the greater the volume or surface area of the sample, the more probable it is that a critical defect will be found. From the last argument, strength must decrease with an increase in volume or surface area of sample. Weibull's statistical approach led to the Weibull distribution function for the strength of material of given volume V: P f — 1 - exp -V a [3.12] where P{ is the probability of failure at a stress level z, the location parameter u-, the scale parameter o, and the shape parameter X are coefficients determined by the characteristics of the material. Time and Temperature Dependence. Time dependence in strength of solids in tension has been observed in many materials including metals, plastics, and polymers. From data on a series of systematic studies conducted by Zhurkov and co-workers (Bartenev and Zuyev 1968, p. 27), it was concluded that the life-length of some typical materials can be expressed by an exponential law: t{ = A1 6 ~B'Z [3.13] 3.2 Strength of Solids 3.2.1 Actual Strength 16 where A ' and B' are constants, and x is the applied tensile stress (constant). Some typical values of the two constants are listed in Table 3.1. It was also observed that the time dependence of the strength decreases as temperature decreases. At a critical low temperature (relative to the melting point of the material), the loading time effect completely vanishes. In other words, tensile fracture will not take place at x < ok no matter how long the material may be stressed. One can view ok in Eqn [3.11] as a limiting strength at the crack length C. The temperature dependence has been incorporated in Eqn [3.13], in that the coefficients are given as a function of temperature: A i — U0/(kT) [3.14] and B' k T [3.15] where e 0 (s) is a constant numerically similar to the period of thermal oscillation of the atoms, k is Boltzmann's constant (J/K/molecule), U0 (J/molecule) is the activation energy of the elementary act of failure in the absence of stress and is similar in value to the sublimation energy for metals and to the energy of chemical bonds for polymers, y is a coefficient which depends on the nature of the structure of the material, and T is the absolute temperature (K). Typical values of UQ and y per molecule are listed in Table 3.2. Table 3.1: Typical values of coefficients in Eqn [3.13] Material log[A'] B' (mm2/N) Poly 10.5 0.35 Aluminum 38 1.04 Zinc 22 0.05 Cellulose diacetate 17 0.38 3.2 Strength of Solids 3.2.1 Actual Strength 17 Table 3.2: Values of U0 and y for several materials. Material Activation Energy (10-21 J/molecule) Material Parameter Y (10"22 mm2/N/molecule) Poly (methylmethacrylate) 378-385 22.6-23.9 Nylon fibre (orientated) 315 2.06-3.12 Zinc (polycrystalline) 175 7-21 Aluminum (polycrystalline) 378 28-63 Aluminum (monocrystal) 357 39 Silver 448 15.6 Platinum 840 10.5-58.9 3.3 Behaviour of Wood Materials at Elevated Temperatures 3.3.1 Short-term Strength Properties 3.3 Behaviour of W o o d Material at Elevated Temperatures 18 At the molecular level, wood is composed of approximately 45% cellulose, 25% hemicellulose, 25% lignin, and 5% extractives. The strength of wood is governed by the state and organization of the cellulose, hemicellulose and lignin fractions. The integrity of the lignin fraction influences the compression strength. At room temperature, the main failure mechanism in tension parallel-to-grain occurs, typically, within cell walls rather than between cells, and is due to the breakage of microfibril in the S2 layer (Van Der Put 1989). This failure mechanism suggests that the shear strength of the middle lamella layer, which is responsible for bonding cells together, is strong enough that cell shear separation is prevented. However, at or above 150°C, the middle lamella layer, which has the highest concentration of lignin, begins to weaken due to lignin flow. The failure mechanism then shifts from cell-wall breakage to separation between cells. Such a change in failure mechanism probably explains, in part, why temperature-strength relationships in wood at elevated temperatures are generally non-linear. 3.3.1 Short-term Strength Properties Mechanical properties that may be affected by heat include the stress at first yielding, modulus of elasticity and the ultimate strength for various loading modes9. These effects may be either immediate or time-dependent or a combination of the two. The time-dependent response is mainly due to creep phenomenon, which has been shown to be greatly influenced by temperature. The immediate effect of temperature on major mechanical properties of wood has been reviewed by Gerhards (1982). He noted that most of the available data were developed on small, clear specimens with moisture contents between 6% and 20%, and That is, tension, compression, bending, shear, torsion, etc. 3.3 Behaviour of Wood Materials at Elevated Temperatures 3.3.1 Short-term Strength Properties 19 tested at temperatures ranging between -50°C and 100°C. Gerhards found that the effect of temperature on modulus of elasticity is generally linear and on strength properties bi-linear to multi-linear. Also, the effects are more p pronounced with increasing moisture content, UJ Properties perpendicular-to-grain are affected to fi a. a greater extent than corresponding properties parallel-to-grain. Compression strength is affected more severely than tension strength. 1.0 .8 .6 .4 .2 .0 I I I MOE i i i i I I \ | 1 1 \ ULTIMATE <k i i STRENGTH >^ i i I 4-I I I I 1- -1 l l 1 1 1 1 250 0 50 100 150 200 T E M P E R A T U R E (°C) Overall, information about the effect of Figure 3.5: Effects of temperature on . c ^ strength and modulus of elasticity of temperature on strength for temperatures ° J spruce in tension parallel to grain between 100°C and 288°C is lacking. The available information pertains mainly to the responses of small, clear wood specimens parallel-to-grain. These data are probably not representative of the behaviour of structural lumber containing naturally occurring characteristics such as knots and slope-of-grain. Ostman (1985) showed that the ultimate tension strength of clear, 1-mm-thick dry spruce specimens was affected to a greater extent than the modulus of elasticity (Figure 3.5). The losses amounted to 70% and 50% respectively at 250°C after several minutes of exposure. It was also apparent that the wood underwent structural changes corresponding to a transition to a glassy state at around 200°C: The strain at failure had increased with increasing temperature to 200°C then it appeared to decrease (not shown in Figure 3.5). Knudson (1975) studied tension and compression strengths for temperatures to 288°C and a duration of exposure up to one hour for clear Douglas-fir using 4.8-mm-square cross-sections with a moisture content of 12%. Both tension and compression "hot" strengths decreased steadily with increasing temperature. There was no significant duration 3.3 Behaviour of Wood Materials at Elevated Temperatures 3.3.1 Short-term Strength Properties 20 effect, except at 288 °C. When specimens were heat-treated up to 150°C and then reconditioned back to original conditions the ultimate tensile strength was not significantly affected. In any case, the reconditioned strengths were always higher than the "hot" strength. Knudson also found that the dynamic modulus of elasticity, obtained by vibration testing, was not affected by temperature or duration of heating. This finding contradicts the results of James (1961), which show a negative, linear reduction of approximately 10% from 20°C to 100°C on the basis of sonic measurement. Knudson's data, among others, suggest that there are two effects of heat on the strength of wood. One arises from the softening effect, which is immediate, linear, and probably partly recoverable. The other relates to a loss of material due to pyrolysis which begins at around 150°C, starting with hemicellulose. Lignin begins to break down at approximately 200°C. Cellulose decomposes abruptly at 280°C (Schaffer 1966). Perpendicular-to-grain Strength Properties. A majority of the work concerning strength properties of wood perpendicular-to-grain originated from studies on wood drying and formation of drying defects. These studies include Greenhill (1936), Barnard-Brown and Kingston (1951), Ellwood (1954), and Kollmann and Cote (1968). As concluded by Gerhards (1982), the effects are generally linear. Suzuki et al. (1982) evaluated small, clear specimens of Japanese white fir, subjecting them to bending and torsion tests at temperatures ranging from -30°C to 175 °C. As much as 50% of the stiffness was lost when the specimens were tested at 175°C compared to the results at 20°C. Parallel to the grain, strength losses were only 20%. Longitudinal and transverse bending strength decreased almost by 50% when wood was heated from -35°C to 175°C. The effect of grain angle was found to obey Hankinson's formula and was unaffected by temperature: 3.3 Behaviour of Wood Materials at Elevated Temperatures 3.3.1 Short-term Strength Properties 21 F Lsin"8 + FRcos"0 [3.16] where Fh and FR are the strengths in the longitudinal and radial directions, respectively. F e is the strength at a grain angle 0, and n is a constant. The exponent n ranged from 1.8 to 2.0 for the various temperatures tested. 1.2 * .9 UJ > UJ a. • » , | G R E E N 1 ' . -TENSION STRENGTH 0 0.4 0.8 1.2 1.6 DURATION OF EXPOSURE (hour) Figure 3.6: Effect of duration of heating on modulus of elasticity and maximum strength in tension perpendicular-to-grain (adapted from Youngs (1957)) In relation to the drying behaviour of wood, Youngs (1957) studied the effects of temperature, moisture content, and time on perpendicular-to-grain tension and compression properties of small, clear specimens of red oak. The temperature ranged from 27°C to 82°C. The moisture contents ranged from 6% to green. The tests included both short-term strength tests at various levels of moisture content and temperature, and the effect of duration of heating. Ultimate tensile strength was affected the most. Moisture content effects were generally non-linear whereas temperature effects were generally linear. Also, moisture content tended to amplify the effect of temperature. The effect of temperature was more pronounced at a grain angle of zero degree than at 90 degrees. This grain-angle effect was probably caused by the prominent ray cell structure typical of red oak. The effect of heating duration on most of the strength properties was significant, particularly at both the extremes of moisture content and temperature. Overall, the degradation rate was found to be linearly related to the logarithm of time. Figure 3.6, which was derived from Youngs' work (1957), shows the heat duration effects at 8 2 ° C on both modulus of elasticity and maximum stress in tension. These tests were conducted at room temperature after heat exposure. 3.3 Behaviour of Wood Materials at Elevated Temperatures 3.3.2 Creep 22 The properties in the perpendicular-to-grain direction are affected more severely by heat than those in the parallel-to-grain direction. Since lower-grade materials tend to possess more severe grain deviations, it is reasonable to hypothesize that the effects of temperature and duration of heating are grade-dependent. Also, the major defect in lumber are knots. In these defective regions, significant perpendicular-to-grain stresses can be induced by an external load, or differential temperature or moisture distributions, or a combination of these factors. 3.2.2 Creep Wood behaves in a visco-elastic manner under load up to a critical stress. In this load range, its deformation consists of instantaneous elastic, delayed elastic and viscous responses10. The viscous response is time dependent. Beyond the critical stress, the deformation becomes largely "plastic". Furthermore, viscous and plastic responses are non-linear functions of the applied stress and the duration of loading, and are significantly affected by temperature and time of exposure. However, under typical conditions of short-term testing at room temperature, the viscous flow is largely suppressed. Bach (1965), and Kadita et al. (1961) attempted to segregate the individual temperature effects by each of the deformation components. Others (Kitahara and Okabe 1959, Davidson 1962, Arima 1967, Youngs 1957) included creep measurements as influenced by a temperature-stress history. Other studies produced mainly a "blended" response of the three deformation components. Schaffer (1982) characterized the longitudinal creep behaviour of dry Douglas-fir clear wood specimens at temperatures up to 275 °C. His results showed that, at 275 °C, a total creep strain of approximately 0.005 was obtained in approximately two hours under 1 0 Viscous response is the non-recoverable part of creep deformation whereas delayed elastic response is the recoverable part. 3.3 Behaviour of Wood Materials at Elevated Temperatures 3.3.2 Creep 23 a load of 5% of the ultimate load. At 140°C and under a load of 50% of the ultimate load, the total creep strain obtained was about 0.001. Arima (1966) studied the influence of temperatures up to 180°C on the compressive creep of wood, using oven-dry Japanese Hinoki (Chamaecyparis obtusa Endl.). The stress applied was 0.43 MPa in the radial direction and 1.74 MPa in the longitudinal direction. These stress levels represented about 7 to 16% of the proportional limit stress value obtained from a corresponding short-term compression test, depending on the test temperature. Not surprisingly, the creep rate was higher in the radial direction than in the longitudinal direction, and it increased with increasing temperature. For a given elapsed time, the creep strain increased linearly with temperature. Regression relationships for various loads, relating creep strain eT at specific times and temperature T, were expressed in the form of e T = [3.17] where eY and e2 were regression coefficients. Hirai et al. (1981) tested Douglas-fir in bending, by heating the specimens in an enclosure with an electrical heater. A definite positive trend between creep strain and temperature was observed. Fushitani (1968) evaluated heat-treated wood in tension and found that creep strain increased with temperature and duration of the heat treatment. Youngs (1957) found that creep strain increased with increasing temperature and moisture content. These studies indicate that in studying deformation behaviour of lumber exposed to elevated temperatures, we must not ignore creep effects even for relatively short times of exposure. 3 A Resistance of Lumber Exposed to Fire 3.4 Resistance of Lumber Exposed to Fire 24 Figure 3.7 shows a schematic diagram of a cross section of a defect-free wood member, which has been exposed to fire. In segment from a cross section, the outer surface will normally be completely blackened, consisting mostly of char. Beneath this char layer, the wood will appear to be quite normal ("unbumt" wood). The transition between the two zones is usually "abrupt". The temperature at which this transition takes place has been reported to be between 280°C and 300°C, depending on the thickness of the specimen, the duration of exposure, and the severity of the fire. There may exist a central region that is relatively unaffected by the fire. As the char front advances, this region will reduce in size. CENTRE LINE CHAR The char layer, identified by the formation of fissures, is considered to have FIRE no strength. The wood directly underneath will sustain some pyrolysis, to an extent that depends on the temperature attained and the duration of exposure. FIRE 300 °C INITIAL TEMPERATURE The load carrying capacity (resistance effect) of the member is reduced by the size of the char layer and any weakening due to pyrolysis that has occurred in the "unburnt" wood. Other structural damage can also be induced as a result of differential thermal expansion and shrinkage due to drying which may cause T E M P E R A T U R E PROF ILE 'A D MOISTURE CONTENT PROFILE Figur3-9.hg3 Figure 3.7: Behaviour of wood exposed to elevated temperature 3.4 Resistance of Lumber Exposed to Fire 25 cracks to develop and expand. The thermal damage can be modified by the presence of moisture in the wood, an applied stress field, or by the severity of the exposure condition. Failure of the member occurs when the load carrying capacity is reduced to below the load which is actually present. The time it takes for this event to happen, measuring from the start of the fire exposure, is termed the time-to-failure (t{). The process leading to failure is illustrated in Figure 3.8 which shows hypothetically how tf may be affected by the grade of material. Two Douglas-fir members, one Visual Grade Select Structural and one No. 2, are used in this illustration. Supposing that they are both designed to resist the same tension load. Furthermore, it is assumed that the load present at the start of a fire produces a stress equal to one-third of the characteristic strength of the material. The dotted lines represent the "apparent strength ratio"11 of the unburnt section, versus time of the fire exposure. These lines slope downward, £ and assume a linear rate of Jjj a. strength degradation. The solid lines represent the hypothetical stress in the member, which increases at a rate depending on the charring rate (() and the initial cross-sectional geometry. 1.2 1 -2 0.8 0.6 0.4 0.2 0 S T R E S S ••••••••v.... S T R E N G T H - '>\\i*^— -*-i^*:T * • ss _ NO.2 * * NO. 2 -10 15 TIME-TO-FAILURE (min) 20 25 Figure 3.8: The failure process in structural wood members in fires The strength ratio is defined as the ratio of strength relative to the short-term strength at room temperature. Since the strength varies across the cross section due to the temperature and moisture content variation (see Figure 3.7), the "apparent strength ratio" can not be determined analytically. In the case of bending, it is assumed that the strength of the outermost fibre of the unburnt section governs (Lie 1977). 3.4 Resistance of Lumber Exposed to Fire 26 The stress in the No.2 grade, which in this example is larger in cross-section to begin with (because of its lower characteristic strength), will increase at a slower rate at any given time than in the Select Structural grade (see the difference in the slope between the two solid lines in Figure 3.8). The failure point is given by the intersection of the dotted and solid lines. From this example, the No.2 grade member is predicted to have a longer time-to-failure. However, the prediction depends critically on the assumed charring and strength degradation rates, and these factors may be a function of wood quality. As the quality of lumber decreases, these rates at the failure locations may be significantly influenced by the presence of defects such as knots. The predicted difference between the two grades also depends on the difference in size assumed in the calculation, which may or may not present in practice. Given a certain fire exposure, because of variability in the initial material strength and the parameters oc' and £, the time-to-failure t{ will be a random variable. Its distribution form may be difficult to determine in closed-form. However, if the distribution of tf is determined, the rekability of a member can be easily determined for any exposure time. Clearly, this reliability is conditional on the fire occurring. 3.4.1 Strength Models Several different approaches have been proposed for the prediction of the structural resistance of bending members in fire exposures. They are all based on Elastic Transformed Section Theory 1 2. 1 2 The theory assumes that the cross section of a member is reduced i n area by the formation of the char layer wh ich carries no load. The load is then redistributed to the remaining section according to the stiffness coefficients of indiv idual layer expressed as a function of temperature. Since plane sections are assumed to remain plane, the strain therefore varies linearly across the depth of beams subject to a uniform moment. In the case of tension, the strain is constant across any cross-section. 3.4 Resistance of Lumber Exposed to Fire 3.4.1 Strength Models 27 Hall (1968), Lie (1977), followed by King and Glowinski (1988), developed similar mathematical models to predict time-to-failure t{ of heavy timber beams and columns exposed to A S T M E-119 fire conditions. The model developed by Lie (1977) has been adopted by N B C C 1 3 , for determining the t{ of "heavy" timber glue-laminated beams and columns. Lie (1977) assumes that the member cross-section is reduced by the amount of char formed in the fire exposure. The member fails when the cross-section reaches a critical size. This critical size is determined by the rate of charring, the residual strength and stiffness of the unburnt material, and the load applied. For members exposed to fire on all sides, the governing equation for tension or compression (short column) is k1 b , 2Cff where b and d are the breadth and depth of the member before the fire, k' is the ratio of the load to the load-rarrying capacity of the member, a' is the residual strength of the unburnt wood section expressed as a fraction of the room-temperature short-term strength of the material, and ( is the rate of charring. The fire resistance rating is given by tf. A corresponding equation for beam exposure is k_l b _ 1 _ a1 b - 2 C t f ( 2CtA [3 .19] where d > b. In the model proposed by King and Glowinski (1988), four distinct layers were assumed: an outer char, followed by a "hot" layer, then a "warm" layer, and finally an 1 3 The Nat iona l Bui ld ing Code of Canada (Part 3). 3.4 Resistance of Lumber Exposed to Fire 3.4.1 Strength Models 28 unaffected layer at the core. The char layer was assumed to have no strength; the "hot" layer 60% of normal strength; the "warm" layer 80% of normal strength. The respective modulus values assumed were 0, 75, and 90% of the unaffected value. Failure of any layer occurred when the calculated stress (based on the Elastic Transform Theory) exceeded a previously established critical value. The load-carrying capacity of the beam was reached when the calculated stresses in all layers exceeded their respective critical values. Failure was defined by the occurrence of a specific sequence of failure events involving the different layers. Based on very limited glue-laminated timber beam and column fire test data, Lie's model, based on £=0.6 mm/min and a'=0.8, predicts accurately the tf of members loaded at full design load but underestimates the tf of members loaded at only partial design load. The reverse is true with King and Glowinski's model. In general, it is difficult to pinpoint which is the more accurate model because of the limited test data. Conceivably, if wood is homogeneous and without defects, and if the parameters a and £ are accurately determined with respect to the fire exposure applied, both models should predict tf for any size of timber. On the other hand, Lie (1977) commented that the performance of sawn timber cannot be predicted reliably because of the effect of shrinkage cracks. Konig (1991) pointed out that the charring rates assumed by various building codes vary considerably, with values up to as high as 1.0 mm/min. A rate of 0.6 mm/min is considered the norm for clear, medium density softwood exposed to A S T M E-119 fire conditions14. In some codes, higher rates are used to compensate for the loss in strength and modulus of elasticity of the unburnt portion, or to compensate for the loss of section due 1 4 A S T M E l 19 time-temperature conditions: 538°C at 5 min ; 704°C at 10 min ; 843°C at 30 min ; 927°C at 60 min ; 1010°C at 2 h ; I093°C at 4 h; and 1260°C at 8 h or over. 3.4 Resistance of Lumber Exposed to Fire 3.4.1 Strength Models 29 to the "round-off" effect at corners15. In other words, the charring rates are calibrated to the loss of load carrying capacity. For dimension lumber, using a unified charring rate to account for both the loss of material due to charring and loss of strength in the unburnt section may prove to be too unreliable. Moreover, the reduction in strength and stiffness of the unburnt portion is not necessarily the same for all grades of lumber. Probabilistic t{ Models. Bender et al. (1985) proposed a model for prediction of tf of glue-laminated beams, taking into account the strength variations of lumber and end-joints between laminates. The ultimate moment carrying capacity of the beams was calculated on the basis of randomly generated strength properties of individual laminates and laminate length data which affect the number and location of end-joints. This information was used with a fire endurance prediction model to calculate the t{ of the beam during an ASTM E-119 fire exposure. Using Monte Carlo simulation, the distribution of t{ was estimated. The charring rate and the strength reduction factor for unburnt wood were assumed to be constant. Woeste and Schaffer (1981) discussed the necessary procedures for probabilistic based design of wood floors exposed to fire. The objective of their reliability analysis was to determine the probability of failure given that a fully developed fire had occurred. The formulation was based on the first order second moment reHability calculation method which implies all the variables are a random Normal variable. The variables were fire severity, dead-plus-live load, material properties and charring rate. The "apparent" strength degradation parameter a was empirically developed on the basis of tf data on 42 floor assemblies provided by Lawson (1952). Gammon (1987) outlined the general requirements for probabilistic design of wall assemblies for fire safety but did not actually perform any reliability calculations due to lack 1 5 When a wood member is exposed to fire on all sides, the corners tend to char more severely because the heat is coming from both sides thereby producing a rounded appearance. 3.4 Resistance of Lumber Exposed to Fire 3.4.2 Experimental Data 30 of data. However, it was noted that, in order to overcome data limitation, an approach based on conditional reliability, in which some of the design variables are treated as constant, may be used. 3.4.2 Experimental Data Very limited test data are available on the endurance of structural lumber subjected to fire. Noren (1988) compared the t{ distribution between high-quality and low-quality spruce lumber loaded in bending and exposed to an ISO 834 fire exposure16. The cross-sectional dimensions of the lumber were 45 by 120 mm. The high-quality material was relatively clear of knots whereas the low-quality material contained an edge knot in the central 1/3 span. Each specimen was loaded in bending to 1/3 or 1/6 of the expected strength of the specimen. The expected strength was individually estimated from bending tests on "matched" specimen at room temperature. The central-third portion was exposed to fire. The data obtained were t{ and estimated short-term strength. Noren noted that the mean tf of the low-quality material was at least as high as that of the high-quality material. This should not be surprising since the low-quality members were subjected to E .4 in z ill o E5 -2 S o OL Q_ £ .4 111 • 5 2 £ o a. -HIGH G R A D L O W G R A D E load to 1/6 of estimated strength 10 15 20 TIME-TO-FAILURE (mint 25 A load to 1/3 of / / I estimated strength f I' 5 10 15 20 TIME-TO-FAILURE (min) 25 Figure 3 . 9 : Modelling of t{ data of Noren (1988) by Weibull distribution 1 6 The specimens were matched by their position in the log and, in the case of the lower-grade material, by the size and location of the knots. Matched pairs were produced by ripping a thick plank into two pieces of lumber so that one was nearly the mirror image of the other in grain and knot appearance. 3.4 Resistance of Lumber Exposed to Fire 3.4.2 Experimental Data 31 lower stresses than the high-quality ones. However, during the initial period of fire exposure, the probability of failure of the low-quality material appeared to be higher than that of the high-quality material for both load ratios, as indicated by fitting a Weibull distribution to the observed tf data (Figure 3.9). The failure probabilities are indicated by the area under the distribution curve. These early failures of the low-quality material were probably due to the presence of some "very" weak pieces in the population. 3.4.3 Factors Affecting Strength Distribution In this Section, the variables which affect reliability calculations, and the influence of temperature on these variables are discussed. Size Effect. The strength of a piece of lumber in tension has been explained by "the weakest link" theory; that is, its strength depends critically on the weakest "link" among individual "links" constituting the piece of lumber. Given that the strength of the individual links is identically distributed and independent, and that the piece of lumber can be considered to be composed of a "large" number of these links, the strength of lumber can be approximately modelled by a Weibull distribution, regardless of the underlying strength distribution model of the links. However, when this theory is used to explain lumber strength data, these assumptions are violated "somewhat" since the strengths of individual "links" in a piece of lumber can be considered neither identically distributed nor independent of each other. Typically, the weakest link in the piece is associated with a defect — typically, a "large" knot. In fact, tests on dimension lumber show that a majority of the failures, among different specimens, initiated near a knot. The remainder related mostly to slope-of-grain. However, it is often difficult to accurately pin-point the failure location because there are many "weak" links in any given piece of lumber, and the strengths of these links may be 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 32 highly correlated. That is, it is difficult to discern which is "the worst defect" among several very similar defects. The weakest-link concept has been used to assess the size effect in lumber (Madsen and Buchanan 1986). A longer piece of lumber is considered to be made up of a larger number of links, and, therefore, is more likely to possess a weaker link. Generally, the weakest-link theory implies a relationship in the form of: O j _ ( Vn\t\ °2 2 [3.20] where O j and o 2 are the respective strengths of members of volume V1 and V 2 . The value of the parameter T] is determined experimentally. It depends on the stress (compression, tension or bending), and varies with strength level and species (Barrett and Lau 1994). No data are available to indicate its dependency on temperature. In general, Eqn [3.20] is supported by experimental data for the effect of length in both tension and bending. There are contradicting data on the effect of breadth. Bohannan (1966) could not verify the existence of a breadth effect in relatively clear lumber tested in bending. Tests by Madsen and Stinson (1982) showed that, for beams with the same depth but of varying breadth, and tested over the same span, strength increased as the width was increased. Madsen and Buchanan (1986) observed a definitive breadth effect in tension. Lumber Grade. Traditionally, the allowable properties of visually-graded lumber was established using A S T M D-245 "Establishing Structural Grades and Related Allowable Properties for Visually Graded Lumber" based on the principle of strength-ratio. This standard provides strength ratios for knots, slope-of-grain, splits, and other natural characteristics. Strength ratios, such as those associated with a knot, are applied to a clear 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 33 wood strength property to account for the strength reducing effect of the knot. Also, the ratios are a function of the defect only and do not depend on the clear wood strength itself. However, the strength ratio relationships are different for different types of defects. The design strength value of each lumber grade is derived from the basic strength of the clear wood, and adjusted according to the strength ratio pertaining to each of the defects that are permitted in the grade. Recently, the concept of in-grade testing has replaced the small clear, strength-ratio, approach for estabHshing design properties of lumber. For 38 mm thick dimension lumber, the strength values, in both Canada and the United States, have been revised to reflect the results of full-size in-grade lumber testing programs. These in-grade programs have been implemented to provide characteristic values for lumber for use in reliability-based design. In addition, the in-grade method has been used to study effects of lumber grade, duration of load, moisture content, temperature and size on lumber strength. A temperature factor was developed for correcting test data obtained under different local temperatures to a nominal temperature of 23 °C. The grade effect on strength observed in the in-grade test data differs from that implied in A S T M D-245. For instance, the in-grade data typically show that Visual Grade No.l and No.2 have no significant differences and Stud grade is better than No. 3. The effect of other factors such as moisture content and duration of load may be influenced by the grade of the wood (see following discussions). Moisture Content. It is well known that as wood absorbs water into its cell wall its strength is reduced. On the basis of small, clear specimen behaviour, the strength reduction is a linear function of moisture content for moisture contents below the fibre saturation 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 34 point11. The behaviour of lumber is somewhat different, as it is affected by grade. High-grade lumber tends to retain approximately the same characteristics as exhibited by small, clear specimens. Low-grade lumber strength, on the contrary, shows little dependence on moisture content. Moisture also affects behaviour of lumber exposed to fire in two other ways. First, its presence changes the apparent heat conduction characteristics of wood. Second, it takes up heat through vaporization (Schaffer 1967, White 1988). The vapour pressure developed in heated wood impedes the diffusion of flammable gases to the burning surface. Some of the moisture vapour migrates inward into the undamaged wood. White and Schaffer (1981) found that the peak inner moisture content of wood had risen 26 to 100% above its initial equilibrated value (see Figure 3.7, points B and C). The moisture peak advanced at about the same rate as the char front. The temperature at the peak-moisture location was consistentiy about 105°C for southern pine specimens and between 110°C and 130°C for Douglas-fir specimens. This difference in temperature was explained by the fact that southern pine is more permeable than Douglas-fir. As noted by Jonsson and Pettersson (1985), the effect of moisture redistribution is wide-reaching — from complicating heat conduction equations to affecting the apparent thermal conductivity coefficients. Since moisture transport is sigriificantly related to permeability, the moisture effect is also species-dependent. After exposure to a "standard" fire for 30 and 60 minutes, Kallioniemi (1980) showed that the moisture content of spruce glue-laminated beams was not significantly affected when it was measured from a distance of at least 20 mm from the char front. When the moisture content was between 18 and 26%, the rate of charring was reduced by about 45% from that of wood at 11% moisture content. ICallioniemi did not observe as significant an increase in the peak moisture content as did White and Schaffer (1981). 1 7 The fibre saturation point of wood defines the point in moisture content, at which free water begins to appear in the cell cavities. This moisture content varies, in general, between 24% and 30%. 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 35 Since the moisture content of a wood member changes when it is exposed to fire and since moisture content cannot be reliably measured by any conventional means at temperatures near charring, it will be difficult to isolate the effect of moisture on fire endurance during a fire exposure test. Duration of Load (DOL). The DOL effect in wood refers to the behaviour of wood in response to long-term loading; that is, its ability to carry a given load depends critically on the length of time it is required to carry the load. This behaviour of wood has been studied for lumber of different grades and sizes (Karacabeyli 1988). In a test of nominal 2x8 and 2x4 spruce lumber of two qualities in bending, Karacabeyli observed that the effect of lumber quality or size was not significant. The general DOL effect, however, departs significantly from that suggested by Wood (1951) for small, clear specimens. Contrary to Karacabeyli's results, Gerhards (1988) reported that, on the basis of constant-load results, lower-grade lumber tended to have shorter times to failure when tested at room temperature. This grade effect was more pronounced in longer durations, though he cautioned that the results might not be statistically significant. For load durations of one hour or less, stress ratio differences attributable to grade effect amounted to a maximum of 3%. Foschi et al. (1989) expressed Karacabeyli's results by a "damage accumulation" model. The model for nominal 2x6, No.2-&.-Better hemlock lumber is shown in Figure 3.10. This damage accumulation concept assumes that the rate of damage in a member at any time, is a function of the stress applied at that time, and the total damage accumulated to that time. Also no damage will accumulate if the stress is below a certain threshold. This threshold was determined for hemlock lumber to be 53.3% of its short-term strength. For 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 36 the spruce data above, the thresholds for the be 42 and 37%, respectively. Fridley et al. (1989, 1990) investigated the effect of temperature on the duration-of-load effect in structural lumber. A trend toward shorter times to failure with increasing temperature for equal stress ratios was observed. It was suggested that the temperature effect was consistent between grades. The effect of temperature was found to be greater as the duration got longer. The short-term stress ratio differences attributable to temperati temperatures between 23°C and 55°C (Fig two lumber qualities evaluated were found to .4 -.3 1 ' ' ' 1 -2 0 2 4 6 LOG TIME (in hours) Figure 3 .10: Duration-of-load effect in 2x6, No.2-&-Better hemlock lumber effect were in the order of 0.2%/°C for 3.11). From these studies, there exists little or no indication of a grade effect on the effect of load duration, for load durations of one hour or less at temperatures up to 55 °C. The damage accumulation model developed by Foschi et al. (1989) indeed suggests that there is no D O L effect if the stress is less than a certain threshold. A t temperatures near the charring temperature of wood, significant DOL nfiU3-(3.HG3 1.1 0 z Karacabeyli (1988) 2X8 Spruce high ^ — and low quality tested @ room temperature \ X Wood's curve Fridley el al. (1988) 4 x V \ \\J 23 °C 2x4 Douglas-fir 38 "C SS and No.2 1 1 1 1 N 54 "C 1 1 0 2 4 6 8 10 12 14 16 TIME (log min) Figure 3 .11: Effect of temperature on duration-of-load effect as affected by grade 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 37 effect on creep has been observed in clear wood for time periods as short as two hours (Schaffer 1982). But it is not clear whether this effect is due to DOL alone or to both DOL and duration of heating. It is possible that under those "mild" fire conditions which produce "long" time-to-failures, neglecting DOL effect may lead to a significant overestimation of the time-to-failure. This condition may occur in members which are concealed behind highly protective membranes, such as gypsum board. In such a situation, accurate estimation of the time-to-failure has little implication in design for life safety since failure will probably occur in the latter stage of the exposure and will not impact on the time available for evacuation of occupants. As implied by current code specifications, the behaviour of the structure in the first 45 minutes of exposure is generally more critical than during subsequent times. Because of charring during fire exposure, the stress in a member due to an originally imposed constant load will increase — in a way mimicking a ramp-load test (Figure 3.8). Thus, it may be acceptable to use ramp-load data to predict stress-history effect. Duration of Heating. This factor is analogous to duration of load, in that heat-duration effect is a function of heat flux just as load-duration effect is a function of load. This factor has received relatively little attention in the research literature, nonetheless its effect can not be ignored. It is possible that the effect of duration of heating accumulates in two stages: the first stage occurs at temperatures just above the boiling point of water. Work in the area of high-temperature drying of lumber provides an indication of the significance of this first-stage effect. Gerhards (1988) found that high-temperature dried Douglas-fir 2x4 lumber lost about 12% of its bending strength, compared to ordinary drying. On the other hand, both Koch (1971) and Gerhards (1983, 1986) found that the loss of bending strength was 3.4 Resistance of Lumber Exposed to Fire 3.4.3 Factors Affecting Strength Distribution 38 insignificant in southern pine and yellow poplar. This first-stage effect is probably attributed to the harmful effect of steam, the significance of which is linked to the permeability of wood. For higher temperatures, the effect will be proportional to pyrolysis which in turn is directly related to duration of heating. A damage accumulation model, similar to one develop for DOL (Barrett etal. 1979), maybe used to explain this effect, however, no data are available. 3.4.4 Rate of Charring The rate of charring of wood depends on the kinetics of wood combustion, in addition to the external fire exposure characteristics. Wood combustion is an extremely complicated process involving the evolution of flammable gases and the diffusion of these gases to and away from the burning surface (mass transfer). In addition, the heat generated from the burning gases and oxidizing char in turn fuels the decomposition process through conduction of heat inward (heat transfer). These two transfer processes, however, are continuously modified by the effects of the combustion. The chemical composition of the decomposition products are functions of temperature, wood species and density, while the transfer processes depend on wood species, moisture content, permeability, and other morphological factors. Furthermore, the thermal properties influencing these processes are constantly varying, as is the temperature itself. The charring of wood has been a subject of intensive research. Browne (1958), Schaffer (1966), Hall etal. (1968), Hadvig (1981), Leicester (1983), Barnett (1984), and Jonsson and Pettersson (1985) have each reviewed the available literature. Significant experimental studies during the same period included work by Thomas et al. (1967), Schaffer (1967), Kanury and Blackshear (1970), Lee et al. (1977), and White (1988). 3.4 Resistance of Lumber Exposed to Fire 3.4.4 Rate of Charring 39 The rate of charring has been defined as either the rate of weight loss or the rate of advance of the char-wood interface. The latter definition has been more widely used (Schaffer 1966). Under a sufficientiy high constant exposure temperature, wood chars rapidly in the first few minutes. After the formation of the first few millimeters of char, the rate then stabilizes (Jean 1963, Lawson et al. 1952, Truax 1959). Blackshear and Murty (1962) stated that this uniform rate corresponded to a steady state of combustion under constant boundary conditions. The charring rates under A S T M E-119, C A N / U L C S101 1 8 , ISO 834, JIS 1301 1 9 or D I N 4102 2 0 exposures are similar as all these standards have similar temperature-time curves. For fire safety design of heavy timber structures, Lie (1977) recommended use of a charring rate of 0.8 mm/min for light, dry wood, 0.6 mm/min for medium-density softwood, and 0.4 mm/min for high-density, moist wood. Simple analytical expressions for the fire performance of glue-laminated beams and columns described in Appendix D-2.11 of the N B C C implicitly assume a charring rate of 0.6 mm/min. Swedish Building Code SBN 1976 relates charring rate to the opening factor21 of the fire load and recommends a lower limit of 0.6 mm/min and an upper limit of 1 mm/min. Table 3.3 shows some mean charring rates obtained from studies on spruce, Douglas-fir and southern pine. 1 8 "Standard Method of Fire Endurance Tests of Building Construction and Materials," published by Underwriters' Laboratories of Canada. 1 9 "Fire resistance tests standard," published by the Japan standard organization JIS. 2 0 "Fire resistance tests," published by the German standard organization DIN. 2 1 The opening factor is a parameter governing the severity of the fire. It is the ratio of the area of opening to the total boundary area multiplied by the square root of the height of the opening.. Table 3.3: Chamng rates of some common wood species Specimen Configuration Moisture Content (%) Fire Exposure Charring Rate (mm/min) Applicable Range (min) Source Breadth Direction Depth Direction Spruce timber beams 38 to 50 mm thick 12 British Standard 0.64 5 to 30 Lawson et al. (1952) Douglas-fir members 47 by 92 mm 12 A S T M E-119 0.81 1.2 up to 14 Southern pine board 25 mm thick 7 A S T M E-119 1 - up to 10 Schaffer (1966) Douglas-fir laminated to 191 mm thick slab 7 - 12 A S T M E-119 0.652 Truax(1959) Spruce and fir beams 75 by 150 mm to 125 by 200 mm 12.5 - 19 D I N 4102 0.667 1.04 up to 60 Dorn and Egner (1961) Spruce (Picea jezoensis Carr.) laminated to beams 180 by 450 mm 12.8 JIS-1301 0.601 0.8 up to 30 Imaizumi, IC (1962) Timber beams of various species 13 to 50 mm thick dry service British Standard 0.635 -- Lawson, et al. (1952); Webster, etal. (1951) Douglas-fir 12 A S T M E-119 0.6 10 or greater Schaffer (1967) Southern pine 0.75 White oak 0.48 3.4. Resistance of Lumber Exposed to Fire 3.4.4 Rate of Charring 41 Effect of Wood Anatomy. Wood chars ten times more rapidly in the radial and tangential directions, than in the direction of grain (White 1988). This phenomenon is not well understood. There appears to be a small difference, up to 10%, between the rates in the radial and tangential directions. Normally, the rate of charring will decrease with increasing wood density and with the presence of extractives in the wood. Other less-influential factors include Hgnin content and inter-cellular structures (Roberts 1971, Bhagat 1980, Sauer 1956, Lee et al. 1977). Of all the anatomical and morphological features, density is the most important factor determining charring rate. Effect of Permeability. Permeability influences the movement or build-up of combustible volatile components and water vapour. Species with low permeability in the longitudinal direction tend to char at a slower rate in the transverse direction than species with high permeability (Schaffer 1967). Permeability becomes increasingly important with increasing moisture content. Mathematical Modelling. Bamford et al. (1946) attempted to model temperature distribution within a thermally decomposing body by using a modified one-dimensional heat conduction equation of the form: „d2T . ~ dT K + Q = p c [3.21] dx2 dt 8t where K, c and p were respectively the thermal conductivity, specific heat and relative density. W denoted the weight of volatile products per unit volume of wood and Q denoted the heat evolved (or, if negative, adsorbed) at constant pressure per unit weight of volatile products formed. The rate of volatile generation, dW/dt, was modelled by an Arrhenius expression: 8W_ ( E ) — = 9 « P - — [3.22] 3.4. Resistance of Lumber Exposed to Fire 3.4.4 Rate of Charring 42 The Arrhenius expression is an empirical expression proposed by Swedish physicist Arrhenius for modelling the rate of reaction of reactants in gaseous states. The independent variable in this expression is absolute temperature T and the other parameters are activation energy E, universal gas constant R and a material constant (p. Since K, E, and Q are constantly modified by the conditions in the combustion and pyrolysis zone, theoretical treatment using Eqn [3.21] and Eqn [3.22] for pyrolysis of wood, which is a solid-state reaction, is overly-simplified. More recent work focused on modifying the heat conduction equation to account for various aspects of the combustion process experienced with wood. Thomas et al. (1967) and Kung (1972) added a convection term modelling the effect of volatile flow. Knudson (1975) and Atreya (1983) accounted for the heat of vaporization of water by incorporating a sharp peak at 100°C in the specific heat function. Fredlund (1985) and Aerotherm Corporation (White and Schaffer 1978) included an Arrhenius-type function for surface recession of the char layer. Fredlund (1985) also considered the effect of mass transfer of moisture in solving the heat conduction equation. Fredlund's model has been the most comprehensive. While an Arrhenius function expressing the degradation rate as a function of temperature is retained in many of these models, Kanury (1972), Thomas et al. (1967), and Hadvig (1981) assumed that wood pyrolysed abruptly at a critical temperature. This assumption is considered appropriate for real-life fires since the temperature gradient in an exposed member will be "steep" across the wood-char boundary. The approach is simple as no integration is required through the tihickness of the burning member to determine the total amount of volatile gases evolving at any one time. Roberts (1971), and Jonsson and Pettersson (1985) outJLined theoretical and experimental requirements for the mathematical treatment of charring but contended that 3.4. Resistance of Lumber Exposed to Fire 3.4.4 Rate of Charring 43 pyrolysis in the presence of moisture is an extremely complicated problem. Unfortunately, moisture movement cannot be conveniently neglected (Fredlund 1985, Jonsson and Pettersson 1985). Empirical Modelling. Early work by Lawson et al. (1952), Vorreiter (1956), followed by Schaffer (1967), then by White (1988), led to the establishment of several similar, empirical models for the charring of wood. These models have the general form of either dx _ „ — ~ Tlj t [3.23] o t or x = T]2 tn [3.24] where x is the location of the char-front in the direction of charring, dx/dt the instantaneous rate of advance of the char front, t the time and r\l and r\2 are regression constant. The exponent n in Eqn [3.23] determines whether the rate of charring is increasing (n>0), constant (n=0), or decreasing («<0) as time increases. Truax (1959) and Vorreiter (1956) showed that, with Eqn [3.24], n attained a value of 1, provided the initial non-linear rate data were excluded from the regression. Schaffer (1967) and White (1988) expressed their data as a time-location model. It has the form of A comparison of these models is given in Table 3 .4 . [3.25] 3.4. Resistance of Lumber Exposed to Fire 3.4.4 Rate of Charring 44 Table 3.4: Empirical charring models for some common softwood wood species Lawson etal. (1952) Spruce timber beams 38 to 50 mm thick exposed to A S T M E-119; moisture content 12%. — = 1.041 r 0 2 dt where x = location of char front, mm; t = time, min. Vorreiter (1956) Dried spruce plates 10 mm thick placed horizontally and exposed to fire from underneath. 1.3 x = 0.345 P - Pc where x = location of char front, mm; t = time, min; p = relative density of wood; p c = relative density of char. Schaffer (1967) Douglas-fir laminated to 75 mm thick planks and exposed to A S T M E-119; moisture content ranged from 6 to 18%. t = [ (2.27 + 0.046 a ) ) p + 0.33 ] x where x .= location of char front, mm; t = time, min; p = relative density of wood; co = moisture content of wood, %. Schaffer (1967) Douglas-fir laminated to 75 mm thick planks and exposed to constant furnace temperatures of 538, 816, 927°C; moisture content ranged from 6 to 18%. t k m l — exp I 3.-0 j F U r J where k = (1.125 + 0.0227 o>) p + 0.178 T = temperature, K; / =4.184 joules/cal; R = 8.14 joules/(gram-mole-K); £ = 3108 cal/gram-mole; x = location of char front, mm; t = time, min; p = relative density of wood; a) = moisture content of wood, %. White (1988) 63 mm thick specimens from eight species exposed to A S T M E-119; moisture content ranged from 6 to 16%. t = * x L 2 3 where l n W = 3 - 4 7 P _ ° - 0 1 P  d ~ 0-005 d + 0.014 (j - 1.92 p2 - 0.001 r - 1.56 p = relative density; d = a treatability parameter, mm; G) = moisture content, %; r = annual ring orientation with respect to the fire-exposed surface, degree. 3.5 Time-Dependent Lumber Strength Models 45 3.5 Time-Dependent Lumber Strength Models The concept of linear damage accumulation was introduced in Section 3.4.3 in the examination of the duration-of-load effect in wood. Other approaches to model this time-dependent behaviour include a fracture model (Nielsen 1978) which considers crack-opening and crack-lengthening as the main cause of damage, a chemical kinetics model (Caulfield 1985, van der Put 1989) which recognizes the effect of stress on the potential energy barriers impeding molecular motion, Liu and Schaffer's application of statistical theory for the absolute reaction rate of bond formation and breakage (1991), and Fridley's proposal of a "strain energy density" parameter reaching a certain critical level as a criterion for impending failure (Fridley et al. 1992). These models are discussed individually beginning with the approaches based on linear damage accumulation. 3.5.1 Damage Accumulation Approach Use of damage accumulation as a phenomenon to explain fatigue failures under repeated loads in brittle materials was first introduced by Miner in 1945, in what has been known as Miner's rule (Miner 1945). For a material subject to repeated loads, the theory postulates that a finite amount of "damage" is incurred each time the load is applied and that this damage "accumulates". By assuming that the damage incurred per cycle as the reciprocal of the number of cycles required to fail the specimen at the same load, Miner was able to show experimentally that failures tended to occur as the sum of such fractions more or less equaled one. This phenomenon has been observed on various aluminum alloy specimens tested at different cyclic loads for differing numbers of cycles. Accordingly, the criterion for failure is 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.1 Damage Accumulation Approach 46 where nvn2 and n3 are the number of cycles at stress levels Sv S2 and S3, and Nv N2 and N3 are each the number of cycles required to fail the specimen when only the corresponding stress level is applied. Since the ratio l/7Vi can be viewed as the rate of damage per cycle at the stress level S i ; we can express the failure criterion as f U da , _ . — dt - 1 [3.27] where a represents the damage state and tf is the time to failure. Most of the work in wood concerns the derivation of appropriate damage rate functions. The models are listed in Table 3.5 . Table 3.5: Damage accumulation models for duration of load effect in wood Wood (1951) Barrett and Foschi (1978) Barrett and Foschi (1978) — =A (T - x n ) B + C a d t 0 Foschi etal. (1989) — =A(x - T n o ) B + C ( x - x n o ) D a ^ j v 0 u ' v 0 u ' Gerhards (1979) da -A + Bi 77 ~ 6 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.1 Damage Accumulation Approach 47 A l l of the models assume that the rate of damage (da/dt) in a member at any time t i s a function of the stress x applied at that time. A l l models, except Gerhards (1979), include a stress threshold x 0 below which stress has no effect. Barrett and Foschi (1978) as well as Foschi et al. (1989) included the total damage accumulated to that time as an additional variable. In all models, the damage variable a is assumed to take on a value between 0 and 1, where 0 denotes the damage is nil and 1 denotes the damage has reached the point of failure. A l l these models are empirical in the sense that they are not based on any particular failure mechanism. 3.5.2 Fracture Mechanics Approach Nielson's fracture model (Nielson 1978) defines the life-length of a linear viscoelastic material, isotropic or orthotropic, subject to an applied stress, by a process of crack-growth initiation and crack propagation. In the case of orthotropic materials, the cracks must be found simultaneously in the principal plane and the plane of minimum resistance to crack extension. The growth initiation phase involves cracks gradually opening but not increasing in length until the opening reaches a critical width. For a material subject to a constant stress x, E • /(«.) = [3.28] determines the time ts at which the critical crack opening has been reached and at which the cracks wil l begin to increase in length. The variable E is the Young's modulus in the direction of the applied stress, oK is the short-term strength of the cracked material, and J(t) is the creep function of the material, generally assumed to be uniform, and may be taken as the longitudinal strain response of the material if it is uniaxially loaded by a unit stress applied at time t = 0. 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.1 Fracture Mechanics Approach 48 When the crack width reaches the limiting width as dictated by Eqn [3.28], the crack will begin to lengthen. Failure is deemed to occur when the rate of this lengthening increases catastrophically. The time tCK at which this event occurs is given by "CR Y, Y F(d) e dd [3.29] where Y = ' a N 4 Z = — (1 + fsQ') T C o* denotes the ideal strength of the material without the crack, u is a parameter depending on the creep function, Q' represents the degree of resemblance to a parabolic shape of a crack tip, and the function F is related to the creep function J(t) such that F(EJ(t)) = t [3.30] Both ts and are functions of the modulus of elasticity, the stress intensity factor, and the creep function of the material. Neilsen (1978) and Clouser (1959) suggested a creep function in the form of ( 1 + a'tb ) 7(0 = [3.31] where a' and b' are function parameters. For wood parallel to grain, Neilsen found that a' = 1/3 and b' = 1/4. Although Neilsen's postulation is reasonable for the physical phenomenon of rupture, it requires knowledge of the viscoelastic creep behaviour of the material at the crack tip. As pointed out by Foschi and Yao (1986), this creep function would have to be obtained by calibration since such a property will be difficult to obtain and will be highly variable due to localized conditions of grain orientation and density. Creep parameters 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.3 Kinetic Energy Barrier Approach 49 measured from a standard creep test on straight-grain wood would, at best, be regarded as a lower-bound value. 3.5.3 Kinetic Energy Barrier Approach Caulfields Model. According to Caulfield (1985), rupture is a phenomenon which interrupts the normal stress-strain process of a material under load. Typically, this phenomenon is unrelated to the material's stress-strain behaviour, and therefore can not be readily expressed in mathematical functions of basic material constants such as modulus of elasticity or Poisson ratios — at least not to the same degree of rigor as is possible with elastic deformation or viscous flow. Theoretically, the rupture process must be evaluated by starting from inherent bond strength. Caulfield approached the problem on the basis of the theory of absolute reaction rates coupled with a hypothesis for creep-rupture phenomena due to duration-of-load and rate-of-loading effects. Caulfield states that, according to the kinetic theory of matter, all atoms and molecules are in motion. Each molecule occupies a certain energy state and to "jump" in and out of this state the molecule must overcome a potential energy barrier. In a state of equilibrium, macroscopic motion is nil since there are approximately the same number of jumps to and from an equilibrium state (a state of minimum energy). The number of jumps (u) per unit time to and from a state of equilibrium is given by k T ( - A P ^ h CXP R T [3.32] where A p is the potential energy barrier, T the absolute temperature, h Planck's constant, k Boltzmann's constant, and R the universal gas constant. For a material under an external stress, the potential energy barrier is distorted, and the tendency to jump the barrier in the direction of the applied stress is greater than in the opposite direction. The net number of jumps, A V , per unit time equals 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.3 Kinetic Energy Barrier Approach 50 _ k T ( - A p A V — exp — h [ R T exp ( x 8 2 k T exp 6 ^ 2 k T [3.33] where x is the applied stress, and 5 is the volume of the moving element. Multiplying the term A V by A0, where X0 is the distance of the jump, gives the localized dislocation per unit time. Treating this term as the rate of straining (de/dt), Caulfield obtained the expression de dt h 6 X P R T exp ( x 8 2 k T exp -x 6 2 k T [3.34] Since exp(xo/2£T) » exp(-x8/2A:T) for any valid values of x, Eqn [3.34] can be simplified to de dt kT X„ exp ( " A P " <RT/ exp x 6 2 Jt T [3.35] Caulfield then assumed that rupture occurs at a critical limit of the localized dislocation (eCT). Eqn [3.35] is similar in form to Gerhards' damage accumulation equation (Table 3.5). Given that the stress is constant, Eqn [3.35], when integrated from t = 0 to t = tf, leads to the well-known relationship between stress x and the logarithm of the time-to-failure tf: t{ = A exp( -Bi) [3.36] where h e A _ c r — exp kT kn V I A P > R T [3.37] and B = 2 k T Rearranging the variables in Eqn [3.36], we obtain the familiar form of [3.38] x = i l n ( A ) - -^ln(t f ) B B [3.39] 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.4 Statistical Theory of Absolute Reaction Rate Approach 51 When the stress is not constant but increases linearly with time (x—k0 t), as in ramp loading, the result of integrating Eqn [3.35] leads to xf = I l n ( A B) + 1 ln(* 0 ) [3.40] B B where xf is the stress at failure provided B-x{ » 1. 3.5.4 Statistical Theory of Absolute Reaction Rate Approach This approach was proposed by Liu and Schaffer (1991) as an extension of earlier work by Hsiao and others (Hsiao 1966, Hsiao et al. 1968, Hsiao and Ting 1966) and Schaffer (1973). If/denotes the fraction of unbroken elements or bonds in the direction of applied stress, then, according to Hsiao et al. (1968), the rate of change of/is given by | =7C(1 -f)-KJ [3.41] at Where ( E \ K = co exp - — - Y 0 <P« [3.42] \ K 1 ) is the rate of reformation of broken elements, and Kh = cob exp| - + pQ <p(0 j [3.43] is the rate of rupturing of unbroken elements, cor and tob are respectively the frequencies of the jump motion of the elements with respect to forming and breaking processes, E is the activation energy, R the universal gas constant, T the absolute temperature, y 0 a n ( i Po a r e positive quantities that modify the energy barrier as a consequence of the applied stress in the direction of each element, and x is the longitudinal stress acting along a group of parallel elements. 3.5 Modelling Time-Dependent Lumber Strength Behaviour 3.5.5 Strain Energy Density Approach 52 The influence of KT was ignored in Liu and Schaffer's model because they reasoned that KT is much smaller than Kb for high values of stress, and for fast loading rates at which viscous response is negligible. Given that the elements are oriented completely in the direction of the stress, the external load q(t) is equal to (p(t)/(t) = q(t) [3.44] provided/is independent of element orientation. Eqn [3.41] then becomes J = ~Khdt [3.45] 3.5.5 Strain Energy Density Approach In examiriing the stress-strain histories of specimens tested in various duration-of-load studies, Fridley (1992) found that a critical value of the strain-energy density might be linked to the onset of impending failure of the specimen. He showed that this critical value did not vary significantly among the various studies regardless of the loading history or differences in moisture content or temperature. Thus, a criterion based on a common critical value was proposed: ^CR  = l^°^dt t 3 - 4 6 ! which has a mean value of 0.0559 mm-N/mm3 (8.11 in-lb/in3) of all studies examined. For the purpose of prediction, the problem reduces to finding the strain rate as a function of stress level, moisture content and temperature. Fridley (1992) assumed that total strain is the sum of elastic (ee), viscoelastic (ek), viscoplastic (ev), and mechanosorptive (ems) strains. 4.0 RELIABILITY ANALYSIS OF MEMBERS EXPOSED TO FIRE This chapter discusses the application of reliability-based design concepts to the design of light wood-framing members (Light Framing and Structural Light Framing) for fire safety. It introduces the need to develop a t{ model in order for reliability analysis to be carried out effectively and efficiently. Light Framing and Structural Light Framing are a class of dimension lumber typically 38 mm thick, and up to 286 mm wide. As noted in Chapter One, the light framing grades of dimension lumber are widely used in residential, commercial and industrial buudings. A n analysis of the behaviour of these types of members in fire is needed to support international efforts to develop fire safety design as an engineering discipline and to develop national fire performance criteria for light-frame wood structures. 4.1 Performance Function Most fire safety requirements can be expressed as time-based criteria including time to flashover, time to collapse, and time available for the orderly egress of occupants. These times may be measured from the time of ignition or from the onset of flashover. Take, for example, the structural requirement of a member supporting a fire separation, the limit state of this requirement is the state at which the time to failure tf is exactly the same as the time demanded by a code or authority having jurisdiction (tr). The performance function (G) for this requirement can then be written as: G = t ( - t r [4.1] with the limit state corresponding to G = 0. The probability of the event G < 0 denotes the failure probability. The complement of this probability, that is, the probability that G^O, represents the reliability of the member at t = tr 53 4.1 Performance Function 54 As pointed out in Section 3.1.1, the failure probability, given a certain tr, can be determined from actual observations of the variable tf. For many light structural framing members, t{ can be obtained through testing since the time involved will be within practical limits. The tests, however, maybe expensive given the range of sizes, grades and species to be characterized. For analytical purposes, the variable t{ will need to be modelled as a function of its parameters: t{ = ti{xx ... * n) [4.2] where the parameter setxv.xn may include the fire itself, the member size and geometry, the load on the member, and the quality of the material. The performance function becomes: G = t{ - t [4.3] - t{(Xl ... xn) ~ tr In general, the performance function G for a structural wood member loaded in tension and exposed to a fire can be written as: G = t((q,o0,C,-) ~ tr [4.4] where q is the initial load on the member, o 0 the strength of the member, and f the charring rate of the member. 4.2 Governing Equation for Failure in Tension The tf of a tension member exposed to fire depends critically on the failure criteria assumed. In reality, the member fails as soon as the tension resistance capacity is reduced to less than the applied load (see Figure 3.7). If the material is homogeneous and 4.2 Governing Equation for Failure in Tension 55 conditions are uniform, the resistance capacity is the product of the cross-sectional area and the unit strength of the material. However, wood is not a homogeneous material. Furthermore, when wood is exposed to fire, the internal temperature will not be uniform. For these two reasons, the stress in the member is usually not uniform, and as the member is deformed and "damaged" under the effects of load and heat, the distribution of stress will change. Thus, an analytical solution to the resistance capacity is difficult. A n upper and lower bound may be constructed from the mirumum and maximum temperature of the cross section, provided uniform behaviour can still be assumed. The following analysis assumes that the char layer has no strength and the effect of temperature can be adequately characterized on the basis of the mean temperature of the unburnt section. To be consistent, the strength model used in the analysis must also be based on the mean temperature of the member evaluated. For a member exposed to fire, the cross sectional area (A) of an unburnt section is given by: A = A(ej = (b - 2 e) (d - 2 e) [4.5] where b is the width, d is the thickness of the original member, and e is the thickness of the char. The original cross sectional area is given by A^b-d. The charring rate £ is given by de/dt. The stress (x) due to an applied load q at time t is where q is expressed as a function of the initial load q0 and t. Writing e also as a function of t, Eqn [4.6] becomes 1 = ip^TToy ^ 4.2 Governing Equation for Failure in Tension 56 The stress in the member just prior to the start of the fire is given by T o = X [ 4 - 8 ] where the subscript zero denotes t = t0, the starting time of the fire. A t the time of failure t{, the stress (tf) is * ' — [4.9] f A ^ e ^ ) ) Taking the difference between Eqn [4.8] and Eqn [4.9], we obtain ^ = x p ^ y y " ^ 1 4 1 0 1 where x 0 is the stress at the beginning of the fire and t f is the stress at failure. Substituting k'-aQ for i 0 to express the initial stress as a fraction k of the short-term strength o 0 of the member, and xf by the apparent strength o u of the member at failure, which is assumed to be a function of o0, the temperature history T(t), and stress history x(t), gives o „ ( r ( , , . T ( , ) . „ 0 ) - ^ = 7 ^ y - * [ 4 . U 1 Eqn [4.11] governs the time to failure t{ of a member stressed in tension and exposed to fire 2 2. From this equation, tf can be solved, either explicitly or implicitly, provided the In the case of traditional heavy timber design, because a significant portion in the interior zone of such members remains relatively unaffected by a fire even after a prolonged exposure, most codes generally ignore the effect of history, and accept that, ou(T(0,T(0,o0) = a'o0 and the tf function Eqn [4.11] becomes _ ? ( ? 0 ' f f ) _ % a'aQ 0 A[AQ,e(tf)) AQ where a1 is a constant coefficient in the range of 0.5 to 0.85, depending on jurisdiction (Konig 1991). This approach mandates a unified reduction in strength but disregards differences in duration of exposure and final temperature of the member. This approach, however, has been deemed unreliable for describing the fire performance of light-framing members (Hay 1990). 4.2 Governing Equation for Failure in Tension 57 various functions and variables are known. Since the variables are usually distributed, t{ is a random variable. 4.3 Probability of Failure The calculation of the probability of failure, in accordance with Eqn [4.1], requires the tf distribution, as well as the probability density functions of the variables in the equation. The results will therefore depend critically on the distribution of the apparent strength ou at failure. This variable is a function of the temperature and stress histories to which the member has been exposed. While the significance of the variables in Eqn [4.11] will be discussed, their distributions and time-dependence are generally unknown. In order to solve for tf, ou{-) must be known for all likely combinations of temperature and stress histories. This function will be clifficult to characterize since it involves two independent time-dependent variables — temperature and stress histories. Although a range of t( may be obtained through experimental testing, the tests will be expensive, given the range of sizes, grade and species to be characterized. An analytical model is necessary given that test data will be limited in scope. In the present approach we hypothesize that the tf function — Eqn [4.11] — can be modelled on the basis of the damage accumulation concept conceived by Miner (1945). This approach and the resulting model will be discussed in Chapter 7. The experimental data acquired to calibrate such a model are documented and analyzed in Chapters 5 and 6. On the assumption that an analytical model is available for the calculation of the t{ distribution, the reliability indexes or functions can be calculated either through Monte Carlo simulation, or by an algorithm developed by Rackwitz (Ang and Tang 1990, page 4.3 Probability of Failure 58 361) which approximates the probability of failure on the basis of "equivalent" independent Normal distributions of the variables in the performance function. Stress, Charring and Temperature Histories. The stress history can be obtained from the relationship where e(t) represents the charring history. The charring and temperature histories can be obtained from actual measurements or from an appropriate heat transfer model which predicts charring rate and mean temperature as a function of time, given the conditions of the imposed fire. 4.4 Treatment of Variables The following sections include discussions of the variables which affect the performance calculations, and how these variables may, in turn, be influenced by other temperature-dependent factors. 4.4.1 Fire Exposure Absolute versus conditional probability. The type of fire assumed will affect the P f calculation since the assumed fire is a definite event with a known severity. This particular fire leads to a charring rate and a strength-degradation rate, both required for the calculation of te The resultant probability of failure at t = tr is therefore conditional on such a fire occurring. If the fire exposure is unknown a-priori, then, for each conceivable fire, we 4.4 Treatment of Variables 4.4.1 Fire Exposure 59 need its probability of occurring. The outcome, then, is the absolute probability of failure due to fire. In most design cases, it is sufficient to consider a single or several conditional probabilities rather than the absolute probability unless the problem involves an optimization and the parameters to be optimized also depend on the probabilities of various types of fires occurring. A n example of this type of analysis is illustrated in Lie (1972). Normally, this is not the case in structural design and probably not the case in structural fire safety design. In order that conditional reliability may be used, we must select one or several appropriate fire exposure(s) known as design fire(s). The severity of the design fires may be calibrated to building size and occupancy. The reliability analysis should consider the sensitivity of P{ to selected design fires. 4.4.2 Temperature Wood temperature (as well as charring) depends on the conditions of the design fire. These conditions, which are commonly referred to as the boundary conditions, and the properties of the wood and the char determine how temperature would rise inside a specimen. Accurate predictions of wood temperature in members require knowledge of the properties of wood and char and various heat transfer coefficients including those at the boundary. Modelling by conventional heat transfer theory will likely be complicated since the thermal properties of wood are a function of temperature; heat transfer is affected by mass transfer of volatile gases and moisture; and, the thermal properties of char are different from those of wood. Furthermore, it should be noted that failures in light framing are usually associated with such defects as knots. In regions associated with knots, temperature distribution will be greatly influenced by the size, orientation, and location of the knots, and shrinkage 4.4 Treatment of Variables 4.4.2 Temperature 60 cracks which may develop in these regions as a result of the rising temperature. The information on knot size, pattern, and types is typically not available a-priori. Because of these uncertainties, in most literature reviewed, temperature predictions and measurements were normally restricted to examination of relatively clear wood. Exploratory studies should therefore be conducted to determine the difference in temperature between clear and defective regions. Further work is needed to assess the impact of temperature models on rekability assessment in commercial grades of lumber. Any strength testing for the effect of temperature should be such that the reference temperature is measured both in relatively clear wood and in regions containing defects. 4.4.3 Rate of Charring The rate of charring governs the amount of unburnt material available at any time t to resist the structural load. This variable becomes increasingly important with increasing member cross sectional area. As member cross sectional area increases, temperature-rise in the interior zone becomes increasingly insignificant, and, therefore, the time to failure of the member will be determined principally by charring rate. The rate of charring of wood depends on the kinetics of wood combustion, in addition to the external exposure characteristics of fire. Wood combustion is an extremely complicated process. The thermal properties influencing these processes are constantly varying as the charring process evolves. Little quantitative work has been done on the effect of knots on charring rate. However, it has been observed that wood chars irregularly around knots and that the rate is generally slower than in the adjacent clear wood, due probably to higher density and ease of moisture migration particularly in regions with edge knots and the associated high grain 4.4 Treatment of Variables 4.4.3 Rate of Charring 61 deviation. These charring irregularities will preclude any sensible measurement of the rate of charring in such regions. A n "apparent" rate will need to be developed. It is suspected that in wood containing by edge knots, the loss of load carrying capacity due to charring may be insignificant compared to the loss due to elevated temperatures near charring because of the development of shrinkage cracks. In any case, further exploratory studies should be carried out to provide guidance as to how charring should be modelled in regions containing knots. 4.4.4 Initial Load The load q has been assumed to be a function of the initial load q0 and the time t in Eqn [4.11]. In current design practice, the load during a fire is assumed to be unaffected by the fire so that where t0 denotes the starting time of the fire. Furthermore, q0 is assumed to be the design structural load or a fixed proportion of it. In reliability analysis we may treat q0 as a variable and q as a function of time. In this case, the load q0 is the sum of the dead loads which act on the member, and the live load which depends on the occupancy and snow load if the structure is required to support a roof. These loads have been considered as random variables in reliability studies involving wood structures and have been statistically characterized for common load cases (Foschi etal. 1989). In general, on the basis of available statistical information on the load, a load function, q(t), may be simulated for a period of time, say, tN minutes. Now assume a fire 4.4 Treatment of Variables 4.4.5 Initial Load 62 starts at time t - t0 < tN . The load at time t0 is given by q(t0). In solving Eqn [4.11] for t{, one can set % = l(t0) [4.14] This procedure is repeated for different t0 to obtain a ^probability density distribution^tf) from which the probability for tf < tT, given t0, can be calculated. That is, The total probability over the time period N is P(t{<tr)= ^P(t[<tr\to)f(t0)dt0 [ 4.16] where f(tQ) is the probability density distribution of tQ. Assumingy(^0) is uniform, Eqn [4.16] reduces to 4.4.5 Short-term Strength (grade effect) Visually graded structural light framing members are graded according to the Standard Grading Rules for Canadian Lumber published by the National Lumber Grading Authority (NLGA), Vancouver, B.C., Canada. In visual grading, all four faces of lumber are inspected and a grade is assigned based on the natural characteristics of the wood such as slope of grain, size and location of knots, checks and splits, as limited by the appropriate grading rule. The design strength values of visually-graded lumber are derived from tests of representative material sampled from production. In mechanical grading, the lumber is passed through a grading machine which determines the average and minimum modulus 4.4 Treatment of Variables 4.4.5 Short-term Strength (grade effect) 63 of elasticity. These values are used to sort lumber into grades with predetermined strength properties specified in the N L G A grading rules. In reliability calculations, the effect of the unit strength of the material should be considered from two points of view. First, when the principal stress is tension, an increase in the member's cross-sectional area may be required in design as the lumber grade decreases — either the dimension b or d, or both, will increase as a result. Considering the rate of change of stress in a burning member under tension, we can write 8T _ dz dA de a7 J A ~de~ ~dt [ 4 1 8 ] Since dx/dA = -q/A2 from Eqn [4.8] and dA/de = - 2 b - 2 d + 8-e from Eqn [4.5], 3x dt I \ -1< o ( (bd)2) (-2b -2d + 8e) — [4.19] d t Assuming that q0 and de/dt do not depend significantly on b and d, and since e is small relative to b or d at the beginning of the fire, 3 T 1 + T T ( T + 1) — « = L [4.20] dt r2b3 d3 where d = T-b, T being the member's aspect ratio. Thus, the rate of stress increase will, initially, be proportional to the inverse oibord raised to the third power. Given the same design stress, larger volume should lead to longer time to failure, that is, higher reliability, because of the slower rates of stress increase with section reduction, provided all other factors are equal. Also, Eqn [4.20] is only valid when the aspect ratio T does not change. If only one dimension (either b or d) is allowed to increase or decrease, then, the rate of stress increase will be proportional to the inverse of that dimension raised to the second power only. 4.4 Treatment of Variables 4.4.5 short-term Strength (grade effect) 64 Other grade-dependent factors affecting reliability must also be considered in addition to volume of material. First of all, the time to failure of the material under elevated temperatures may be dependent on the grade since defects such as knots may play a more significant role as the grade is lowered. For instance, the strength degradation rate a' may be higher with lower-quality material. If this is true, the use of lower-quality material will have a negative effect on fire endurance. Other factors which may show a dependence on grade include the apparent charring rate and the thermal conductivity. The effect of grade can be analyzed given the short-term strength distributions of grade of lumber are known. The procedures are listed in Table 4.1. The above procedures will be applicable to any grade of lumber, including M S R Table 4.1: Procedures to analyze the effect of grade on the reliabiHty of members exposed to fire Step Procedure (1) A short-term strength value a0 is randomly generated from the known short-term strength distribution of the grade being considered. (2) The temperature history and charring history of the member can then be calculated given a specified fire exposure. (3) On the basis of the short-term strength value, the temperature and the charring histories, a £f value is calculated. (4) Repeat Steps (1) through (3) until a sufficiently large sample of ts values is generated. (5) Determine the reliability function and indexes from the t( distribution as simulated. (6) Steps (1) through (5) are repeated for another grade of lumber of which its short-term strength distribution is known. lumber grades, provided that the within-grade strength distribution at room temperature is known and is within the range of strength values to be studied in this thesis. 5.0 E X P E R I M E N T A L W O R K 5.1 Scope and Assumptions The main experiment was primarily designed to provide data to calibrate a t( damage accumulation model developed as described in Chapter 7 for structural lumber stressed in tension and exposed to elevated temperatures. Supplementary experiments were included to determine temperature distributions in the lumber that was tested. Other data obtained included the moisture content of the specimens before and after the tests and the relative density of the specimens. Two experiments similar to, but separate from the main experiment, were also carried out to obtain t{ data for the purpose of testing the model that was developed. No exposures higher than the charring temperature of wood were included since char was deemed to have no strength. In calculating reliability indexes, charring and temperature histories needed for a given fire scenario are given as inputs to the model. The charring temperature of wood is taken as 288°C (550°F). Although there were no intentions to vary the initial moisture content of the test specimens, some natural variation occurred. The range of moisture content was 9-11%. This range is consistent with typical ranges expected of softwood lumber stored indoors for several months. The major experimental work involved exposing "matched" samples of structural lumber to elevated temperatures and testing these samples in tension at controlled rates of loading until failure. The tests were based on ramp-loading so the stress history applied to the specimens would bear some resemblance to the stress history experienced by wood members during fire exposure (see Figure 3.8). 65 5.2 Experimental Design 66 The temperature distribution in a piece of lumber heated from outside is generally nonuniform (i.e. in the direction of heat-flow, a gradient must exist). No attempts were made to measure this gradient in the major experiment. The gradient, however, was characterized in one of the supplementary-studies. For this thesis it is hypothesized that the location of failure in a lumber member will not change as a result of an increase in temperature. 5.2 Experimental Design The experimental variables were rate of loading and temperature of exposure. Eighteen groups of 60 specimens were evaluated in the main experiment (Table 5.1): Six groups were tested using a ramp-load rate of 1.85 kN/s; six groups at a rate of 0.2 kN/s; and six groups at 0.067 kN/s. For each rate of loading, one of the six groups was tested at 150°C, one at 200°C, one at 250°C, and the remaining three groups were tested at room temperature (~20°C). The room-temperature groups served to provide the reference short-term strength distribution of the samples. The loading rate of 1.85 kN/s produced, on average, a failure time of one minute at room temperature. The other loading rates (0.2 and 0.067 kN/s) led to mean failure times of 10 and 30 minutes, respectively, at room temperature. The times to failure of those tested at the other temperatures were considerably shorter. The corresponding rates of stressing were 0.601, 0.065 and 0.024 MPa/s. The following paragraphs elaborate on the various aspects of the experiments. Table 5.1: Experimental design and sample size of each different combinations of variables Rate of Temperature of exposure loading (°C) (kN/s) 20 150 200 250 1.85 180 60 60 60 0.2 180 60 60 60 0.067 180 60 60 60 5.2 Experimental Design 5.2.1 Equipment for Exposure to Elevated Temperatures 5.2.1 Equipment for Exposure to Elevated Temperatures 67 When a piece of lumber is heated from outside, its surface temperature rises faster than its centre temperature. The temperature gradient depends on the applied heat flux, the method of heat transfer, thermal properties of samples, heating period, and the moisture content. In the literature, large-scale tests on lumber were usually accomplished by radiant heating. A high heat flux was used to minimize the time required to reach the target temperature. However, a higher heat flux tends to induce a greater temperature gradient and greater tendency for the volatile gases to ignite. In the present experiment, the test materials were heated by conductive heat transfer. The apparatus consisted of a pair of aluminum platens, insulated on the outside and heated electrically inside. Each platen was 2440 mm long by 100 mm wide by 50 mm thick and was constructed from two 25-mm-thick aluminum plates laminated together. The heating rods, embedded inside these aluminum plates, were 2500 mm long, and ran parallel to the longitudinal axis of the platens. The temperature of the platen was controlled by a microprocessor-based controller. A manually-operated mechanical clamping device forced the platens against the wide faces of the specimens during testing. Heat was transferred from the heated platens to the specimens by conduction. The length of specimen exposed was approximately 2440 mm (exposed region). Figure 5.1 shows cross- and longitudinal-sectional views of the apparatus. The complete mechanism was housed within a lumber tension testing machine. Parts and suppliers list is provided in Appendix I. The length of member between the grips of the tension machine was 3660 mm. 5.2.2 Sampling Methods The experimental design is based on a technique referred to by the wood community as the matched statistical sample technique, or matched groups. This technique 5.2 Experimental Design 5.2.2 Sampling Methods 68 requires that individual groups of specimens be matched to yield "similar" tension strength distributions. The accuracy of the group matching depends on the sample size chosen and the variability of the property of interest — in our case, tension strength — and whether a concomitant property is used for the matching. Traditionally, 60 specimens per sample has been recommended (Jones 1989). In this study, the specimens were matched on the basis of the concomitant variable modulus of elasticity (MOE) measured with a Cook-Bolinders M S R machine. THERMOCOUPLE > A INSULATION THERMOCOUPLE ALUMINUM PLATEN HEATING ROD SPECIMEN (a) LINEAR THERMOCOUPLE LINEAR DISPLACEMENT ) DISPLACEMENT TRANSDUCER ^ / \ ( TRANSDUCER (b) INSULATION HEATING PLATEN HEATING ROD Figure 5.1: Cross-section (a) and longitudinal-section (b) views of the heating apparatus and the test specimen 5.2 Experimental Design 5.2.2 Sampling Methods 69 To determine whether 60 specimens per sample was reasonable, sampling errors for 60, 100 and 200 specimens per sample were simulated using Monte Carlo technique. Typical correlation coefficients (R2) between M O E and tension strength have a range of 0.4 to 0.6 . Therefore, the value of 0.5 was assumed. The parent distribution was provided by the Canadian Wood Council, to which a Normal distribution function2 3 was fitted. From this Normal distribution, pairs of sample values having a R 2 of 0.5 were simulated. Of each pair, one value was assumed as an "actual" tension strength value and the other a predicted value from a measurement of the concomitant variable MOE. In total, a pool of between 1500 and 5000 pairs of observations (i.e., 1500 to 5000 "specimens"), depending on the sample size evaluated, were randomly generated. These "specimens" were ranked according to the order of the "predicted" value, which were then distributed into 25 groups in the following manner: the first 25 specimens were taken from the rank list and distributed randomly, one per group, then the second 25 specimens and so on, until the list was exhausted. In general, the distribution of the "actual" values agreed with the Normal distribution used in the simulation. The correlation coefficient between "actual" and "predicted" values also approximated the original R 2 of 0.5 . The variance of "actual" tension strengths (between groups) at a rank was computed from all the group values of the same rank. The standard error is the square-root of the variance divided by N-1. These calculations were carried out for the three sample sizes and the results are plotted in Figure 5.2 versus the normalized rank (percentile). As expected, the standard errors are generally higher toward the "outer" percentiles. Between percentiles of 20% and 80%, standard errors are approximately 5, 4, and 3% of the mean of the population respectively for sample sizes of 60, 100 and 200. At the fifth percentile, the corresponding standard errors are approximately 8,6, and 5%. A l t h o u g h a lognormal distribution is preferred, Normal distribution would not affect the outcome and simplify the simulat ion considerably. 5.2 Experimental Design 5.2.2 Sampling Methods 70 It was concluded that the sampling standard errors of 60 specimens represented an < UJ acceptable compromise between o z accuracy and costs of experiment. ^ 3 a. < a. Q_ < UJ 5.2.3 Material Sampling w H o 40 60 PERCENT I LE 100 Figure 5.2: Sampling errors (standard errors) as affected by sample size and percentile in the sample The study material was intended to cover as wide a range of strengths as possible for one major Canadian species primarily used for structural applications. Machine Stress Rated (MSR) lumber of the Spruce-Pine-Pir (SPF) species group was selected for the study. This species group constitutes more than 50% of the total output of softwood lumber in Canada. The materials were taken from three M S R grades rather than from a single grade to widen, as much as possible, the strength range. Approximately 1600 pieces of 2x4 lodgepole pine (Pinus contorta Dougl.) lumber, made up of equal number of pieces in each of the 1650f-1.5E, 2100f-1.8E and 2400f-2.0E grades, were sampled. Pieces with obvious defects situated near ends of boards (unexposed region) were discarded to minimize the number of failures in this region. The remairting lumber was stored indoors in Vancouver for approximately three months. During this period, the moisture content stabilized at 9-11%. After "conditioning", the specimens were planed to a thickness of 35 mm from a nominal thickness of 38 mm to provide a uniform surface for heating. The entire sample was then evaluated for the modulus of elasticity (MOE) value using a Cook-Bolinders M S R machine. Based on this ranking of M O E values, groups of 60 specimens were formed as described previously. The groups were wrapped in plastic sheets to prevent significant changes in moisture content thereafter. 5.2 Experimental Design 5.2.3 Material Sampling 71 5.2.4 Test Procedures Figure 5.3 shows schematically a typical heating and loading sequence for the experiment. The "start-time" (t=0) was the moment when contact was made between the platens and the specimen. Once in contact with the specimen, the platens were maintained in position and the temperature of the platens maintained at a constant exposure temperature. The tension test was initiated at t0 seconds (t0= 1500 s) after the start-time. Just prior to the initiation of the tension test, the clamping pressure of the platens was reduced (by unwinding a cranking wheel half a turn) to ensure that there was little friction between the specimen and the platens. The tension load was increased at a constant rate k0 (= 0.067 kN/s in the example shown in Figure 5.3) using a load-control test system. The temperature of the specimen at the centre of cross-section, 610 mm left and right of the middle of the heating length, was measured with ungrounded, type-K thermocouple probes sleeved with stainless steel. These probes had a outside diameter of 1.6 mm. Holes of the same diameter were drilled to 17.5 mm deep from the narrow face of the specimens to accommodate the probes. The heating and loading histories were recorded with a microprocessor-based data acquisition system. Values computed were the maximum tension load, the time to failure, the initial stiffness based on a linear regression model of the load versus deformation in the TEMPERATURE (X) 300 LOAD (kN) 200 100 TEMPERATURE OF EXPOSURE TENSION TEST 30.067kN/sec ( f 1000 2000 TIME (s) 160 120 80 40 3000 Figure 5.3: Schematic diagram of a typical heating and loading sequence of the experiments 5.2 Experimental Design 5.2.5 Temperature Distribution 72 load interval of 10 to 30 kN. For those specimens tested at elevated temperatures, the deformation history up to the time of failure was also recorded. 5.3.5 Temperature Distribution Lengthwise. Temperatures in the lengthwise direction of the specimens were measured to determine if the distribution was uniform. Six such tests were conducted. In each test, five thermocouples placed within the exposed region along the central longitudinal axis at intervals of 530 mm as shown in Figure 5.4 . The exposure temperatures were 165°C and 225°C 2 4 . Temperatures near the ends of the heating platens were also examined in more detail to determine if the temperature of the specimens declined significandy towards the end of the platens. The locations of those thermocouples are shown in Figure 5.5. In these tests, the thermocouples were placed at 50 mm intervals. Transverse. Temperatures at five locations across the thickness (Figure 5.6) of six specimens were measured. These tests provided data on the distribution of temperature in the principal direction of heat-flow for the development of an appropriate temperature model. The temperature distribution model was needed to predict the mean temperature of the specimens, given that only a limited number of temperature measurements would be made in the main experiment. The temperatures of exposure in this study were 150, 200 and 250 °C, with three replicates each. These two temperatures were used during the exploratory phase of the experimental work since the temperature of exposure for the main experiment had not selected. 5.2 Experimental Design 5.2.5 Temperature Distribution 73 -1060 mm -530 mm 0 mm 530 mm 1060 mm I w \ * f 1 f f ^ S P E C J M E N ; -L. 35 mm W3 W4 0 T H E R M O C O U P L E W2 W5 Figure 5.4 Test set-up for temperature distribution analysis in the lengthwise direction of specimens 5.3.6 Other Physical Data Moisture Content. The moisture content of the specimens was obtained near the centre of the specimens using a resistance-type moisture meter. Two samples were cut out, 25-mm-thick, from each tested specimen, one in the exposed region and one in the unexposed region, for moisture content evaluation using oven-dry method. Relative Density. The relative density of the specimens was obtained based on the estimated weight (g) of the specimens at zero moisture content and the as-tested volume (cm3) of the specimens determined from dimension measurements. 50 50 50 50 W 3 W1 W 4 W 2 W 5 35 mm E N D OF P L A T E N Figure 5.5 Test set-up for temperature distribution near the platen end in lengthwise direction of specimens 20 ( \ 20 4 \ 20 t \ 20 t \ \ t V } \ f \ f _wa—4_ A A A -—r— I -4— - W 4 - - • • — | - -W2___4__ 35.0 ^ 9 . 5 23.5 J_7.5 11.5 5.5 Figure 5.6 Test set-up for temperature distribution in the transverse direction of specimens 6.0 T E N S I O N T E S T RESULTS In reporting the tension test results, we should keep in mind that, since wood strength is time-dependent, a reference to such a property without quantifying the load history is, stricdy speaking, incomplete. As we have noted previously, the time dependent behaviour usually increases with increasing temperature. At the other end of the temperature scale, near absolute zero, this dependence completely vanishes. For wood, the time-dependence effects at elevated temperatures are masked and eventually dominated by pyrolysis. The pyrolysis rate is a function of temperature and duration of exposure. The mean failure time of the room-temperature group tested at the rate of loading of 0.2 kN/s was approximately 10 minutes. The tension strengths obtained with this group are, by definition, equivalent to the characteristic short-term strength of the tested material. This property serves as the reference strength from which design values are derived. It will later be shown that the rate-of-loading effect for tension strength at room-temperature is negligible, within the range of rates (0.067-1.85 kN/s) studied. Clearly, the effect of rate of loading would increase as the temperature of exposure increases. However, the pure rate-of-loading effect may not be apparent because of the dominance of pyrolysis processes and because the two events occur simultaneously. The discussion on the rate-of-loading effect is therefore delayed until Chapter 8 so that the analysis can be dealt with more effectively using the tf model developed in Chapter 7. The test data from the main experiment are tabulated in Appendix II. 6.1 General Observations As expected, most specimens failed in a brittle manner. Failures occurred mostly near a knot or knot cluster and were accompanied with a loud noise. There were no 74 6.1 General Observations 75 significant differences among the various groups as far as mode of failure was concerned or in the manner with which failure occurred. However, the higher the temperature, the lower was the noise of the failure. In a majority of the tests conducted at elevated temperatures, stains deposited by escaping vapour and volatile materials were easily spotted around the knots. Longitudinal and radial drying checks were abundant, especially near knots where stresses in tension perpendicular-to-grain would be quite high. Samples of the tested specimens were examined under an electron scanning microscope. Some of these samples are shown in Figure 6.1 . The examinations showed LAU-S567 Figure 6.1: Cell-wall degradation as a function of exposure temperature 6.1 General Observations 76 that some of the wood samples had undergone significant thermal degradation. These specimens were exposed to the temperatures indicated in each picture for approximately 30 minutes. The degradation appears most evident in the middle lamella layer (a "bonding" layer found between two adjacent cell walls) where kgnin content is high. Lignin is known to soften at temperatures as low as 150°C. Generally there was a gradual weakeriing of the middle lamella layer with increasing severity of exposure. Because lignin does decompose at lower temperature than cellulose, compression strength of clear wood, which relies on the lignin fraction to resist cell-wall buckling, will be affected to a greater extent than tension strength. This finding concurs with data compiled by Gerhard (1982). 6.2 Failures outside the Exposed Region Despite our effort to exclude specimens having an obvious "worst" defect in the unexposed region, approximately 20 to 25% of the test specimens failed outside the heat-exposed region. These occurred mostiy in the room-temperature tests. The data from these tests have to be "censored" in order for the room-temperature results to provide the appropriate reference strength for the high-temperature results. The "product limit" method (Bury 1975, page 515) was used to estimate the cumulative distribution of tension strengths (and times to failure) based on survival probabilities. The specimens with failures outside the exposed region were treated as "censored information" in the sense that the unknown strength value of the exposed region was necessarily higher than the observed strength value. For a sample containing outside failures, we can write f ( * ' ) = i - n N ~ i [6 .1] ' = 1 N - i + 1 6.2 Failure outside Exposed Region 77 where F(tf) is the nonparametric cumulative probability of failure (CPF) of tf, j is defined by^ <, tf <> xj+1,Nis the original sample size, and i is the order of a failed specimen (within the exposed region) in the complete sample. Note that Eqn [6.1] reduces to when there is no censored information in the sample. Eqn [6.2] is the nonparametric CPF of typical uncensored samples. Figure 6.2 shows how the cumulative distribution functions for the room-temperature groups tested at the loading rate of 1.85 kN/s compares. This is intuitively correct since, on average, the failure strength of the centre 8-foot portion ought to be greater after the failures in the "unheated" zone are removed from the test data. It is important to note that the censoring has little effect on the cumulative distribution functions at low probability levels. Figure 6.2: The effect of censoring on cumulative frequency distribution of sample containing outside failures 6.3 Temperature Variations 6.3 Temperature Variations 78 The temperature histories of the specimens were quite consistent within any one temperature exposure regime. The coefficient of variation of centre-line temperature of any individual test group at any given exposure time ranged from 1 to 3%. Higher exposure temperatures generally led to higher temperature variations. The variability appeared to be related more to initial moisture content variation of the specimens than to the density variation. Specimens with higher initial moisture content tended to be lower in temperature because larger amounts of heat were required to evaporate the moisture. 6.3.1 Lengthwise Variations within Specimen The results of the six tests to determine the lengthwise temperature variations in the specimens tested at elevated temperatures are examined here. The purpose of these tests was to assess the uniformity of the lengthwise temperature distribution in the heated region of the test specimens. Figure 6.3 shows the results for one of the six tests. Typical to all tests, there was a slight drop in temperature toward the ends of the platen. The variations observed are consistent with typical irregularities associated with using thermocouples in wood. The drop in temperature near the two ends of the platen was not considered significant. Figure 6.3: Temperature distribution along the longitudinal axis within the exposed region(for locations of thermocouples, see Figure 5.4) 6.3 Temperature Variations 6.3.2 Transverse Variations within Individual specimen 6.3.2 Transverse Variations within Specimen 80 This section examines the results of the transverse temperature distribution tests (see Figure 5.6). Mean specimen temperature was calculated using two different techniques. For temperature distributions conforming to a parabolic function, the mean temperature T is given by 2 r + L T= - ^ [6.3] 3 where Tc is the temperature at the centre given by the thermocouple W3 and Ts is the surface temperature (given by the mean of the platen thermocouple readings). The "mean" can also be estimated as the area weighted average of the five thermocouple readings (Wl, W2, W3, W4, W5) and the two platen thermocouple readings (SI and S2) according to T +T T +T T +T T +T T +T T +T j, _ X S I W 5 + W 5 W 2 + W 2 W 4 + W 4 W l + W l W 3 + W 3 S2 ^ . 1 w _ 12.74 11.67 11.67 11.67 11.67 12.74 Figures 6.4, 6.5 and 6.6 show values as calculated in accordance with Eqn [6.3] in comparison with readings from the five thermocouples (Figure 5.6, Section 5.3.5) and with the weighed average temperature (Tw) of these thermocouple readings. With the exception of an initial period (< 150 s), the curve computed using Eqn [6.3] indeed agrees closely with the curve of the weighed average temperature. Eqn [6.3] therefore was used to calculate the mean temperature for all specimens. 6.3 Temperature Variations 6.3.2 Transverse Variations within Individual specimen SI Figure 6.4: Temperature distribution in the direction of principal heat-flow (thickness direction) at an exposure temperature of 150°C (note: for locations of thermocouples, see Figure 5.6) 6.3 Temperature Variations 6.3.2 Transverse Variations within Individual specimen 82 Figure 6.5: Temperature distribution in trie direction of principal heat-flow (thickness direction) at an exposure temperature of 200°C (note: for locations of thermocouples, see Figure 5.6) 6.3 Temperature Variations 6.3.2 Transverse Variations within Individual specimen S3 Figure 6.6: Temperature distribution in the direction of principal heat-flow (thickness direction) at an exposure temperature of 250°C (note: for locations of thermocouples, see Figure 5.6) 6.4 Moisture Content Distribution 84 6.4 Moisture Content Distribution The initial moisture contents of the specimens had a range of approximately 9 to 11%. The moisture contents after exposure were considerably lower, depending on the severity of exposure. Table 6.1 summarizes the within-group means and standard deviations of initial and final moisture contents. The mean and standard deviation data, except those of the room-temperature groups (20°C), were computed from oven-dry moisture contents. As for the room-temperature group, no oven-dry results were available so the data were based on moisture-meter readings. 6.5 Relative Density Distribution The relative density was calculated using an estimated oven-dry weight of specimen divided by volume of specimen measured just prior to test. The volume was estimated from dimension measurements. The oven-dry weight was estimated from the weight and moisture content of specimen at test. The relative density distributions were fairly consistent by groups. Figure 6.7 shows a typical distribution. 0.2 0.4 0.6 0.8 RELATIVE DENSITY Figure 6.7: Cumulative frequency distribution of relative density 6.4 Moisture Content Distribution 85 Table 6.1: Means and standard deviations (S) of initial and final moisture contents of specimens tabulated by sample Rate of loading (kN/s) Temperature of exposure (°C) 20 j 150 200 j 250 Mean (%) S j Mean (%) i (%) S (%) Mean (%) S ! Mean (%) j (%) S (%) Initial Moisture Content 1.85 10.3 0.61 j 10.1 1.31 10.2 0.49 10.4 0.66 0.2 9.8 0.51 j 10.3 0.43 10.3 0.42 10.2 0.87 0.067 9.2 0.52 j 10.5 0.32 10.4 0.35 10.4 0.36 Final Moisture Content 1.85 10.3 0.61 | 8.0 0.42 5.7 0.92 2.7 0.62 0.2 9.8 0.51 j 7.4 0.52 5.3 1.0 1.9 0.48 0.067 9.2 0.52 j 7.1 0.43 4.0 1.04 1.3 0.35 6.6 Strength Distribution — Room Temperature 6.6.1 Expected versus Observed 86 6.6 Strength Distribution — Room Temperature Figures 6.8, 6.9, and 6.10 show the cumulative frequency distributions of the maximum tension strength, censored, plotted by group, respectively, for each of the three rates of loading. Shown in each figure are the distributions for 150, 200, and 250°C, and for room temperature, of which the room-temperature data are examined in this section. The absence of appreciable differences in the cumulative frequency distributions among the groups tested at room temperature suggests that the samples were indeed satisfactorily matched. Statistically, the null hypothesis that the data sets are consistent with a single distribution can not be rejected by the Kolmogorov-Smirnov (K-S) tests (Press, et al. 1992, p. 617). The K-S statistic is the maximum value of the absolute difference between two cumulative distribution functions. 6.6.1 Expected versus Observed The short-term strength distribution of the test material has been estimated from the test data as well as from published distributions of the three M S R grades in the sample. It would be worthwhile to compare these two estimates to determine if the test material as sampled was indeed a representative sample of the population from which the material was drawn (the null hypothesis). The population distribution G(x) is given by FAx) FAx) FAx) G(x) =-L— + -1— + - *±-L [6.5] 3 3 3 where Fx(x), F2(x) and F3(x) are the distributions of the three M S R grades respectively. Ft(x), F2(x) and F3(x) are typically expressed as a Weibull (Fw) or a Lognormal (FhN) distribution. The cumulative distribution function of a two-parameter Weibull model, Fw(x; o,X), is given by 6.6 Strength Distribution — Room Temperature 6.6.1 Expected versus Observed 87 Fw(x) = 1 - exp [6.6] If in Eqn [6.5] we le t i^*) = Fw(x; av A J , F2(x) = Fw(x; o 2, A 2), andP3(x) = Fw(x; o3, X3), then 1 ' J±Y> J±Y> J±v* [6.7] Figure 6.8: Strength distribution at room temperature, 150, 200, and 250°C for a rate of loading of 1.85 kN/s 6.6 Strength Distribution — Room Temperature 6.6.1 Expected versus Observed 88 Figure 6.9: Strength distribution at room temperature, 150, 200, 250°C for a rate of loading of 0.2 kN/s 6.6 Strength Distribution — Room Temperature 6.6.1 Expected versus Observed 89 Figure 6.10: Strength distribution at room temperature, 150, 200, 250°C for a rate of loading of 0.067 kN/s 6.6 Strength Distribution — Room Temperature 6.6.1 Expected versus Observed 90 Table 6.2: Parameters of Weibull distribution (Barrett and Lau 1994) The Weibull shape and scale parameters were provided in a report (Barrett and Lau 1994) prepared for the Canadian Wood Council on in-grade data previously obtained on the three M S R grades (Table 6.2). Note that these parameters are valid for a gauge length of 3660 mm and a moisture content of 11-13%. On the basis of these parameters, the expected distribution G(x) is plotted in Figure 6.11. Also plotted are the nonparametric, uncensored distributions from the room-temperature tests for the three rates of loading. These distributions were also valid for a gauge length of 3660 mm. As seen, the nonparametric distributions from test closely mimic the expected distribution. This comparison shows no 1.0 Weibull distribution parameters MSR grade o X (N/mm2) 1650f-1.5E 31.7 3.84 2100f-1.8E 44.2 4.27 2400f-2.0E 49.8 4.41 >-o •z. Ill z> a LU Lt LL LU > I— 5 O 0.8 0.6 0.4 0.2 0.0 20 40 60 80 ULTIMATE TENSILE STRENGTH (N/mm2) Figure 6.11: Comparison between observed and expected distribution G(x) 6.6 Strength Distribution — Room Temperature 6.6.2 Weibull Probability Plot 91 evidence to reject the null hypothesis that the samples were drawn from the population representative of commercial production that would be produced by combining the three M S R grades, which is also the conclusion of the Anderson-Darling statistics for test-of-fit (Press etal. 1992, p. 621). 6.6.2 Weibull Probability Plot The use of 2-parameter Weibull distribution to approximate G(x) would simplify the analyses for distribution behaviour considerably but the relevance of such an approximation should first be examined. For a 2-parameter Weibull distribution, the quantile Xm of order m is determined by l [6.8] ( 1 ) o In I 1 -1) > So given a set of N ordered observations, say Xt, i = 1..JV, plotting ln(X f) versus ln(ln((7V-r- 1)/(N+1-0)) should produce a linear relationship if the observations are Weibull distributed. This plot is shown in Figure 6.12 for a set of Xi generated from G(x). This analysis shows that the function G(x) derived from Barrett and Lau (1994) can indeed be approximated reasonably well by Weibull distribution. 6.6.3 Effect of Rate of Loading The effect of rate of loading may also be observed in Figure 6.11 where the three groups of room-temperature data obtained at each rate of loading had been combined and plotted versus cumulative frequency. The data were not censored since they were all room-temperature data. As indicated, these rate-of-loading data are not significantly different from each other, as confirmed by the K-S statistics. On the basis of various data available from different authors, Karacabeyli and Barrett (1993) derived a relationship by which the 6.6 Strength Distribution — Room Temperature 6.6.3 Effect of Rate of Loading 92 mean bending strength should decline, on average, by approximately 5% over this range of rate of loading. However, high fluctuations between experiments are to be expected when the mean time to failure is relatively short such as ours. 6.7 Strength Distributions — 150°, 200° and 250°C Referring back to Figures 6.6, 6.7, and 6.8, where the cumulative distributions of the high-temperature ultimate strength data have been plotted alongside the censored room-temperature distributions, it can be observed that the strengths of the high-temperature groups were sigriificanuy lower than the room-temperature results. The within-group means and standard deviations are given in Table 6.3. In the most severe exposure (250°C), the average reductions in strength ranged from 50 to 70% depending on rate of loading. Without any doubt, slower rates of loading imply longer exposure times therefore + c + 4 . 0 0 2 . 0 0 0 . 0 0 - 2 . 0 0 - 4 . 0 0 - 6 . 0 0 2 . 0 0 2 . 5 0 3 . 0 0 3 . 5 0 4 . 0 0 4 . 5 0 In(Xi) Figure 6.12: Approximation of the expected strength distribution G(x) by Weibull distribution 6.6 Strength Distribution — Room Temperature 6.6.3 Effect of Rate of Loading higher strength reductions. 93 Also observed from the distributions shown in these figures, and from the standard deviations in Table 6.3, are the behaviour that the ultimate tension strength actually became less variable as severity of exposure condition increased. The same observation was made by White (1988). Since this behaviour is important to reliability analysis, it must not be overlooked in the development of models to predict lumber strength behaviour at elevated temperatures. The two-parameter Weibull distribution was chosen to fit the individual data group, for reasons discussed before. The Weibull distribution parameters are tabulated in Table 6.4. 6.7 Strength Distribution — J50°C, 20CfC, 25CrC 94 Table 6.3: Means and standard deviations (S) of tension strengths computed by samples Rate of Temperature of exposure (°C) loading (kN/s) 20 150 200 250 Mean (N/mm2) S (N/mm2) Mean (N/mm2) S (N/mm2) Mean (N/mm2) S (N/mm2) Mean (N/mm2) S (N/mm2) 1.85 36.6 13.43 29.8 9.09 22.7 7.38 18.7 5.78 0.2 37.5 13.12 25.7 7.48 19.7 7.41 14.5 4.23 0.067 37.7 12.97 23.8 6.62 17.6 5.63 13.4 3.71 Table 6.4: Weibull distribution parameters for tension strength Rate of Temperature of exposure (°C) loading (kN/s) 20 150 200 250 o (N/mm2) X o (N/mm2) X 0 (N/mm2) X o (N/mm2) X 1.85 47.0 2.63 33.5 3.49 25.6 3.29 20.8 3.42 0.2 46.5 2.94 28.5 3.76 22.1 2.76 16.6 4.03 0.067 47.2 3.00 26.3 3.71 19.6 3.47 14.8 3.87 7.0 T I M E T O FAILURE M O D E L L I N G In generalizing the approach based on damage accumulation, we may write | ^ = F ( T ( 0 , T{t), a) [ 7 . l ] where the rate of damage, da/dt, in a unit volume of material at any time t is expressed as a function of the stress x(t) and the temperature T(t) at the time t, and the damage a accumulated to the time. In this approach, tf is the time at which a = 1. Expression [7.1] implies that the damage accumulates at a rate depending on the temperature history and stress history to which the member is subjected. The successful application of this theory depends on the proper selection of the functional form of F. In other words, we need an appropriate model for F. 7.1 M o d e l Development Out of the various approaches discussed in Section 3.5, the most promising starting point appeared to be the kinetic strength model. This model was the basis of models developed by Caulfield (1985), van der Put (1989), and Liu and Schaffer (1991). If/ denotes the fraction of unbroken elements or bonds in the direction of applied stress, then, according to Hsiao et al. (1968), the rate of change of/is given by | =7C(1 - / ) - KJ [7.2] at where I E ^ K - co exp - —±- ~ Y 0 <p(t) is the rate of reformation of broken elements, and [7.3] Kh - cob exp ( E, \ \ [7.4] 95 7.1 Model Development 96 is the rate of rapturing of unbroken elements; u)r and cob are, respectively, the frequencies with respect to forming and breaking of bonds; ET and Eb are the activation energies for bond reforming and bond rupture; R the universal gas constant; T the absolute temperature; Yo a n d P 0 a r e positive quantities that modify the energy barrier as a consequence of the applied stress in the direction of each element; and tp is the longitudinal stress per bond. Following the arguments made by Liu and Schaffer (1991), the value of Kr is ignored since loading rates are generally fast enough that bond reformation is unlikely and since strain is seen to be proportional to stress in lumber subject to tension at room temperature. Under elevated temperatures, bond reformation is even less likely since strain rate increases with increasing stress (an observation made in our experiment). Assuming that bonds are oriented in the direction of the applied stress, the bond stress ip(t) and the external stress x(t) are related by V f{t) L J provided that/is independent of bond orientation. Eqn [7.2] then becomes (I), = " ^  ™ The subscript t indicates the bond rupture process is an effect due to stress. We now turn our attention to the effect of thermal degradation. Intuitively, bonds can be broken as a result of pyrolysis and the process will affect the strength of wood in tension independent of the effect of stress. The rate of change of / as a result of pyrolysis 7.1 Model Development 97 therefore should bear a strong relationship with the rate of change of density of the material. We can express this change by an Arrhenius-type expression (Roberts 1970): (df) -dt t|/ exp R T [7.7] where t|t is a coefficient depending on the anatomical property of the material (we may refer to this as a species effect). The subscript T signifies that this is a pyrolytic process. The apparent rate equation for/— assuming the effects can be added — then becomes dt df + dt 7 ( E^ t|/ exp R T t - / w b exp [7.8] RT + P0 «P(0 Zhurkov (Bartenev and Zuyev 1968, p. 27) found that activation energies in thermal degradation are of the same order of magnitude as those derived from strength tests. On the basis of several independent studies, Stamm (1966) arrived at a similar conclusion as Zhurkov. We may therefore assume t h a t £ T = Eh = E, and Eqn [7.8] simplifies to ( E ^ Tt " e x p l R T [7.9] Substituting the term (p(t) by Eqn [7.5] and expressing T - T(t), df dt exp R T{t) ) u) - / co exp + Po f I [7.10] Eqn [7.10] can be generalized as a four-parameter — av a2, a3, and aA — model for bond breakage as a result of both stress and pyrolysis: df dt exp T(t)j f a exp f [7.11] Note that these parameters must be positive real numbers greater than zero. Furthermore, we assume 7.1 Model Develop, merit 98 f\ = ^ J\t=0 * [7.12] where o 0 is the short-term strength and o* is the ideal strength of the material. Thus/can have a maximum value of 1. The failure criterion is / = 0. If we treat 1-/ —a, where a is a damage parameter, then Eqn [7.11] is equivalent to a damage accumulation model of the following form: da dt exp T(t)) a + (1 ~ a) a3 exp (I-a) [7.13] where av a2, a3, and a4 are model parameters. The initial value of a is given by It =o 1 0 [7.14] where o* is a parameter depending on the other model parameters and a reference short-term strength o 0 determined in a "standard" test (see Section 7.2.2), and failure is governed by the criterion a\t = t-1 [7.15] 7.1.1 Key Model Characteristics In order for a damage-accumulation function to be applicable to time-dependent lumber-strength behaviour, the function must first possess the ability to describe how "damage" is actually accumulated in lumber under ramp loading at room temperature. Researchers in this field have generally agreed that damage should initially accumulate very slowly for a major portion of the loading history25. Only when the applied load nearly reaches the ultimate load should the damage start to accumulate significantly. When failure is imminent, the rate approaches infinity. Such a phenomenon implies that most of the damage occurs near the time of failure. This explains why we do not generally observe O n the basis of observed stress-strain behaviour and acoustic emission of reported rate-of-loading experiments. 7.1 Model Development 7.1.1 Key Model Characteristics significant rate-of-loading effects at room 0.0025 temperature at rates such as those used 0.0020 in our study. The hypothesis is also RATE 0.0015 supported by Zhurkov's work (Figure IMAGE 0.0010 3.4). Figure 7.1 shows that such s behaviour is indeed predicted by the 0.0005 model using parameters values shown in 0.0000 Table 7.3 (page 110). 99 i r r i i i i i i L i i i L 1 i J 40 80 TIME (s) 120 160 Figure 7.1: A typical damage rate function at room temperature for a loading rate of 1.85 kN/s Also from Eqn [7.13], the rate of ( m o del parameters listed in Table 7.3 p. 110) damage increases with increasing temperature and stress, which is, of course, an essential condition in order that the model can explain strength reductions at elevated temperatures. 7.2 Approach to Mode l Fitting The set of coefficients which "best" fits the test data was found by minimizing the normalized sum of square of the differences between predicted tf from the model and observed t{ from the experiments. These differences were evaluated at N arbitrarily chosen percentiles of the tf distributions. The normalized sum of square of the differences (Q) was given by 1.0 - -—-L± N k- 1 [7.16] where | t f j and (^t{ j were, respectively, the predicted and experimental kih percentile t{ values for the i t h temperature of exposure and jth rate of loading. 7.2.1 Single-Valued versus Randomly-Varied Coefficients 7.1 Model Development 7.1.1 Key Model Characteristics • 100 The coefficients ax, a2, a3, and aA may either be treated as being single-valued coefficients or as random variables conforming to a specific distribution function such as Lognormal. If, for example, we treat a1 as a Lognormal random variable, its value will then be chosen randomly from a Lognormal distribution / L N ( « j ; A I P ax). The parameter al is replaced by the location parameter ^  and the scale parameter O j . Treating a coefficient as a random Lognormal variable has the effect of replacing the coefficient with two independent coefficients, which increases the complexity of the analyses. In modelling room-temperature DOL behaviour, model parameters, in the case of the Canadian model, are treated as randomly-varied coefficients, each governed by a distribution function (Foschi etal. 1989). In Foschi's case, the approach permitted a better fit of the model to test data. Since the experiments could not have accounted for all sources of variations, by allowing the parameters to vary in the fitting, we, in fact, calibrate those variations not included in the model. If all coefficients are single-valued, there will only be one t{ given an initial strength o0. This contradicts observed t{ behaviour under normal exposure. In our case, we have seen a contraction of the variability of tf data from room temperature to the elevated temperatures suggesting that the model should not require any more variability to be introduced other than that of the short-term strength parameter. Because of variations in dimensions, temperature and stress histories, we expect t( will vary slightly, in addition to the variation caused by the parameter o0. But the model can easily take these variations into account through their effect on the temperature and stress histories. 7.2.2 Model Consistency w.r.t. Input Parameter o 0 7. / Model Development 7.1.1 Model Consistency w.r.t. Input Parameter o0 101 Barrett and Foschi (1978) as well as Foschi and Yao (1989) pointed out that when the stress history x(t) = k01 is entered into a duration-of-load model, the failure time t{=oQ I k0 should be predicted if o 0 is the strength determined in a standard ramp-load test with rate of loading k0. This internal "consistency" was maintained by making one of the parameters in their model a dependent variable. In this study, the parameter o 0 is introduced, in conjunction with o* to define the initial damage condition in accordance with Eqn [7.14]. Consequently, we have to address the legitimate issue raised by Foschi and Yao (1989). Given x(t) = k01 where k0 is the rate used to obtain the short-term strength o 0 such that o 0 = k0 tf, then according to Eqn [7.13], da _ — — exp dt * T a + a ( 1 - a) exp v 1 - « [7.17] Att = 0 l f - o [7.18] and at t = tf =o0 / k0, [7.19] Eqn [7.19] can be enforced, for a given o 0, by making o* dependent on the input variable o 0 and the other coefficients. The dependence relationship is derived as follows: f 1 C tf f da - j exp J o | t = 0 J o a + a (1 - oc(0) exp 1 - a(f) dt [7.20] Integrating out the left-hand side, 7.2 Approach to Model Fitting 7.2.3 Methods and Procedures 102 ° 0 _ [*< — - e x p a* Jo T a + a {1 - a(t)) exp kQ t 1 -a(t) j dt [7.21] Rearranging the various terms and replacing tf by o 0 /k0, a*=-exp T a2 + a (1 - a(r)) exp *o ' l - a ( 0 J i f [7.22] Eqn [7.22] expresses o* as a function of o 0 obtained at the rate of k0, and the coefficients a,, « 2 , « 3 , and A 4 . Unfortunately, the integral in Eqn [7.22] does not have a close-form solution. A numerical solution to this expression is possible but the extra time required in the minimization process is prohibitively long. Therefore a "look-up" empirical equation from which the dependent value can be calculated was developed. First, given discrete values of and o 0, we find o* by solving for the root of the function / ( o * ) - f f ( « r ay ay a4, a*, oQ) - -2 - 0 [7.23] where tf (•) is obtained by integrating Eqn [7.13] using Runge-Kutta's method. Note that this approach is no different from solving Eqn [7.22]. The value of o* was found to change relatively little with a2 and a3. Finally, with some trial and error, the relation o* — exp 15488.96 - 0.4917 1.02X1CT6 — +0.036 0.0034 a, - 23.4 [7.24] was found to closely approximate the true solution of Eqn [7.23], given a2 = l.Ox 10 1 0 and « 3 = 1 .8xl0 7 (note: these values were solution values obtained without imposing the consistency condition). Generally, Eqn [7.24] estimates the dependent variable to within 7.2 Approach to Model Fitting 7.2.3 Methods and Procedures 103 ± 5 % of the exact solution, provided a2 or a3 does not each change by more than ± 1 0 % from the above values. This empirical function is used to express o* as a function of ax, aA and o 0 in the minimization process. Figure 7.2 compares the approximate solution with the exact solution for ax between 15900 and 16900, a4 between 0.060 and 0.070, and o 0 between the maximum and minimum observed values. Figure 7.2 : Comparison of the value of the dependent variable o* calculated from Eqn[7.24] and the numerical solution of Eqn [7.23] 7.2 Approach to Model Fitting 7.2.3 Methods and Procedures 104 7.2.3 Methods and Procedures The minimum of Eqn [7.16] is found by the Polak-Ribiere algorithm as described in Press et al. (1992), p. 413. This method is a member of the family of methods referred to as the Conjugate Gradient Methods. Generally, conjugate methods make use of the vector of first partial derivatives of the function with respect to the coefficients to determine the direction of traverse in seeking the minimum. The procedures used to find the best-fit coefficients are summarized in Table 7.1. The computer program PARAFIT, which is listed in Appendix III, implements these procedures. The objective of using PARAFIT is to find the set of coefficients — and aA — such that Eqn [7.16] is minimized. The inputs to PARAFIT are the short-term strength o0, and the temperature and the stress histories. Given values of the coefficients — o*, Table 7.1: Procedures to determine the best-fit values of the model parameters Step Procedure (1) The minimization is started with initial values of the set of coefficients. For those coefficients to be treated as a random variable, the corresponding Lognormal parameters are entered. (2) A short-term strength value a 0 is randomly generated from the known short-term strength distribution. In our case, it is generated from the nonparametric distribution. (3) The variable coefficients are generated from their corresponding Lognormal distributions. The single-valued coefficients remain unchanged. (4) The temperature history and charring history is calculated given the specified exposure condition. (5) On the basis of the short-term strength value a 0, the temperature and the charring histories, and the set of coefficients, a tf value is calculated on the basis of the Runge-Kutta method. (6) Steps (2) through (5) are repeated until a sufficiently large sample of tf values is generated. (7) Compute the sum of square of differences between predicted and observed tf in accordance with Eqn [7.16]. The observed values are generated from fitted Lognormal distribution parameters. (8) Calculate the gradient vector as required by the Polak-Ribiere Conjugate Gradient method and revise the set of coefficients. (9) Iterate Steps (1) through (8) until the minimum of Eqn [7.16] is found. The same sets of random numbers are used in each iteration. 7.2 Approach to Model Fitting 7.2.4 Modelling Temperature Histories 105 ax, a2, a3, and a4 or their distribution parameters (see discussion in the previous section) — a sample of tf is simulated in accordance with Eqn [7.13] for each temperature-stress history. The nonparametric tf percentile values for each temperature-stress history are then determined, and entered into Eqn [7.16] as the predicted values. The observed percentile values are Lognormal parametric values from the experiments. The input short-term strength o 0 is generated from the nonparametric distribution of the actual room-temperature test results to which the censoring (for location of failure) has been applied. First, a random number r between 0 and 1 is generated. Given this value, the value of o 0 is interpreted by the following formulae: r ~ -P[(°o) , ] P[(o0)i + l] ~ P [ (o 0 ) , . ] [7.25] where (o0) ; and (o 0) j + 1 are the two ordered values such thatP[(o 0)J z r ^ P[(o0)i+l], and P(-) is the nonparametric percentile value. 7.2.4 Modelling Temperature Histories Temperature histories needed as input to the model, are expressed in terms of the mean temperatures of the materials, which in turn depend on time and temperature of exposure. The unit of temperature was expressed in Kelvin (K) for analytical purposes or in Celsius (°C) for presentation purposes (K=°C+273). Furthermore, to ease the computational effort, a continuous function to express the mean temperature history as a function of the time and temperature of exposure was developed. Since the mean temperature could not be measured, it had to be interpreted from measured temperature data. This section discusses the bases by which the mean temperature was calculated from measured temperature data and the development of a 7.2 Approach to Model Fitting 7.2.3 Modelling Temperature Histories 106 model to express the temperature history, as a function of the exposure temperature and time. Experimental Results. The experimental temperature distributions have been discussed in Section 6.3 in which it is noted that the mean temperature can be predicted with acceptable accuracy using this equation: x T = - ^ [7.26] 3 where Tc is the temperature at the centre and T s is the exposure temperature. This expression gives the theoretical mean temperature value of a distribution conforming to a parabola. The supplementary experiments described in Section 5.3.5 had a total of five thermocouple readings across the thickness. These readings, weighed by tributary area, were averaged. The results compare reasonably well with values calculated using Eqn [7.26]; thus, Eqn [7.26] was used to calculate the mean temperature for each specimen in the major experiment. The individually calculated mean temperatures were then averaged by each temperature of exposure. The final result was assumed to be the temperature history for each exposure temperature. The following describes two approaches to find a function to fit the calculated mean temperature histories using the duration and exposure temperature as input. Modelling - Theoretical Approach. From Boyce and DiPrima (1986), p.552, the analytical solution for two-sided heating of a medium at an initial temperature T 0 and subject to a constant boundary temperature Ts is given by T'(x,t) = + E b - n u cc t / 1 sin(n -nx/1) [7.27] n = 1 7.2 Approach to Model Fitting 7.2.3 Modelling Temperature Histories 107 where a2 is the thermal diffusivity of the medium, t is the lapsed time, / is the thickness of the medium between the two heated surfaces, x is the distance measured from one surface, and ' 4 ( TQ - T s ) n odd b_ = \ n V i [7.28] 0 n even Integrating Eqn [7.27] from x = 0 to x = I, and dividing the result by /, gives the mean temperature of the medium, that is T=T 4- 8 ^ 0 ~ ^ y J _ g - n 2 n 2 a 2 t / l 2 [7.29] S 2 1 TT n-1,3,5,... n which defines T in terms of / and the thermal diffusivity (a2) of the medium, a 2 = 1.043 X10"7 m2s"1, was derived by fitting Eqn [7.29] to the experimental temperature data. 7.2 Approach to Moid Fitting 7.2.3 Modelling Temperature Histories 108 LU UJ Q-LU 250 200 150 100 50 Model: Y = T s + P0 n2 (A - T) exp (- n2 K t) + (n = 1, 3, 5, ...total five terms) Observed Predicted - 150°C Observed Predicted - 200°C Observed Predicted - 250'C 1000 2000 TIME (s) 3000 4000 Figure 7.3: Temperature history predicted — theoretical approach (assumptions: one-dimension heat-transfer; no mass transfer) O o UJ I -UJ a. LU 250 200 150 100 50 Y = ( P 0 T + P 1 t) (1 -exp (-K t /P 0 ) ) Observed Predicted-150°C Series2 Predicted - 200°C Series6 Predicted - 250°C 1000 2000 TIME (s) 3000 4000 Figure 7.4: Temperature history predicted — empirical approach Eqn [7.30] 7.3 Results of Model Fitting 109 The summation was carried out to the fifth term of the infinite series [n =1,3, 5,7 and 9). This fit is shown in Figure 7.3, which is not accurate enough to describe the temperature history. Modelling - Empirical Approach. The experimental data suggest a model of the following form ( Kt' T - T = 1 — exp T - TQ = 0 for Ts > TQ [7.30] where T 0 is the room temperature (K), Ts the temperature of exposure (K), t the time (s), andP 0, Pv and/C are model parameters. With this model, the initial rate of increase of the mean temperature is given by K- (Ts-T0). The model approaches the linear model given by ^o" (Ts-T0)+Pi't as time t is increased. Both are reasonable assumptions. The fit of this model to the test data is illustrated in Figure 7.4. The parameter values are: P 0=0.66514 K 1 , P^O.011514 K-s 1 , 7C=0.002242 s 1, and T 0=293 K. It should be noted that in using this approach, we assumed that there was no heat movement in or out of the narrow faces of the specimen. 7.2.5 Experimental tf data The experimental t{ data, as shown in Figure 7.5, were first fitted with Lognormal distributions. These distributions are shown in Appendix IV. The t{ model was fitted to the distributions rather than to the actual data because it was more efficient to deal with the continuous function than with the discrete data in the minimization process. Table 7.2 summarizes the parameter values by each group. 7.3 Results of Model Fitting Table 7.2: Lognormal distribution parameters =threshold, /i,=location, o=scale) of the experimental t{ distributions (8 no Rate of Temperature of Exposure (°C) loading 20 150 200 250 (kN/s) M o 6 (s) a 5 (s) V- a 8 (s) a 1.85 4 .170 0.499 1500 4.03 6.235 1500 3.82 0.217 1500 3.64 0.204 0.20 6.390 0.434 1500 5.94 0.270 1500 5.66 0.295 1500 5.43 0.277 0.067 7.510 0.429 1500 7.01 0.2 18 1500 6.71 0.284 1500 6.47 0.222 7.3 Results of Mode l Fitting The model, as fitted to the experimental tf is illustrated in Figure 7.5 with the actual experimental tf data. The fitted parameter values are tabulated in Table 7.3. Figure 7.5 shows the model values expressed as cumulative frequencies, in comparison with the actual nonparametric distributions of the experimental ts data. The model indeed fits the data very well at temperatures of 20°C, 200°C and 250°C. It underpredicts the actual values at 150°C. Table 7.3: Model parameters as determined using PARAFIT da dt a2 + (1 - a) a3 exp f x(0 1 (1 - a) ax (K) a2 (s1) « 3 aA (mm 2N-') 16400 l . O x l O 1 0 1.8X107 0.065 7.3 Results of Model Fitting 111 It - Sl-T -A I 1500 1550 1600 .8 .6 .4 2 I j If >~ • r ' 1650 1500 1750 2000 2250 2500 Ml 250°C 1000 2000 3000 TIME TO FAILURE (s) Figure 7.5: Fitting of the model (parameters listed in Table 7.3) to experimental data (note: solid lines are the predicted values and dots are observed data; rates of loading are given along the top margin and exposure temperatures along the right margin) 7.3 Results of Model Fitting 7.3.1 Discussion 112 7.3.1 Discussion Prior to arriving at the present model, several other forms of damage accumulation functions had been rejected because the alternative models failed to predict properly the distribution behaviour of the t{ data at 200 and 250°C — particularly the significant contraction of the variance of the tf data. This lack of fit was considered unacceptable since it would adversely affect the prediction of the fire performance of structural lumber. In contrast, the present model fits the observed data very well overall, and exceptionally well at 200 and 250°C (Figure 7.5). The model does exhibit some difficulty in fitting the data at 150°C, particularly for the slowest rate of loading (0.067kN/s). The reason the fit at 150°C is less accurate may be explained by the fact that, at this exposure temperature the mean maximum temperature of the specimens was only 125°C. A t this temperature, the degradation process predominantly involved softening of the material and dehydration or hydrolysation of the hemicellulose fraction. These processes are different from the pyrolytic processes associated with temperatures at 200°C or higher. There were several problems encountered in fitting of the proposed model to the test data. First, as implied by the model, the rate of damage approaches infinity as the damage is approaching the value of one. This, of course, could not be tolerated in the numerical integration of the damage function using Runge-Kutta's method. A n upper limit (10 5) was placed on the rate. Furthermore, the model appears to possess many localized minimums. A different set of initial values of the parameters might lead to a different minimum. Also, limits were placed on the model parameters to prevent the minimization to wander off to unrealistic values. These problems were overcome by carrying out numerous runs with different starting points of the model parameters. 7.4 Model Evaluation and Testing 7.4 Model Evaluation and Testing 7.4.1 Relevance with Published Data 113 7.4.1 Relevance with Published Data According to Eqn [7.10] and Eqn [7.11], ax = E / R, a2 - t|f, a3 = u)b, and a4 = P0, where E, as defined previously, is the activation energy for bond breaking and reforming, R is the universal gas constant, cob is the frequency of bond breaking process, I|J is the preexponential constant in the Arrenhius equation for weight loss, and P0 is a positive quantity that modifies the energy barrier as a consequence of an applied stress in the kinetic strength model. Since ax = EIR = 16400 K, substituting iv = 8.313 J/mole/Kwe obtain £ =136 kj/mole. This value is very close to the value — 124 kj/mole — given by Stamm (1966) for coniferous wood. Also, values reviewed by Roberts (1970) ranged from 105 to 147 kj/mole for small specimens (sizes in the order of 10 mm). Schaffer (1973) calculated a value for wb of 0.784X 106 s"1 for dry Douglas-fir versus our value of 1.8x 107 s'1. This is of the same order of magnitude as Schaffer's value. Roberts (1970) reported values between 6 X l O 7 to 7.5 X l O 8 s"1. Schaffer (1973), on the basis of work done by Brokaw and Foster (1958), quoted a value for P0 of 2.87 X10"7 mm 2-N _ 1 for clear, dry Douglas-fir. Our value is 0.065 mm 2 -N _ 1 as given by aA, which is substantially larger than Schaffer's value. Since this variable is a modifier of the energy barrier impeding molecular motion, it is not surprising that our value is higher because the tested material contains defects and moisture. Defects and moisture should theoretically make it easier for the molecules to jump the barrier, since these are strength-reducing factors. Having substituted the actual values of av a2, a3, and aA into Eqn [7.24], the value of o*, which represents the ideal strength of wood, is given by the expression 7.4 Model Evaluation and Testing 7.4.1 Relevance with Published Data 114 * _ ( 0.463 ^ o — exp a, o ( -0 .218 a 0 + 508.0 [7.31] Furthermore, substituting a mean value of o 0 of 48.11 N/mm 2 estimated from the censored lognormal distribution, the mean value for o* is 502 N/mm 2 , which is approximately 10 times the mean short-term strength. This ratio is reasonable given that similar ratios calculated for various materials range from 2 to 20 (Bartenev and Zuyev 1968, page 8, Table 1). The value of I|J is 1.0 X 10 1 0 s"1 in the present study. When this value and the value of E/R of 16400 K are entered into Eqn [7.7], then, ' df) v dt t|j exp = - l . O x l O 1 0 exp R T ( [7.32] 16400 This expression denotes the rate of degradation due to pyrolysis alone. Given at t=0 the mean value of /of 0.1, as implied from the ratio of the mean short-term strength to the mean ideal strength, the time at which /attends a value of 0 is approximately 3.2 hours when the element's temperature is maintained at T = 473 K (200°C) according to Eqn [7.32]. That is, all the bonds would be broken as a result of the pyrolysis at 3.2 hours. Similar calculation gives 27 seconds at T = 573 K (300°C) which is not unreasonable given that 561 K (288°C) is the nominal charring temperature of wood. In reality, the time-to-zero-strength will be shorter because of degradation due to stress or other strength-reducing factors. 7.4 Model Evaluation and. Testing 7.4.1 Relevance with Published Data 115 1 A . I Model Predictions for Verification Data The accuracy of the model was evaluated against tf results of two separately-conducted experiments. The data from these experiments were not used in the determination of the model parameters. However, these experiments were conducted on matched groups of 60 specimens of SPF M S R lumber sampled for this study, therefore these groups have the same short-term strength distribution at room temperature. The first group had an exposure temperature of 250°C (523 K) and a constant load of 40 kN applied at all times. The second sample was tested at an exposure temperature of 225°C (498 K) and a rate of loading of 0.133 kN/s with the load applied at the same time. These two tests are referred to as Verification Test I and II. Table 7.4 summarizes the conditions of these two tests. Verification Test I. A total of 500 Rvalues were generated using the model and the steps described in Table 7.1 — with the exception of Steps 7, 8, and 9. The model parameters listed in Table 7.3 were used in Step 1. The input short-term strength o 0 were generated using Eqn [7.25]. 7 A Model Evaluation and Testing 7A.2 Model Predictions of Verification Data Table 7.4: Conditions of Verification Test I and II conducted on samples whose data have not been exercised in the modelling Inputs to Model Conditions of Experiment Short-term strength Temperature History Stress History Test I Temperature of exposure = nonparametric room- Eqn [7.28] with T = t(0 = 13.0 250°C (523 K); load constant temperature 523 K (N/mm2) at 40 kN starting at t = 0 distribution from main experiment Test II Temperature of exposure = nonparametric room- Eqn [7.28] with T = z(t) =0.042 t 225°C; load rate k0 = 0.13 kN/s temperature 498 K (N/mm2) starting at t = 0 distribution from the mean experiment Note: These data were not used for model parameter development. Figure 7.6: Verification I — predicted Rvalues and test data These predicted t{ values are plotted in Figure 7.6 as a nonparametric cumulative distribution with the observed tf. The agreement is reasonably good over the full range of o 0 values evaluated. In general, the predicted values are conservative as compared to the observed values at small percentiles. The mid-range percentile values are predicted exceptionally well. The conditions of the test simulate the performance of a tension member stressed to nearly the 5th percentile characteristic value while the member is in contact with a hot surface at temperatures near charring. Such a situation is probable in a concealed space, protected by wallboard with fire approaching from the outside. 7.4 Model Evaluation and Testing 7.4.2 Model Predictions of Verification Data 1 18 Verification Test II. The same procedures as above were used to generate the predicted values. This comparison is shown in Figure 7.7. The predictions are very conservative as compared to the observed values. These underpredictions are due to the fact that the model is generally conservative when mean temperatures of members are less than 150°C. Figure 7.7: Verification II — predicted Rvalues and test data 8.0 M O D E L PREDICTIONS In Chapter 7, we developed a model capable of predicting the tf of structural lumber subject to a temperature-stress history. In this chapter, this model is applied to characterize the short-term strength behaviour of lumber and the rate-of-loading effect in lumber up to charring temperatures. Furthermore, the effects of several input variables including lumber grade are evaluated from the standpoint of their impact on member reliability. The discussion is focused on analytical approaches rather than on reliability indexes because of the lack of critical data such as temperature histories for actual fire scenarios or "design" fires. 8.1 Short-term Strength of Lumber One of the most important pieces of information required for fire safety engineering is the strength of material subject to a given temperature history. Also important to engineers is the residual strength of the material after it is subsequently reconditioned back to normal conditions. Both properties can be evaluated using our model but in the latter case the results can only be regarded as a lower-bound value. Two cases — one representing a constant, uniform material temperature and the other an exposure to a constant temperature at the surfaces of the material — have been considered. The analytical procedures discussed in this chapter are generally applicable to any prescribed temperature histories below charring and any constant-load or ramp-load stress histories. Note that, the effect has been examined on the basis of mean strength only using the test material from our experiment as examples. The short-term strength of the test material at time t, where tf>t>t0 (see Figure 5.3), was determined by entering into the model a hypothetical stress history equivalent to a strength test 119 t(0 = 4 (t - t ) fort>t A [8.1] x (t) = 0 for t < tQ where z(t) is the stress, A is the cross sectional area of the member, kQ is the rate of loading corresponding to the definition of short-term strength of lumber, and t0 is the time at which the hypothetical test begins. To minimize any duration-of-load effect, particularly at elevated temperatures, k0 = 1.85 kN/s was used. The resulting value o0=x(tf) is the short-term strength of the material at the tf determined by the model. The value is expressed as a ratio to the short-term strength at room temperature obtained using the rate of 0.2 kN/s (strength ratio). 8.1.1 Constant Uniform Material Temperature The temperature history for this case was T(t) = C where C is any constant temperature. For each t0 ranging from 5 s to 3600 s, the model was run with C increasing gradually from 20°C to 300°C in accordance with the procedures tabulated in Table 8.1. The calculated short-term strengths, for durations (tf) of 120, 600, 1800, and 3600 s, are plotted in Figure 8.1 against the input temperature C. The strength-ratios as obtained are, approximately, 0.9 at 50°C, 0.7 at 100°C, 0.4 at 200°C, and 0 at 290°C. Generally, for Table 8.1: Procedures for analyzing the effect of temperature on short-term strength Step Procedure (1) A sample of 500 a 0 is generated from the nonparametric distribution of room-temperature short-term strength. (2) For an input temperature C and the input sample values of a0, a total of 500 t{ values are generated using the model for a start time t0. The mean t; was calculated. The stress T=£0-(mean t;), where k0= 1.85 kN/s, is assumed to be the mean short-term strength at temperature C and the duration mean t(. The above process is repeated for various t0 values ranging from 5 s to 3600 s. (3) Step (2) is repeated for another temperature C. (4) Strength ratios are calculated from the predicted mean short-term strengths. These strength ratios are compared in Figure 8.1. 8.1 Short-term Strength of Lumber 8.1.1 Constant Uniform Material Temperature 121 temperatures up to 150°C, the relationships are approximately linear and not significantly different among the different durations evaluated. From 150°C upward, the effect of temperature increases sharply, and duration starts to become important. A t these higher temperatures, longer durations tend to reduce the temperature needed to effect the same reduction in strength. For example, it takes 120 s to reduce the material to zero strength at 290°C, compared to 3600 s at only 200°C. The predictions given in Figure 8.1 provide the temperature-duration-strength relationship required for structural analyses of light-frame member exposed to elevated temperatures. Shown also in Figure 8.1 are tension strength data of Ostman (1985), Knundson (1973), and Schaffer (1970) on small, dry and clear specimens of spruce or Douglas-fir. The comparisons with these data show that lumber at 9-11% moisture content is more 50 100 150 200 TEMPERATURE (°C) 250 300 Figure 8.1: Effect of temperature on the short-term strength as predicted using the damage accumulation model 8.1 Short-term Strength of Lumber 8.1.1 Constant Uniform Material Temperature 122 adversely affected by temperature than small, dry and clear specimens — which is not surprising since lumber strength is determined by defects and they are affected more severely than clear-wood material. One observation, common to every set of data shown, is the sharp increase in the temperature effect at approximately 200°C. This phenomenon is probably caused by a change in the failure mechanism, a change in the heat conduction characteristics of the material, or perhaps a phase-shift of the cellulose fraction to glassy state. 8.1.2 Constant Surface Temperature In this evaluation26, the effect of exposure conditions similar to our experiment on the strength degradation process of the lumber is examined. The exposure temperatures evaluated using the model ranged from room temperature to 300°C. This range required a temperature model for which no actual data at 300°C, or between room temperature and 150°C were available. Although Eqn [7.30] has been demonstrated to accurately predict the mean temperature of specimens between 150 and 250°C, its extrapolation to temperatures below this range becomes unreasonable as the exposure temperature is near room temperature27. To overcome this problem without doing more tests, the coefficient P{ of Eqn [7.30] was expressed as a linear function Eqn [8.3] of T s for temperatures below 150°C (423 K). The model becomes T - T x 1 o P (T ~T ) + P t 1 0 v  1 S  x 0 > 1 1 — exp [8.2] 2 6 Normally, before the model can be used to characterize the strength degradation process of a member resulting from an externally-imposed condition, the temperature history of the member in relation to the imposed conditions must first be defined. This history may be calculated using an applicable heat-transfer model for wood-based building system exposed to fire. Heat-transfer modelling, however, is beyond the scope of this thesis. 2 7 As T s approaches T 0 and Pl remains unchanged (not decreased), the model will eventually predict a mean temperature higher than the temperature of exposure. Intuitively, P, should also depend on T s and should eventually reduce to zero when T s = T0. 8.1 Short-term Strength of Lumber 8.1.2 Constant Surface Temperature 123 where TQ is the room temperature (K), T s the temperature of exposure (K), t the time (s), and P o=0.66514 IC1, 7C=0.002242 s \ T 0=293 K, andP, is a function of Ts: T - T PAT.) = 0.011514 —5 °- for T < 423 K (150°C) 150 - T 0 [8.3] = 0.011514 for Ts > 423 K (150°C) This temperature model is shown in Figure 8.2, on the basis of which, the reduction of the short-term strength during the various stages of exposure, as a function of the temperature and duration of exposure up to one hour, is illustrated in Figure 8.3. The results show that at Ts = 323 or 373 K (50 or 100°C), and approximately one hour of exposure, the reductions amount to 7% and 28%, respectively. As explained earlier, predictions at these two temperature levels are conservative since the degradation processes are not pyrolytic in nature. The predictions for 200 or 250 °C, however, should be reasonably accurate because the model fits the test data very well at these two temperatures (see Figure 7.5). At 300°C temperature of exposure, which is beyond the range of our data, the model predicts a reduction of 80% after about half an hour, which is a reasonable value (Richardson 1996). Overall, these predictions are conservative for nominal 38-mm-thick2x4 lumber28. A correction factor may be applied to the temperature model to account for differences in thickness. This factor will not be discussed since it is beyond the scope of this thesis. Since the temperature model has been developed based on 35-mm-thick SPF lumber, it is likely that the mean temperature of nominal 38-mm-thick lumber will be overpredicted by the model. 8.1 Short-term Strength of Lumber 8.1.2 Constant Surface Temperature 124 250 — 200 U UJ UJ O. s UJ 150 100 50 1000 2000 TIME (s) 3000 4000 Figure 8.2: Temperature model in accordance with Eqn [8.2] and Eqn [8.3] 1.2 0 50 100 150 200 250 300 TEMPERATURE OF EXPOSURE (°C) Figure 8.3: Short-term strength as a function of temperature of exposure and duration of exposure 8.2 Rate-qf-Loading Effect 8.2 Rate-of-Loading Effect 125 Before two different rate-of-loading tests can be compared at an elevated temperature C, they should possess approximately the same duration of exposure (t{) — otherwise the results will be influenced by the effect of pyrolysis. Experimentally, the same-duration requirement is difficult to achieve because it means that we must know the tf a-prior and then adjust the test starting time (t0 of Figure 5.3) according to the rate of loading such that both tests end at approximately the same time. The model as developed, however, can easily be used to simulate the rate-of-loading effect. The analytical procedures T a b l e 8 - 2 : Procedures for analyzing the effect of temperature on rate-of-loading effect are discussed in Table 8.2. The duration of 1800 s was selected, at which the rate-of-loading effect was evaluated. Based on the model, the strength ratios for the loading rates of 1.85, 0.2, and 0.067 kN/s were obtained. The results are plotted in Figure 8.4 against temperature C. It appears that strength-ratio reductions with decreasing rates within the range of rates evaluated increased little with increasing temperature (the lines are almost parallel). It should be noted that the reductions (about 2-5%) in strength ratios at 20°C were mostly due to the model's consistency requirement (see Section 7.2.2)2 9. Had these differences not existed, the reductions at the higher temperatures will be less than those Step Procedure (1) For a given rate of loading and a given temperature C, mean tf values are evaluated by selecting appropriate tQ values such that the resulting mean t( values span over the duration target. (2) The strength ratios are calculated for each t{ value obtained. The strength ratios corresponding to the duration target is then interpolated from the calculated values. (3) Steps (1) and (2) are repeated for another temperature C. (4) Steps (1), (2), and (3) are repeated for another rate of loading. (5) The strength ratios calculated can then be compared. 2 9 Because no statistical significant differences were found i n the room-temperature test data between the three different rates of loading. WOOD TEMPERATURE (°C) Figure 8.4: Effect of rate of loading on short-term strength as a function of wood temperature at a duration of 1800 s shown in Figure 8.4. Overall, the effect of rate of loading appears to be small compared to that of temperature. 8.3 Reliability Analysis The model was applied to calculate member reliability as affected by lumber grade. The sensitivity of member reliability to variation in both temperature and stress were also examined. The grade effect was analyzed based on properties published for M S R grades 2400f-2.0E and 1650f-1.5E. These two grades are used extensively in engineered wood systems. Generally, 2400f-2.0E is a premium grade comparable to Visual Grade Select Structural. 1650f-1.5E is a lower grade comparable to Visual Grade No.2. The premium grade has a characteristic tension strength value approximately twice that of the latter. 1.3 Reliability Analysis 1.3.1 Grade Effect 127 8.3.1 Grade Effect The complete analytical procedures are detailed in Table 8.3 . In this particular exercise, only the input short-term strength was treated as a random variable. The random strength value was generated using the Weibull distribution parameters listed in Table 6.2 according to the formulae (Bury 1975): ( 1 ^ Table 8.3: Procedures to determine the reHability indexes of different grades of structural lumber In 1 1A [8.4] Step Procedure (1) For each grade, five thousand a 0 values are generated from the corresponding Weibull distribution. The stress history is T(£)=8.26 N/mm 2 for 2400f-2.0E and 4.56 N/mm 2 for 1650f-1.5E. (2) Each strength value a„ is entered into the model to calculate a Rvalue. This process is repeated for all a 0 values. The calculated tl values are then sorted into an ascending order. From the ordered values the nonparametric cumulative frequency distribution is determined. (3) The probabilities of failure P{ at £=60, 120, 600, 1200, 1800, 2700 and 3600 seconds are the cumulative frequency values at those durations. (4) The reliability index is calculated from the probability of failure: P=3>'(1 -P(). (5) Steps (2) through (4) are repeated for different constant temperatures C ranging from 423 to 523 K (150 to 250°C). (6) Steps (1) through (5) are repeated for another grade. where r{ is a randomly-generated number between 0 and 1, xx is the corresponding randomly-generated short-term strength value, and o and X are the Weibull parameters. The member stress was assumed to be constant at 1/3 of the 5th percentile of short-term strength distribution. The stress histories defined were x(t) = 8.26 or 4.56 N/mm 2 , respectively, for the two grades. The reliability index p, defined by Eqn [3.5] was calculated for a constant temperature history of T(t)=C where C ranged from 423 to 523 K (150° to 250°C). Figure 8.5 shows the reliability index P plotted against temperature for various durations between 60 s and 3600 s. The significant decreasing trend of p with increasing temperature or duration is certainly expected. Also not surprisingly, M S R grade 1650f-1.5E 8.3 Reliability Analysis 8.3.1 Grade Effect 128 shows a lower P value than 2400f-2.0E over the whole range of temperatures or durations evaluated. The differences, however, appear to be insignificant in regions of low probability of failure (P values > 1.0) but increase substantially in regions of high probabilities of failure (P values < 1.0). Since in design we generally aim for a low probability of failure, the differences in P between the two grades are therefore insignificant, particularly in view of the fact that wood-based systems are generally designed for a target p value between 2.4 and 2.8. Such a spread of P values is not uncommon among similar structural designs according to current code specifications. When the lines drawn in Figure 8.5 are extrapolated to 20°C, they converge to a single P value because duration has no effect at or near room temperature. This value is approximately 2.5 based on calculations at 20°C. It should be noted that the value as calculated depends on the stress or stress history entered into the reliability analysis. 2.5 1.5 0.5 2400f-2.0E 1650M.5E 0.006 0.002 0.07 0.15 0.3 0.5 150 175 200 225 250 TEMPERATURE (°C) Figure 8.5: Reliability indexes of structural lumber as a function of material temperature and duration for the M S R grades of 2400f-2.0E and 1650f-1.5E 8.3 Reliability Analysis 8.3.1 Grade Effect , 129 In general, reliability-based designs can make use of reliability plots such as Figure 8.5. Supposing that Figure 8.5 represents a reliability plot of a tension member exposed to a constant-temperature history and that the designer is required to ensure that the probability of failure of the member is no more than 5% (P -1.5) at 2700 s from the beginning of the heat exposure. From Figure 8.5, the designer looks up the mean temperature corresponding to p = 1.5 on the reliability curve for duration=2700 s. This temperature is approximately 165°C. The designer then makes sure that average temperature of the member does not exceed 165°C over the duration of 2700 s — either by specifying an appropriate protective membrane such as a gypsum wallboard or some form of protective coating, or by requiring a larger member cross-sectional size. The above example should not be regarded as a typical real-life example of reliability-based design of a wood member for fire safety. In actual reliability analyses, the stress history is a random event, determined by the charring rate, the dead and occupancy loads assumed to be initially on the members, and assumptions about how the loads on the member degenerate over time during a fire. As noted in Chapter 4, reliability-based design needs a reliability plot expressing P as a function of time measured from the beginning of a fire. The damage accumulation model can be used to produce this plot given proper inputs for the temperature and charring history, and the loads on the member. 8.3.2 Temperature Effect The sensitivity of P to temperature variations depends on the sum effect of many variables including species, density, permeability and moisture content of wood, grain orientation with respect to the direction of heat-flow, exposure condition, and specimen dimensions. Since these variables are unlikely to be related to each other, their sum effect on temperature can be assumed to be Normal distributed (Bury 1975). The randomly-generated temperature history was obtained from 8.3 Reliability Analysis 8.3.2 Temperature Effect 130 T{t) = C [8.5] where C. = / * ( ! + ®-l(r.) Y) [8.6] /j, and Y are the mean and coefficient of variation of temperature, rK is a randomly-generated number between 0 and 1, and ob'O) is the inverse of the standard cumulative Normal distribution function. The value of Y was varied from 0.0 to 0.05 at an increment of 0.01. Given fi = 150°C and Y=0.03, 95% of Q would fall between 150±9°C. Such a range of temperatures is not unexpected among different tests of same exposure. The stress in the member equaled 1/3 of the 5th percentile of the grade's short-term strength distribution. Distributions of tf value were obtained in accordance with procedures detailed in Table 8.4. The results are shown in Figure 8.6 in which the reliability index p for the durations 60 s and 600 s are illustrated. The results are shown for different y values and for each of the two grades: (a) 2400f-2.0E and (b) 1650f-1.5E. As indicated, the Table 8.4: Procedures to determine the reliability indexes as affected by variability of temperature Step Procedure (1) For each grade, five thousand a 0 values are generated from the corresponding Weibull distribution. The stress history is u(t) = 8.26 N/mm 2 for 2400-2.0E and 4.56 N/mm 2 for 1650-1.5E. (2) For each strength value a 0 , a temperature history T(t) =Cl where C, is generated using Eqn [8.5], given a mean temperature /x and a coefficient of variation y. Both the short-term strength a0 and the Q are then entered into the model to calculate a t{. The process is repeated for all values of a 0. The calculated tf values are then sorted into an ascending order. From the ordered values the nonparametric cumulative frequency distribution is determined. (3) The probabilities of failure Ps at t=60, 120, 600, 1200, 1800, 2700 and 3600 seconds are the cumulative frequency values at those durations. (4) The reliability index is calculated from the probability of failure: p=$"'(l -Pf). (5) Steps (2) through (4) are repeated for another value of ii and /or another value of y for each constant material temperature. (6) Steps (1) through (5) are repeated for another grade. 8.3 Reliability Analysis 8.3.3 Stress Effect 131 reliability index P is quite sensitive to temperature variations and that higher variabilities in temperature lead to lower P values. This is not surprising since the effect of temperature on t{ is prominent. Also, the effect of temperature variations is unaffected by grade. 8.3.3 Stress Effect The sensitivity of p to stress variation was analyzed assuming the distribution of this variable is also Normal. The analytical procedures are similar to those used for the analysis of the temperature effect and are tabulated in Table 8.5 . The randomly-generated stress history was given by /JL and Y are the mean and coefficient of variation of stress, rx is a randomly-generated number between 0 and 1, and (f)"^ -) is the inverse of the standard cumulative Normal distribution function. The value of y was varied from 0.0 to 0.15 at selected increments. Temperature was maintained as a constant parameter. The results, plotted in Figure 8.7, show that the reliability index P is generally insensitive to variations in stress. T (t) - q. [8.7] where [8.8] 150 175 200 225 250 (b) MEAN TEMPERATURE (°C) Figure 8.6: Effect of temperature variability on reliability indexes of structural lumber (a) 2400f-2.0E and (b) 1650f-1.5E 8.3 Reliability Analysis 8.3.3 Stress Effect 133 Table 8.5: Procedures to determine the reliability indexes as affected by variability of stress Step Procedure (1) For each grade, five thousand a 0 values are generated from the corresponding Weibull distribution. The temperature history is T(t)=C where C is a constant temperature ranging from 150 to 250°C. (2) For each strength value a 0 , a stress history x(t) =qt where q{ is generated using Eqn [8.8] given a mean temperature i± and a coefficient of variation y. Both the short-term strength a 0 and the qi are then entered into the model to calculate a ts. The process is repeated for all values of a 0. The calculated t( values are then sorted into an ascending order. From the ordered values the nonparametric cumulative frequency distribution is determined. (3) Step (2) is repeated for another value of /z and/or another value of Y-(4) The probabilities of failure P f at t=60, 120, 600, 1200, 1800, 2700 and 3600 seconds are the cumulative frequency values at those durations. (5) The reliability index is calculated from the probability of failure: P=<D" (6) Steps (2) through (5) are repeated for each constant material temperature. (7) Steps (1) through (5) are repeated for another grade. Figure 8.7: Effect of stress variability on reliability indexes of structural lumber for (a) 2400f-2.0E and (b) 1650f-1.5E 9.0 S U M M A R Y , C O N C L U S I O N S A N D R E C O M M E N D A T I O N S 9.1 Summary Mathematical modelling of the fire behaviour of structural wood-frame systems requires knowledge of the fire endurance of the wood members used in these systems. Particularly, we need to know the charring rate as a function of exposure conditions and the strength degradation rate of the unburnt portion of the members, expressed as a function of the members' temperature and stress histories. The charring rate of defect-free wood is generally known. Char is considered to have zero strength. The strength degradation rate depends on the quality of the wood used, in that higher rates may be associated with lower-quality materials. If this is true, the use of lower-quality material will have a negative effect on fire endurance. On the other hand, lower-quality material will generally have a lower design stress, which normally leads to larger sections for a given design condition and thereby to better fire endurance. Reliability analysis can be used to quantify the effect of these two opposing,factors. Generally, for tension loads, we can express the failure function as ajr(0,T(0)-K = T 7 T 7 T 7 - f [9-1] .(,(t f)) o where oH(-) denotes the apparent strength at failure, x(t) and T(t) are respectively the stress and temperature histories from the beginning of the fire (t=0) to the point of failure (tf), k is the initial ratio of load to resistance, q(-) denotes the load during the fire, expressed as a function of the initial load q0 and the time to failure tf, A(-) denotes the cross-sectional area of the unburnt portion of the member expressed as a function of the char thickness e which, in turn, is also a function of tf, and A 0 is the initial cross-sectional area of the 135 9.1 Summary 136 member. This equation provides a solution to the variable tf, provided that the various functions are known. The main objective of this thesis was to develop a model to predict the time-to-failure (tf) for the evaluation of reliability of wood-frame members loaded in tension and exposed to elevated temperatures. Because of difficulties in expressing the time-dependent function ou{-) of Eqn [9.1] in a closed-form, and the need to account for the effects of both temperature and stress histories, the failure behaviour was hypothesized using a damage accumulation approach: da/dt = F[T(t), x(t), a], where the rate of damage, da/dt, in a member at any time t was assumed to be a function F of the stress i(t) applied at that time, the mean temperature of the member T(t), and the damage a accumulated to that time. The damage variable a assumed a value between 0 and 1, where 0 denoted the damage was nil and 1 denoted the member had reached the point of failure. In this approach, tf was the time at which a = 1. The damage accumulation model was formulated after considering a kinetic strength model which accounted for the stress effect on bond strength and a kinetic pyrolysis term. The damage model is given by: da dt exp T(t)) a + (I ~ a) a exp T(0 (I-a) [9.2] where av a2, a3, and a4 were model parameters, T(t) was the temperature history and x(t) the stress history. The initial value of a at t = 0 was modelled by o 0 /o* where o 0 and o* were, respectively, the short-term strength and ideal strength of the material. The ideal strength o* is a dependent variable chosen to maintain model consistency between the input o 0 value and the corresponding value predicted by the model. This model was fitted to experimental data described below. 9.1 Summary 137 The short-term strengths and the corresponding times to failure of approximately 1200 pieces of nominal 2x4 lodgepole pine (Pinus controta, Dougl.) machine-stress-rated lumber were evaluated in tension using three different rates of loading at room temperature and at 150, 200 and 250°C. A lumber tension testing machine was fitted with an attachment for heating the specimens to the desired test temperatures. In short, short-term strength was significantly affected by exposure temperature. Longer durations of exposure generally led to more severe degradations. The rate-of-loading effect was small at room temperature for the range of rates evaluated. At the three elevated temperatures, the rate-of-loading effect was masked by pyrolysis. The damage accumulation model parameters were found by least-square fitting the model to the test data, and the fit was reasonably well. The model coefficients obtained were: ^ = 16400 K, a2 = l . O x l O 1 0 s 1, a3 = 1 .8xl0 7 s 1, and aA = 0.065 m m 2 ^ 1 . These coefficients agreed well with related data found in the literature. The model coefficients — with the exception of the short-term strength o 0 — were treated as single-valued parameters. The variance of the tension strength and tf decreased as the severity of exposure increased. The final variances were much less than the variance of the short-term strength of the material. The model chosen indeed predicted this behaviour. The model also predicted that for wood temperatures below 150°C, durations up to one hour in length had no significant effect on strength. In general, temperature effect on short-term strength was approximately a linear function of temperature. From 150°C upward, the effects of both temperature and duration increased significantly. The reliability of lumber was examined under several hypothetical conditions. Reliability was evaluated as a function of temperature and stress histories. Given that the 9.2 Conclusion 138 i f was known, the performance function G was expressed simply as G = t{ - tr, where tr was any required time to failure. Reliability corresponds to the probability that G^O. The model generated the t{ distributions using Monte Carlo simulation for various input stress and temperature histories, and for two different grades of lumber on the basis of their initial short-term strength distributions. Variations were introduced into the input temperature and stress histories to assess the effects of variabilities on the reliability of member exposed to elevated temperatures. 9.2 Conclusions The failure mode of lumber subject to tension and temperatures up to 250°C is generally brittle in nature. Short-term strength is significantly reduced by temperatures above 150°C. Also, longer durations of exposure lead to higher reductions in strength at temperatures above 150°C. The rate-of-loading effect is insignificant at room temperature for the range of rates evaluated. The degradation effect of exposure to temperatures up to charring, and the duration-of-load and duration-of-exposure effects at these elevated temperatures can be modelled using a damage accumulation approach. The model chosen must process the key characteristic that at room temperature, the damage should accumulate slowly for a major portion of the loading history until the applied load nearly reaches the ultimate load. A damage accumulation model based on a kinetic strength model coupled with a pyrolytic relationship — based on an Arrhenius function of temperature — was developed, and found to explain the experimental data reasonably well. The model as developed predicts that temperature effects on strength are approximately linear for temperatures up to 150°C. Also, at or below this temperature, durations of exposure up to one hour are not important. Both temperature and duration 9.3 Recommendations 139 effects increase sharply as temperature is increased above 150°C. There is little rate-of-loading effect within the rates studied at room temperature. In general, based on a constant tension stress on member of 1/3 of 5th percentile of grade strength distribution, reliability of lumber at temperatures up to 250°C appears not significantly affected by grade of lumber. The differences in the predicted reliability are expected to be ^significant as far as current design practices are concerned. The reliability as calculated are sensitive to variability in temperature, but insensitive to variability in the constant stress. On the basis of comparisons with existing data, lumber at 9-11% moisture content is more adversely affected by temperature than small, dry clear specimens. 9.3 Recommendations Several options may be chosen to further advance the state-of-the-art in this field. First, the damage model could be refined. When the temperature in a material is not constant, the model may be modified to treat the material as an assembly of elements with different local temperatures. Under this assumption each element can then be analyzed for the damage incurred, as a function of its temperature and stress history. The linear damage accumulation rule still applies regarding the criterion for failure. With this approach, the model can account for the effect of thickness through differences in temperature distribution. Second, the model itself may be improved to better fit data up to 150°C, to account for the fact that at or below this temperature the degradation process is due mostly to softening, dehydration, or hydrolysis then to pyrolysis. Second, the model could be extended to consider compression behaviour. When a member is axially loaded in compression, the load becomes eccentric with respect to the major axis of the member during a fire. The outside fibre away from the fire become stressed in tension whereas the inside fibre are in compression but also exposed to much 9.4 Recommendations 140 higher temperatures. The compression effect is therefore expected to dominate the ultimate load-carrying capacity. Although attempts have been made to predict the time-to-failure of such a member due to structural instability, the predictions were generally not satisfactory because the input data were based on small, clear specimens, with no consideration for the effect of duration of exposure or impact of history on the visco-elastic behaviour of the material in compression. This compression behaviour should be investigated to complement the results of this study. Moisture content is important, in that it significandy affects the temperature history of a member exposed to fire. Further research is needed to develop an appropriate model to characterize heat and mass transfer phenomena in wood. Since reliability calculations are sensitive to temperature variations, it is important that factors having a significant impact on temperature calculations are carefully examined and accurately characterized. Models for prediction of heat transfer in wood-based building systems should be vigorously scrutinized as well. In rehabilitating a fire-exposed structure, information about the residual strength and stiffness of members exposed to fire is needed. For members showing signs of charring, or a significant colour change to a brownish colour, or longitudinal drying checks, or a significant staining around knots, the residual strength is unlikely to recover significantly after the members return to normal end-use conditions. On the other hand, members suffering some exposure but without those significant signs of degradation, may be rehabilitated. Work should be done to clarify the extent of strength and stiffness recovery for various grades of lumber. 9.4 Final Remarks 141 9.4 Final Remarks In designing a structural wood member for fire safety, we seek to ensure, with high confidence, that the member will survive a "severe" fire for a specified period. Reliability analysis allows one to express this confidence in terms of a probability of survival. This probability not only allows the safety of a structure to be analyzed in relative terms, but also permits a cost-benefit analysis to be carried out comparing alternative design solutions at the same overall safety level. It is a preferred approach of modern design processes. The current movement is toward a performance-based code format, with performance and performance expectations stated in terms of risk to human life and fire cost. Within such an approach, current methods of determining fire resistance rating no longer provide relevant information. These methods must be revised to produce more accurate performance information. The ultimate objective must be to determine the fire endurance of wood structural members during real fire exposures, and to express the endurance in terms of a time to failure model. At the international level, the design for fire safety in building construction has been aimed toward an analytical approach where fire safety can be "engineered" rather than "prescribed". This approach will involve the development of computer models for the prediction of fire loadings, heat transfer, thermal degradation, structural damage and ultimately for the estimation of the probability of failure. Having considered the various factors affecting the behaviour of wood at room and elevated temperatures, the modelling of the fire endurance behaviour of light framing should be based on empirical data. The foremost task would be to understand how a light-frame member reacts to elevation of its temperature for different durations, in terms of structural damage and material properties, and as a function of the lumber's initial short-9.4 Final Remarks 142 term strength. Once this information becomes available, we can determine if it is necessary to predict temperature and charring accurately at the location of failure. Finally, facing us are some very fundamental problems and challenges affecting reliability analysis: • how to set failure criteria when the material temperature and properties are nonuniform; • how to predict temperature in regions influenced by knots; • how to express charring as a function of grade-controlling defects such as knots; • how to quantify the effect of moisture content such that data obtained need not be restricted to the initial moisture content and exposure conditions. Some of these problems may not be resolved even with extensive experimental testing. For example, even if we know how charring is affected by the presence of a knot, we can not use this information, if the size, type, and location of knots in a member is not known a-priori. The solutions to these problems, may, ultimately, be grounded in the proper utilization of statistical theory, experimental data and computer simulation. 143 Nomenclature A paramter, s AQ amplitude, mm Ag initial cross sectional area of a member, mm 2 A cross sectional area of unburnt portion of a member, mm 2 a0 twice maximum bond elongation, mm a' creep function parameter ax damage model parameter, IC a2 damage model parameter, s"1 a3 damage model parameter, s"1 a4 damage model parameter, mm 2 N" 1 B' parameter, mm/N 2 b breath or thickness of member, mm b0 parameter, mm"1 C constant temperature, K C' length of microcrack, mm c specific heat D' energy of dissociation per single particle, J d thickness of member, mm E modulus of elasticity, N/mm 2; activation energy, J/mole or J/molecule £ r activation energy for bonding reforming, J/mole or J/molecule Eh activation energy for bonding breaking, J/mole or J/molecule e char thickness, mm Fe strength of wood at wood grain angle 0, N/mm 2 FL strength in the longitudinal direction (parallel to wood grain), N/mm 2 >FR strength of wood in the radial direction, N/mm 2 / bond fraction fs probability density distribution of load / R probability density distribution of resistance G performance function h Planck's constant, J-s/molecule K thermal conductivity, W/m-K k Boltzmann's constant, J/K-molecule k0 rate of loading, kN/s k' load or stress ratio / thickness of member; mm N sample size n constant P f probability of failure Q heat transferred, J Q parameter represents degree of resemblance of a parobola to a crack tip q load, N q0 initial load on a member, N 144 R universal gas constant, J/mole/K r resistance effect s load effect T temperature, K or °C To init ial temperature, IC Tc centre temperature, IC Ts surface temperature, IC t time, s to starting time, s *N ending time, s tf time to failure, s tr time required, s k time at which crack start to open, s a critical time, s u potential energy, J/mole critical strain energy density, mm-N/mm 3 activation energy, J/molecule V volume, m m 3 v, volume, m m 3 v2 volume, m m 3 w weight, g X interparticle distance, mm; distance, mm x0 distance between two particles at equilibrium, mm a damage parameter a' ratio of residual strength to short-term strength as surface energy P reliability index Po positive quantities that modify the energy barrier, m m 2 / N 5 volume of the moving element 6 0 period of thermal oscillation of atoms, s 6T creep strain, mm/mm ei regression coefficient, mm/mm e2 regression coefficient, T 1 e c r critical strain, mm/mm <P material constant, g/s; stress per bond, N / m m2 C charring rate, mm/s e grain angle, rad •n constant Til regression constant regression constant Tl3 regression constant Y coefficient of variation Yo positive quantities that modify the energy barrier, m m2 / N 145 p relative density potential energy barrier, J/mole X Weibull Distribution shape parameter K Weibull Distribution shape parameter X2 Weibull Distribution shape parameter X3 Weibull Distribution shape parameter X' distance of jump a Weibull Distribution scale parameter o* ideal strength, N/mm 2 a' quasi-elastic strength (force), N/mm 2 o m strength maximum, N/mm2 °"o short-term strength, N/mm2 strength of material of volume Vx, N/mm 2; Weibull Distribution scale parameter o2 strength of material of volume V2, N/mm 2 ; Weibull Distribution scale parameter Weibull Distribution scale parameter O K actuall strength, N/mm2 ° u ultimate strength, N/mm2 u parameter depending on creep function Y material parameter, mm2/M/molecule T member's aspect ratio. 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Proc, In-Grade Testing of Structural Lumber, Proc. 47363. Chaired by D.W. Green, USDA, Forest Service, Forest Products Laboratory, Madison, W l , pp. 11-14. 150 Jonsson, R. and Pettersson, 0 . 1985. Timber structures and fire: A review of the existing state of knowledge and research requirements. Document D3: 1985, Swedish Council for Building Research, Stockholm, Sweden. Kadita, S., Yamada T., Suzuki, M . and Komatsu, K. 1961. Studies on the rheological properties of wood. II: Effect of heat-treating condition on the hygroscopicity and dynamic Youngs modulus of wood. }. of Jap. Wood Res. Soc. 7(1): 34-37. Kallioniemi, P. 1980. The strength of wood structures during fires. Proc, Symposium on Fire Resistance of Wood Structures, Symposium 29.9...4.10, Tbilis, V T T Symposium 9, Valtion Teknillinen Tutkimuskeskus, Technical Research Centre of Finland. Kanury, A. M . 1972. Thermal decomposition kinetics of wood pyrolysis. Combustion and Flame 19:75-83. Kanury, A. M . and Blackshear, P. L. Jr. 1970. On the combustion of wood, II:the influence of internal convection on the transient pyrolysis of cellulose. Combustion Science and Technology 2:5-9. Karacabeyli, E. 1988. Duration of load research for lumber in North America. Proc, 1988 International Conference on Timber Engineering, ed. by R. Y. Itani, Washington State University, Seattle, W A , September 1988, pp.380-389. Karacabeyli, E. and Barrett J. D. 1993. Rate of loading effects on strength of lumber. Forest Prod. J. 43(5):28-36. King, E. G. and Glowinski, R. W . 1988. A rationalized model for calculating the fire endurance of wood beams. For. Prod. J. 38(10): 31-36. Kitahara, K. and Okabe, N . 1959. The influence of temperature on creep of wood by bending test. J. of Jap. Wood Res. Soc. 10(5):169-175. Koch, P. 1971. Process for straightening and drying southern pine 2 by 4's in 24 hours. Forest Prod. J. 21(5): 17-24. Konig, J. 1991. Modelling the effective cross section of timber frame members exposed to fire. Paper presented at 1991 meeting of the International Council for Building Research Studies and Documentation, Working Commission W18A - Timber Structures. Konig, J. and Noren, J. 1991. Fire tests on timber frame members under pure bending. Proc, 1991 International Timber Engineering Conference, ed. by J. Marcroft, TRADA, London, England, September 1991. 151 Knudson, R. M . and Schniewind A. P. 1975. Performance of structural wood members exposed to fire. Forest Prod. J. 25(2):23-32. Kollman, F. F. P. and Cote, W. A. Jr. 1968. Principles of Wood Science and Technology. I: Solid Wood. Springer-Verlag New York Inc. pp. 149-157. Kung, H.-C. 1972. A mathematical model of wood pyrolysis. Combustion and Flame 19:185-195. Lawson, D. I., Webster, C.T., and Ashton, L.A. 1952. Fire endurance of timber beams and floors. Structural Eng. 30(2):27-34. Lee, C. IC, Chaiken, R. F., and Singer, J. M . 1977. Charring in pyrolysis of wood in fires by laser simulation. 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University of Wisconsin, Madison, WI. Stamm, A. L. 1964. Wood and Cellulose Science. The Ronald Press, New York. Suzuki, S., Tamai, A. and Hirai, N . 1982. Effect of temperature on orthotropic properties of wood. III. Anisotropy in the L-R plane. J. of Jap. Wood Res. Soc. 28(7): 401-406. Thomas, P.H. , Simms, D. L. and Law, M . 1967. The rate of burning of wood. Fire Research Note No. 657. Fire Research Station, Borehamwood, England. Truax, T. R. 1959. Fire research and results at U . S. Forest Products Laboratory. U . S. Forest Serv., Forest Products Lab. No. 1999, Madison, WI. Van Der Put, T. 1989. Deformation and Damage Processes in Wood. Delft University Press, Delft, The Netherlands. Vorreiter, L. 1956. Combustion and heat insulating losses of wood and fiberboards. Holzforschung 10(3): 73-80. Webster, C. T. and Ashton, L. A. 1951. Investigation of building fires. Part IV: Fire resistance of timber doors. National Buuding Studies Technical Paper No. 6, Dept. of Sci. and Ind. Res., H M S Office, London. Weibull, W. 1939. A statistical theory of the strength of materials. Proc, Roy. Swed. Inst. Eng. Res., No. 153, Stockholm. White, R. H . 1988. Charring rates of different wood species. Ph.D. dissertation, University of Wisconsin, Madison, WI. White, R. and Schaffer, E. 1981. Transient moisture content in fire-exposed wood slab. Wood and Fiber 13(l):17-38. White, R. H . and Schaffer, E. L. 1978. Application of C M A program to wood charring. Fire Technology Vol . 14, No.4. Woeste, F. E. and Schaffer, E. L. 1981. Reliability analsysis of fire-exposed light-frame wood floor assemblies. USDA, Forest Service, Research Paper FPL 386, Forest Product Laboratory, Madison, WI. 154 Wood, L. W . 1951. Relation of strength of wood to duration of load. USDA, Forest Service, Report No. 1916, Forest Product Laboratory, Madison, W l . Youngs, R. L. 1957. The perpendicular-to-grain mechanical properties of red oak as related to temperature, moisture content, and time. USDA, Forest Service, Report No. 2079. Forest Products Laboratory, Madison, W l . 155 APPENDIX I — Parts and their manufacturers for the heating apparatus Heating Elements Platens Insulation Temperature Controller Platen thermocouples Wood thermocouples 0.43" diameter custom made @ 8' long rod, three per side, power consumption = 30kW per side, supplied by Gough Electric. Contact: Barney Rosseau (604) 438-8661 Aluminum plates 1" thick 1" thick marinite high density insulation supplied by Fuller Bartells Distribution. Contact: Dave 421-2444 Ogden Model ETR-9080 supplied by Valax. Type J, ungrounded, supplied by Valax, conditioner Ogden 9080-1171 Type T, ungrounded, O M E G A TMQSS-062U-6, conditioner O M E G A 182TC Clamping mechanism Fabricated by Forintek Appendix II Sample Number = 001, Temperature = 20°C nominal spec failure c.c. width thickness weight meter MC TTF TTF@ stiff- coeff rate of coeff pre max UTS estimated corrected rate of number location initial final intial final initial final MC inital final max load ness deter loading deter load load deflection TTF loading (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) (S) (S) (kN/mm) (kN/s) (KN) (KN) (MPa) (mm) (mm) (kN/s) 16 1510 0 88.3 35 17.4 11.4 100.9 97.9 -18.66 1.00 1.700 1.00 0.4 163.0 52.7 -8.74 88.1 1.85 22 2163 0 89.1 35 18 10.7 73.0 71.0 -19.45 1.00 2.220 1.00 0.4 154.1 49.4 -7.92 83.3 1.85 29 2410 0 88.5 35 17.3 11 87.6 87.5 -19.04 1.00 2.290 1.00 0.4 189.9 61.3 -9.97 102.6 1.85 35 990 1 88.6 35 182 10.7 72.9 72.7 -16.61 1.00 1.570 1.00 0.4 119.3 38.5 -7.18 64.5 1.85 52 967 1 88.4 35 19.3 11.6 78.3 78.2 -19.05 1.00 2.320 1.00 0.4 170.4 55.1 -8.94 92.1 1.85 53 2100 0 87.5 35 18.8 10.5 69.9 69.7 -18.65 1.00 2.440 1.00 0.4 162.1 53.0 -8.69 87.6 1.85 61 3205 0 88.7 35 16.8 9.9 65.9 65.7 -16.43 1.00 2.480 1.00 0.4 149.3 48.1 -9.09 80.7 1.85 77 2460 0 87.8 35 18 10.6 107.7 104.2 -20.31 1.00 2.390 1.00 0.4 240.1 78.1 -11.82 129.8 1.85 90 2205 0 86.5 35 17.7 10.3 76.8 73.4 -18.06 1.00 2.060 1.00 0.4 149.3 49.3 -8.26 80.7 1.85 123 932 1 88.2 35 20.4 10.8 100.2 95.3 -22.7 1.00 2.300 1.00 0.4 2136 69.2 -9.41 115.4 1.85 14S 2490 0 88.4 35 18.2 11.3 43.1 40.4 -18.08 1.00 2.480 1.00 0.4 97.8 31.6 -5.41 52.9 1.85 228 2210 0 86.7 35 18 9.8 55.2 55.0 -18.1 1.00 2.670 1.00 0.4 135.5 44.6 -7.49 73.3 1.85 275 2612 0 87.7 35 19.6 9.8 44.5 44.4 -20.72 1.00 2.420 1.00 0.4 99.0 32.2 -4.77 53.5 1.85 299 844 1 87.6 35 18.4 10.4 63.9 61.2 -20.32 0.99 2.470 1.00 0.4 144.3 47.0 -7.1 78.0 1.85 394 2948 0 88.8 35 18 10.2 47.4 47.2 -16.58 1.00 2.650 1.00 0.4 118.0 38.0 -7.12 63.8 1.85 421 2098 0 87.1 35 17.6 10.3 104.6 104.4 -18.16 1.00 1.930 1.00 0.4 196.9 64.6 -10.84 106.4 1.85 443 977 1 88.1 35 18.7 10.9 61.8 61.6 -19.44 1.00 2.700 1.00 0.4 152.5 49.5 -7.85 82.5 1.85 5003 952 1 87.6 35 16.6 10.1 62.5 60.4 -13.28 1.00 1.770 1.00 0.4 102.8 33.5 -7.74 55.6 1.85 5037 1055 1 88.0 35 15.8 10.4 477 43.3 -10.54 100 1.610 1.00 0.4 69.1 22.4 -6.56 37.4 1.85 5103 3600 0 88.1 35 16.6 • 10.6 67.1 49.7 -14.09 1.00 3.170 0.96 0.4 91.1 29.5 -6.46 49.2 1.85 5121 2845 0 87.1 35 14.7 11.4 69.3 64.1 -11.02 1.00 1.600 1.00 0.4 103.2 33.9 -9.37 55.8 1.85 5145 1980 0 88.4 35 16.1 10.8 45.6 42.5 -12.31 1.00 1.770 1.00 0.4 71.7 232 -5.83 38.8 1.85 5152 1185 1 87.5 35 15.4 10.2 48.8 44.5 -11.93 1.00 1.750 1.00 0.4 77.2 25.2 -6.47 41.7 1.85 5179 3155 0 88.8 35 15.9 9.6 50.4 50.2 -12.79 1.00 1.670 1.00 0.4 78.5 25.3 -6.13 42.4 1.85 5204 1193 1 87.8 35 15.2 10 49.3 47.2 -11.84 1.00 2.400 1.00 0.4 105.4 34.3 -8.9 57.0 1.85 5239 3867 1 88.1 35 15.8 98 35.9 35.7 -13.55 1.00 1.600 1.00 04 49.5 16.1 -3.65 26.8 1.85 5269 1642 0 88.6 35 15.6 10.8 35.6 31.6 -9.92 1.00 1.470 1.00 0.4 45.2 14.6 -4.56 24.4 1.85 5289 1850 0 88.0 35 15.6 10.6 62.5 58.4 -12.39 1.00 1.730 1.00 0.4 98.9 32.1 -7.98 53.4 1.85 5290 2632 0 88.5 35 15 10.5 366 36.4 -10.9 1.00 1.530 1.00 0.4 51.1 16.5 -4.69 27.6 1.85 5291 1885 0 88.0 35 14.4 9.9 46.6 40.5 -10.82 1.00 1.700 1.00 0.4 66.5 21.6 -6.15 36.0 1.85 5331 4054 1 88.4 35 15.2 10.1 67.4 64.4 -12.31 1.00 1.550 1.00 0.4 95.8 31.0 -779 51.8 1.85 5355 1508 0 88.1 35 16.4 9.3 74.6 71.7 -13.03 1.00 1.390 1.00 0.4 98.9 32.1 -7.59 53.4 1 85 5388 1553 0 88.9 35 15.8 9.3 37.6 37.4 -11.97 1.00 1.480 1.00 0.4 49.8 16.0 -4.16 26.9 1.85 5447 3645 0 88.2 35 15.9 10.4 33.4 29.9 -13.97 1.00 1.780 1.00 0.4 53.7 17.4 -3.84 290 1.85 8007 3277 0 88.1 35 15.5 9.4 69.2 69.0 -13.9 1.00 1.890 1.00 0.4 119.3 38.7 -8.58 64.5 1.85 8010 3779 1 87.0 35 18 9.8 62.3 58.5 -15.12 1.00 1.870 1.00 0.4 106.9 35.1 -7.07 57.8 1.85 8020 785 1 87.7 35 16.3 10.1 80.2 80.0 -15.65 1.00 1.910 1.00 0.4 141.9 46.2 -9.06 76.7 1.85 8039 1717 0 88.6 35 17 11 77.7 75.0 -13.94 1.00 1.750 1.00 0.4 128.4 41.4 -9.21 69.4 1.85 8075 2630 0 88.6 35 18.1 11.2 24.2 24.0 -14.88 1.00 1.820 1.00 0.4 378 12.2 -254 20.4 1.85 8105 1448 0 87.9 35 17.4 11 69.1 68 9 -13.78 1.00 1.920 1.00 0.4 122.6 39.8 -8.9 66.2 1.85 8141 3440 0 88.6 35 16.5 10.8 41.6 41.4 -13.64 1.00 1.910 1.00 0.4 71.8 232 -5.26 38.8 1.85 8145 3630 0 88.6 35 16.2 10.6 75.9 75.8 -16.13 1.00 1.870 1.00 0.4 1302 42.0 -8.07 70.4 1.S5 8148 2075 0 873 35 20.5 11.6 34.9 28.8 -15.66 1.00 1.780 1.00 0.4 51.5 16.8 -3.29 27.8 1.85 8165 1762 0 88.0 35 16.2 11.5 51.9 51.8 -15.1 1.00 1.920 1.00 0.4 92.6 30.1 -6 13 50.0 1.85 8185 1030 1 87.4 35 18.8 10.5 37.1 36.9 -15.13 1.00 1.710 1.00 0.4 57.4 18.8 -3.79 31.0 1.85 8188 810 87.7 35 18.2 10.4 55.0 52.4 -15.06 1.00 1.920 1.00 0.4 96.7 31.5 -6.42 52.3 1.85 8240 3875 1 88.0 35 18.1 10.4 73.4 73.2 -17.26 1.00 1.690 1.00 0.4 119.2 38.7 -6.91 64.4 1.85 8259 3035 87.8 35 17.4 10.9 43.9 41.3 -14.79 1.00 1.910 1.00 0.4 78.0 25.4 -5.28 42.2 1.85 8262 782 1 88.3 35 16.2 11.1 73.3 73.1 -14.54 1.00 1.840 1.00 0.4 125.6 40.6 -8.64 67.9 1.85 8267 3945 \ 88.2 35 15.5 10.7 39.3 39.1 -13.59 1.00 2.090 1.00 0.4 74.6 24.2 -5.49 40.3 1.85 8273 791 1 87.8 35 15.4 9.4 87.2 87.0 -16.4 1.00 1.800 1.00 0.4 147.3 47.9 -8.98 79.6 1.85 8303 2045 88.0 35 17.4 11.6 71.1 71.0 -17.12 1.00 1.950 1.00 0.4 131.7 42.8 -7.69 71.2 1.85 8335 1048 1 87.7 35 18 10 72.3 72.1 -17.03 1.00 2.030 1.00 0.4 139.7 45.5 -8.2 75.5 1.85 8341 1200 1 88.3 35 16.2 10.2 38.2 38.0 -13 22 1.00 1.680 1.00 0.4 58.0 18.8 -4.39 31.4 1.85 8346 1070 1 86.9 35 16 9.5 53.4 49.3 -15.48 1.00 2.200 1.00 0.4 100.8 33.2 -6.51 54.5 1.85 8365 3203 87.6 35 15.9 9.4 75.2 75.0 -15.16 1.00 1.920 1.00 0.4 137.3 44.8 -9.06 74.2 1.85 8395 850 1 87.9 35 17.4 10.2 85.2 82.6 -18.35 1.00 1.750 1.00 0.4 141.9 46.1 -7.73 76.7 1.85 8434 985 1 88.1 35 15.9 10.2 63.6 63.4 -13.35 1.00 1.910 1.00 0.4 110 2 35.7 -8.25 59.6 1.85 8467 3440 0 87.7 35 18.2 9.4 57.2 57.0 -15.41 1.00 2.100 1.00 0.4 108.0 35.2 -7.01 58.4 1.85 8481 2327 0 88.2 35 16.2 9.9 27.1 26.9 -12.86 1.00 2.090 1.00 0.4 45.7 14.8 -3.55 24.7 1.85 avg= COV (%) = sum -2112 24 88.0 0.62 35 17.0 8.21 10.4 6 61.1 32.2 59.2 33.4 -15.33 -18.92 1.00 0.13 1.97 18.31 1.00 0.52 0.4 0 110.6 40 35.9 40 -7.07 -28.31 59.8 39.97 0\ Appendix II Sample Number = 002, Temperature - 20°C nominal spec failure cc. width thickness weight meter MC TTF TTF@ stiff- coeff rate of coeff pre max UTS estimated corrected rate of number location initial final intial final initial final MC inital final max load ness deter loading deter load load deflection TTF loading (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) (mm) (kN/s) 46 1223 0 88.2 35 17.6 11.1 53.7 53.5 -17.21 0.99 2.210 1.00 0.4 110.4 35.8 -6.41 59.7 1.85 67 3137 0 88.2 35 20 11.5 51.7 51.5 -20.11 1.00 2.720 1.00 0.4 131.5 42.6 -6.54 71.1 1.85 91 3078 0 88.4 35 18.8 11 50.8 50.6 -17.11 1.00 2.210 1.00 0.4 105.2 34.0 -6.15 56.9 1.85 133 3710 1 88.7 35 17.5 10.5 80.9 78.7 -17.83 1.00 1.900 1.00 0.4 150.8 48.6 -8.46 81.5 1.85 134 2960 0 87.8 35 19 10.9 73.6 70.2 -18.11 1.00 2.440 1.00 0.4 157.1 51.1 -8.67 84.9 1.85 164 2956 0 88.5 35 18.8 10.8 62.9 61.1 -20.06 1.00 2.230 1.00 0.4 134.5 43.4 -6.7 72.7 1.85 167 1227 0 88.4 35 17.4 11 51.0 50.9 -17.15 1.00 2.680 1.00 0.4 126.9 41.0 -7.4 68.6 1.85 195 2498 0 88.4 35 21.8 11.3 76.0 74.0 -22.7 0.99 3.000 1 00 0.4 212.9 68.8 -9.38 115.1 1.85 205 3618 0 87.1 35 19.3 10.5 32.8 32.6 -17.92 1.00 2.680 1.00 0.4 80.6 26.5 -4.5 43.6 1.85 219 1317 0 88.9 35 16.8 11.1 56.3 53.4 -17.97 1.00 2.610 1.00 0.4 140.2 45.1 -7.8 75.8 1.85 242 3832 1 86.7 35 17.6 11.2 67.8 67.6 -17.99 1.00 2.470 1.00 0.4 156.9 51.7 -8.72 84.8 1.85 340 1387 0 86.9 35 19 10.9 78.7 78.5 -19.2 1.00 2.450 1.00 0.4 178.0 58.5 -9.27 96.2 1.85 375 1127 1 87.5 35 16 B 11.3 72.4 72.3 -18.2 1.00 2.650 1.00 0.4 181.9 59 4 -9.99 98.3 1.85 407 1712 0 87.9 35 15.6 9 9 71.4 71.2 -16.41 1.00 1.950 1.00 0.4 129.3 42.0 -7.88 69.9 1.85 422 1108 1 88.5 35 17.1 10.5 63.6 634 -18.16 1.00 2.960 1.00 0.4 173.8 56 1 -9.57 94.0 1.85 444 3977 1 88.7 35 18.3 10.6 66.9 63.1 -20.3 1.00 3.190 1.00 0.4 184.0 59.3 -9.06 99.5 1.85 454 2107 0 87.5 35 18.6 10.1 68.3 63.7 -19.36 0.99 1.850 1.00 0.4 121.3 39.6 -6.26 65.5 1.85 492 1993 0 87.3 35 19.9 10.2 82.0 81.8 -20.91 1.00 2.240 1.00 0.4 173.8 56.9 -8.31 94.0 1.85 5035 3795 1 88.4 35 17 10.5 67.9 64.9 -11.62 1.00 1.740 1.00 0.4 110.5 35.7 -9.51 59.7 1.85 5046 1687 0 88.2 35 15.3 10.1 47.3 47.2 -10.76 1.00 1.540 1.00 0.4 65.9 21.3 -6.12 35.6 1.85 5058 2207 0 87.5 35 16.1 10.1 61.5 56.3 -13.19 1.00 1.470 1.00 0.4 83.2 27.2 -6.31 45.0 1.85 5094 921 1 87.7 35 14 8 10.4 49.7 46.8 -11.1 1.00 1.450 1.00 0.4 66.9 21.8 -6.03 36.2 1.85 5125 1150 1 88.2 35 14.4 10.1 72.3 67.0 -12.84 0.99 1.550 1.00 0.4 102.8 33 3 -8 55.6 1.85 5140 1453 0 88.7 35 14.2 9 46.2 41.9 -10.89 1.00 1.380 1.00 0.4 57.4 18.5 -5.27 31.0 1.85 5146 3595 0 87.0 35 16.7 10.3 65.1 65.0 -15.12 1.00 1.560 1.00 0.4 96.3 31.6 -6.37 52 0 1.85 5150 2075 0 86 6 35 16.6 10.2 620 60.0 -14.17 1.00 1.480 1.00 0.4 87.6 28.9 -6.18 47.3 1.85 5193 2463 0 88.1 35 14.7 9.7 84.2 82.2 -14.73 1.00 1.660 1.00 0.4 134.1 43.5 -9.1 72.5 1.85 5199 1357 0 88.0 35 16.6 11.2 51.7 47.7 -13.55 1.00 1.630 1.00 0.4 79.9 25.9 -5.9 43.2 1.85 5247 1857 0 87.4 35 15.8 9.7 73.1 72.9 -12.42 1.00 1.670 1.00 0.4 115.6 37.8 -9.31 62.5 1.85 5248 1530 0 88.2 35 16.2 9.2 32.8 32.6 -9.51 1.00 1.530 1.00 0.4 44.6 14.4 -4.69 24.1 1.85 5258 1777 0 87.7 35 16 9 55.5 55.4 -13.47 1.00 1.900 1.00 0.4 96.9 31.6 -7.2 52.4 1.85 5363 3548 0 88.4 35 17.1 9.5 30.0 26.0 -1268 1.00 1.880 1.00 0.4 48.7 15.7 -3.84 26.3 1.85 5416 1207 1 88.3 35 16.4 96 48.2 45.1 -13.01 1.00 1.870 1.00 0.4 81.9 26.5 -6.3 44.3 1.85 5457 2831 0 88.0 35 15.7 9.5 32.3 32.2 -11.16 1.00 1.880 1.00 0.4 54.8 17.8 -4.91 29.6 1.85 8013 973 1 87.3 35 17.9 10.7 80.3 78.3 -16.95 1.00 1.900 1.00 0.4 145.6 47.7 -8.59 78.7 1.85 8021 3898 1 87.5 35 16.8 10.9 64.6 64.5 -14.88 1.00 1.760 1.00 0.4 105.2 34.4 -7.07 56.9 1.85 8070 1554 0 88.2 35 16.5 10.5 63.9 63.7 -16.3 1.00 1.950 1.00 0.4 118.0 38.2 -7.24 63.8 1.85 8140 3998 1 88.4 35 16.3 10.7 60.7 60.6 -14.92 1.00 1.700 1.00 0.4 96.9 31.3 -6.49 52.4 1.85 8156 1006 1 88.1 35 16.5 10 72.3 69.2 -16.4 1.00 1.690 1.00 0.4 116.5 37.8 -7.1 63.0 1.85 8190 1163 1 880 35 16.2 9.9 64.7 61.6 -14.04 1.00 2.030 1.00 0.4 125.4 40.7 -8.93 67.8 1.85 8197 3013 0 88.1 35 16.6 10.3 53.7 53.6 -14.75 1.00 2.060 1.00 0.4 104.7 34.0 -7.1 56.6 1.85 8212 3520 0 88.5 35 16.6 10.8 31.6 31.5 -15.45 1.00 1.800 1.00 0.4 51.2 16.5 -3.31 27.7 1.85 8219 1561 0 87.8 35 17.4 10.3 71.4 71.2 -13.43 1.00 1.900 1.00 0.4 129.1 42.0 -9.61 69.8 1.85 8225 2747 0 86.4 35 17 9.4 52.2 52.1 -16.57 1.00 1.690 1.00 0.4 83.9 27.7 -5.06 45.3 1.85 8244 765 1 87.3 35 18 9.9 75.7 72.9 -1891 1.00 1.720 1.00 0.4 123.6 40.5 -6.54 66.8 1.85 8256 4015 1 87.6 35 18.3 10.1 72.6 72.4 -16.41 1.00 1.870 1.00 0.4 127.3 41.6 -7.76 68.8 1.85 8284 2918 0 88.3 35 15.8 9.6 36.1 35.9 -13.42 1.00 1.540 1.00 0.4 48.7 15.8 -3.63 26.3 1.85 8286 3470 0 B8.3 35 17.3 9 8 21.4 17.5 -14.79 1.00 1.730 1.00 0.4 30.8 100 -2.08 16.6 1.85 8292 1452 0 87.7 35 17.7 10.5 64.0 63.a -16.99 1.00 1.700 1.00 0.4 100.4 32.7 -5.91 54.3 1.85 8305 2288 0 877 35 16.4 9.8 53.2 53.0 -14.07 1.00 1.770 1.00 0.4 85.8 28.0 -6.1 46.4 1.85 8310 3875 1 87.9 35 18 11.5 56.6 53.2 -14.33 1.00 2.010 1.00 0.4 106.3 34.5 -7.42 57.4 1.85 8359 1542 0 88.0 35 16.6 10.2 64.0 63.8 -16.3 1.00 1.960 1.00 0.4 117.3 38.1 -7.2 63.4 1.85 8416 3741 1 87.8 35 17.1 9 2 56.7 56.5 -16.1 1.00 1.950 1.00 0.4 104.1 33.9 -6.47 56.3 1.85 8423 3057 0 88.1 35 16.2 9.3 51.3 51.2 -14.83 1.00 1.820 1.00 0.4 87.2 28.3 -5.B8 47.1 1.85 8438 2278 0 87.7 35 17.2 10.2 66.2 66.0 -16 1.00 1.800 1.00 0.4 112.8 36.8 -7.05 61.0 1.85 8471 1309 0 88.0 35 15.7 9.5 70.4 67.1 -14.81 1.00 1.630 1.00 0.4 108.9 35.3 -7.35 58.8 1.85 8473 3577 0 87.1 35 17.8 99 33.0 32.9 -16.61 1.00 1.600 1.00 0.4 48.0 15.8 -2.89 260 1.85 8488 3712 1 87.4 35 16.6 9.4 78.2 75.7 -15.87 1.00 1.880 1.00 0.4 142.1 46.4 -8.95 76.8 1.85 8493 3533 0 87.5 35 17.2 9.6 51.3 51.1 -15.51 1.00 1.910 1.00 0.4 91.1 29.7 -5.87 49.2 1.85 8496 758 1 87.1 35 18 10 64.4 62.3 -18.32 1.00 1.970 1.00 0.4 118.7 38.9 -6 48 64.1 1.85 avg = COV (%) = sum = 20 87.9 0.63 35 17.1 8.16 10.2 6.34 59.5 24.8 58.0 25.4 -15.73 -17.59 1.00 0.25 1.97 21.184 1.00 0 0.4 0 110.1 35.2 35.8 35.2 -6.90 -25.82 59.5 35.24 Appendix II Sample Number = 003, Temperature = 20°C nominal spec failure cc. width thickness weight meter MC TTF TTF@ stiff- coeff rate of coeff pre max UTS estimated corrected rate of number location initial final intial final initial final MC inital final max load ness deter loading deter load load deflection TTF loading (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) (mm) (kN/s) 38 3522 0 88.6 35 17.5 10.7 69 8 69.7 -17.72 1.00 1.930 1.00 0.4 128.4 41.4 -7.25 69.4 1.85 72 1347 0 88.2 35 16.7 11 99.4 97.3 -17.64 1.00 1.930 1.00 0.4 185.1 60.0 -10.49 100.1 1.85 92 835 1 88.6 35 15.8 10.3 54.4 54.2 -16.99 1.00 1.950 1.00 0.4 95.8 30.9 -5.64 51.B 1.85 140 1017 1 87.9 35 18.6 11 58.1 58.0 -17.15 1.00 1.950 1.00 0.4 105.9 34.4 -6.17 57.2 1.85 142 2500 0 89.1 35 17.6 10.9 106.3 102.6 -18.92 1.00 1.890 1.00 0.4 193.2 62.0 -10.21 104.4 1.85 ' 156 3743 1 88.7 35 17.6 10.6 66.9 64.5 -18.67 1.00 1.890 1.00 0.4 120.4 388 -6 45 65.1 1 85 160 1183 1 87.7 35 19.2 11.2 121.5 118.6 -22.63 1.00 1.930 1.00 0.4 225 5 73.5 -9.97 121.9 1.85 170 1522 0 86.7 35 18.8 10.8 93.0 90.8 -18.59 1.00 1.890 1.00 0.4 169.7 55.9 -9.13 91.7 1.85 1B2 2772 0 B6.6 35 20.1 10.6 100.8 97.9 -19.87 1.00 1.850 1.00 0.4 190.3 62.8 -9.58 102.9 1.85 234 1745 0 87.2 35 18.9 10.7 87.6 84.2 -19.54 1.00 1.910 1.00 04 161.7 52.9 -8.27 87.4 1.85 235 3900 1 86.5 35 19.5 10.2 76.7 74.7 -21.15 1.00 1.990 1.00 0.4 141.0 46.6 -6.67 76.2 1.85 252 2727 0 88.6 35 16.2 10.2 74.3 72.2 -17.B2 1.00 1.900 1.00 04 133.4 43 0 -7.49 72.1 1.B5 260 895 1 88.0 35 19.3 11 89.2 82.8 -19.61 1.00 2.140 1.00 0.4 158.2 51.3 -8.06 85.5 1.85 281 2548 0 86.5 35 18.6 11.4 98.3 98.1 -21.74 1.00 1.940 1.00 0.4 184.0 60.8 -8.46 995 1.85 311 1760 0 87.8 35 19 11.1 53.9 51.0 -17.09 1.00 1.890 1.00 0.4 95.6 31.1 -5.59 51.7 1.85 324 2393 0 87.3 35 18.4 10.8 92.6 92.4 -18.31 1.00 1.910 1.00 0.4 171.2 56.0 -9.35 92.6 1.85 343 3435 0 87.0 35 16.5 10.1 64.5 60.4 -17.29 1.00 1.920 1.00 0.4 113.4 37.2 -6.56 61.3 1.85 344 1647 0 87.B 35 16.6 10.4 89.6 85.4 -17.35 1.00 1.890 1.00 0.4 164.7 53.6 -9.49 89.0 1.85 352 2797 0 87.5 35 18.2 10.3 89.3 89.1 -18.49 1.00 1.920 1.00 0.4 161.9 52.9 -8.76 87.5 1.85 378 2317 0 88.6 35 17 9.8 44.8 41.5 -17.33 1.00 1.910 1.00 0.4 77.4 24.9 -4.46 41.8 1.85 405 807 1 883 35 18.3 10.8 109.1 106.5 -19.07 1.00 1.950 1.00 0.4 202.3 65.4 -10.61 109.3 1.85 435 825 1 86.7 35 18.4 10.1 78.9 70.8 -18.61 1.00 2 370 1.00 0.4 136.2 44.9 -7.32 73.6 1.85 481 2955 0 88.8 35 17.7 10.3 61.9 59.5 -15.65 1.00 1.880 1.00 0.4 109.5 35.2 -7 59 2 1.85 5011 1253 0 87.5 35 16.2 10.2 50 1 50.0 -11.69 1.00 1.830 1.00 0.4 83.5 27.3 -7.14 45.1 1.85 5041 1282 0 88.2 35 15.8 10.7 41.9 39.7 -13.11 1.00 1.900 1.00 0.4 71.5 23.2 -5.46 38.7 1.85 5060 1670 0 88.6 35 14.4 10.6 37.5 34.3 -11.68 1.00 1.850 1.00 0.4 61.3 19.8 -5.25 33.1 1.85 5070 2220 0 88.4 35 16 10.3 41.4 38.5 -12.98 1.00 1.820 1.00 0.4 70.9 22.9 -5.46 38.3 1.85 5072 3148 0 87.4 35 16.4 9.7 45.8 42.8 -12.92 1.00 1.880 1.00 0.4 78.0 25.5 -6.04 42.2 1.85 5084 755 1 86.5 35 15.3 9.7 54.9 51.5 -14.93 1.00 1.880 1.00 0.4 94.3 31.2 -6.32 51.0 1.85 5096 870 1 87.6 35 15.9 10.5 35.0 33.2 -11.9 1.00 1.840 1.00 0.4 57.8 18 9 -4.86 31.3 1.85 5142 1215 1 87.7 35 14.9 10 65.9 62.1 -15.04 1.00 1.900 1.00 0.4 114.7 37.4 -7.63 62.0 1.85 5198 2373 0 88.4 35 14.8 9.8 33.5 30.3 -11.34 1.00 1 830 1.00 0.4 53.6 17.3 -4.73 29.0 1.85 5200 2353 0 88.1 35 14.9 10 43.0 40.9 -12.9 1.00 1.880 1.00 0.4 74.3 24.1 -5.76 40.2 1.85 5212 923 1 88.1 35 15.7 10.4 42.2 42.1 -12.46 1.00 1.840 1.00 0.4 69.8 22.6 -5.6 37.7 1.85 5226 3147 0 88.3 35 17.4 9.9 43.5 37.7 -12.26 1.00 1.880 1.00 0.4 70.4 22.8 -5.74 38.1 1.85 5250 1345 0 88.0 35 15.8 9.3 36.6 32.8 -12.36 1.00 1.850 1.00 0.4 60.0 19.5 -4.86 32.4 1.85 5260 1155 1 87.3 35 16 9.5 76.0 72.8 -13 1.00 1.890 1.00 0.4 132.3 43.3 -10.1B 71.5 1.85 5273 3363 0 87.1 35 17 10.2 59.1 56.3 -14.03 1.00 1.880 1.00 0.4 103.2 339 -7.36 55.8 1.85 5276 3203 0 87.7 35 15.4 9.8 69.9 69 8 -13.09 1.00 1.900 1.00 0.4 125.2 40.8 -9.56 67.7 1.85 5283 2380 0 88.0 35 16.9 10.2 63.6 61.3 -13.73 1.00 1.920 1.00 0.4 112.8 36.6 -8.21 61.0 1.85 5404 4010 1 88.2 35 14.6 9.2 44.3 38.1 -11.76 1.00 1.930 1.00 0.4 71.1 23.0 -6.04 38.4 1.85 8057 1893 0 87.5 35 18.4 10 74.7 74.6 -15.87 1.00 1.940 1.00 0.4 136.7 44.6 -8.61 73.9 1.85 8109 3066 0 88.5 35 16.2 10.1 51.9 51.7 -16.64 1.00 1.940 1.00 0.4 94.3 30.5 -5.67 51.0 1.85 8121 848 1 88.0 35 16.9 10.3 68.3 68.1 -15.1 1.00 1.960 1.00 0.4 124.7 40.5 -8.26 67.4 1.85 8142 3140 0 88.2 35 16.6 9.4 72.9 72.8 -16.29 1.00 1.940 1.00 0.4 134.3 43.5 -8.24 72.6 1.85 8178 3047 0 88.5 35 17.6 10.2 36.0 35.8 -14.23 1:00 1.900 1.00 0.4 60.6 19.6 -4.26 328 1.85 8205 842 1 88.1 35 17.4 10.1 77.9 66.2 -16.07 1.00 2.750 0.97 0.4 130.6 42.3 -8.13 70.6 1.85 8222 1073 1 87.8 35 17.2 10.9 74.7 74.5 -17.44 1.00 1.920 1.00 0.4 134.9 43.9 -7.74 72.9 1.85 8224 2233 0 88 6 35 15.1 9.6 46.7 44.9 -14.56 1.00 1.880 1.00 0.4 81.3 26.2 -5.58 43.9 1.85 8243 1065 1 88.4 35 15.6 9.2 49.5 49.3 -14.9 1.00 1.880 1.00 0.4 87.6 28.3 -5.88 47.3 1.85 8321 3133 0 sa.1 35 18.7 9.7 55.2 55.1 - -17.54 1.00 1.950 1.00 0.4 101.5 32.9 -5.79 54.9 1.85 8349 1415 0 88.0 35 16.2 9.1 43.8 41.3 -16.07 1.00 1.930 1.00 0.4 78.5 25.5 -4.88 42.4 1.85 8401 3018 0 87.0 35 17.4 98 54.9 54.8 -16.89 1.00 1.950 1.00 0.4 100.6 33.1 -5.96 54.4 1.85 8410 2963 0 87.8 35 16.3 9.5 30.4 30.3 -14.46 1.00 1.930 1.00 0.4 51.5 16.8- -3.56 27.8 1.85 8427 2310 0 88.0 35 17.2 9.9 63.9 60.6 -16.08 1.00 1 880 1.00 0.4 111.5 36.2 -6.93 60.3 1.85 8443 1934 0 88.0 35 16.4 9.6 34.7 34.5 -15.73 1.00 1.910 1.00 0 4 59.3 19.3 -3.77 32.1 1.85 8466 2848 0 88.1 35 17 9.4 54.4 51.3 -14.83 1.00 1.880 1.00 0.4 94.8 30.7 -6.39 51.2 1.85 8472 1920 0 88.2 35 17.4 9.4 43.5 43.3 -18.18 1.00 1.950 1.00 0.4 78.5 25.4 -4.31 42.4 1.85 8486 1493 0 88.0 35 16.9 10 82.6 77.8 -15.26 1.00 1.900 1.00 0.4 144.9 47.1 -9.5 78.3 1.85 8497 3240 0 88.3 35 16.6 10 32 5 30.0 -13.9 1.00 1.860 1.00 0.4 52.4 17.0 -3.77 28.3 1.85 avg = 87.9 35 17.0 10.2 63.6 61.2 -15.97 1.00 1.93 1.00 0.4 113.1 36. B -6.94 61.2 COV (%) = 0.72 7.95 5.44 35.1 36.1 -17.04 0 6.8583 0.39 O 38.2 38.4 -27.11 38.15 sum = 18 Appendix II Sample Number = 004, Temperature - 20°C spec number failure location (mm) c.c. width initial final (mm) (mm) thickness intial final (mm) (mm) weight initial final (lb) (lb) meter M C (%) M C inital final (%> (%) T T F (s) T T F @ max load (s) stiff-ness (kN/mm) coeff deter rate of loading (kN/s) coeff deter pre load (KN) max load (KN) U T S (MPa) estimated deflection (mm) corrected T T F (mm) nominal rate of loading (kN/s) 30 2760 0 89.1 35 17.7 10.2 727.8 727.6 -18.01 1.00 0.203 1.00 0.4 147.6 47.3 -8.2 738.1 0.20 54 990 1 87.8 35 19.3 10.8 721.4 721.2 -18.71 0.99 0.199 1 00 0 4 146.7 47.7 -7.84 733.4 0.20 82 1495 0 88.5 35 18.6 10.2 356.2 351.1 -16.74 0.99 0.195 1 00 0.4 67.7 21 .9 -4.05 338.7 0.20 1 2 5 1755 0 88.8 35 17.3 9 2 716.5 711.3 -16 4 1.00 0.203 1 00 0.4 143.2 46.1 -8.73 716.0 0.20 128 2080 0 88.8 35 16.2 9.9 604.9 600.8 -17.48 1.00 0.198 1 00 0.4 121.5 39.1 -6.95 607.4 0.20 145 1330 0 88.9 35 20 10.1 726.1 722.4 -21.26 0.99 0.199 1 00 0.4 146.9 47.2 -6.91 734.5 0.20 165 2510 0 87.4 35 19.2 10.6 816.7 811 8 -18.07 1.00 0.198 1 00 0.4 164.5 53.7 -9.1 822.5 0.20 191 1965 0 87.4 35 17.1 9 7 712.1 710.5 -19.02 1.00 0.189 1 00 0.4 137.3 44.9 -7.22 686.7 0.20 201 2845 0 86.5 35 18.6 9.9 821.2 816.5 -17.79 1.00 0.205 1 00 0.4 165.4 54.6 -9.3 826.8 0.20 214 3745 1 87.9 35 18.2 10.4 669.5 664.7 -17.15 1.00 0.196 1 00 0.4 132.1 42.9 -7.71 660.6 0.20 233 2490 0 88.7 35 18.6 9.4 746.2 746.0 -19.04 1.00 0.197 1 00 0.4 148.0 47.6 -7.77 739.9 0.20 305 1110 1 88.1 35 17.2 9.9 899.9 899.8 -18.13 1.00 0.197 1 00 0.4 178 0 57.7 -9.82 889.8 0.20 331 1130 1 88.2 35 17.3 10.7 850.3 850.1 -19 .26 1.00 0.195 1 00 0.4 167.3 54.2 -8.69 836.6 0.20 380 3005 0 88.5 35 17.9 10.8 692.5 692.3 -18.6 1.00 0.207 1 00 0.4 140.5 45.4 -7.55 702.6 0.20 383 3030 0 87.7 35 17.7 10.3 802.8 802.6 -18.01 1.00 0.198 1 00 0.4 161.7 52.7 -8.98 808.7 0.20 387 2200 0 88.0 35 379.0 379.0 -12.156 1.00 0.197 1 00 0.4 74.0 24.0 -6.09 370.0 0.20 392 1790 0 87.1 35 18.3 9.4 760.0 759.9 -19.69 0.99 0 191 1 00 0.4 148.2 48.6 -7.52 741.0 0.20 418 2455 0 88 2 35 16.5 9 7 644.0 643.8 -16.46 1.00 0 200 1 00 0.4 128.9 41.7 -7.83 644.3 0.20 423 2265 0 88.9 35 18 9.8 663.1 662.9 -17.84 1.00 0.196 1 00 0.4 133.3 42.9 -7.47 666.4 0.20 455 2140 0 87.4 35 19.2 10 871.1 871.0 - 2 3 3 0.99 0.199 1 00 0.4 177.1 57.9 -7.6 885.5 0.20 477 920 1 87.6 35 17.1 9.5 697.2 697.0 -17.65 1.00 0.201 1 00 0.4 140.6 45.9 -7.96 703.0 0.20 494 1005 1 86.9 35 16.6 9.7 955.3 955.1 -15.94 1.00 0.200 1 00 0.4 192.7 6 3 4 -12.09 963.7 0.20 5054 1520 0 88.5 35 16.4 10.5 285.7 285.5 -10.57 1.00 0.197 1 00 0.4 54.1 17.5 -5.12 270.7 0.20 5069 1130 1 88.4 35 15.4 9.9 327.5 327.3 -11.59 1.00 0.195 1 00 0.4 '63.3 20.5 -5.46 316.3 0.20 5097 1315 0 87.7 35 15.6 9 4 485.6 485.4 -11.7 1.00 0.195 1 00 0 4 96.0 31.3 -8.2 479.9 0.20 5147 1300 0 87.8 35 15.2 9.9 428 8 428.6 -13.09 1.00 0.195 1 00 0.4 83.2 27.1 -6.36 416.2 0.20 5157 3170 0 88.6 35 16 9 5 480.4 475.0 -14.05 1.00 0.190 1 00 0.4 91.7 29.6 -6.53 458.6 0.20 5171 930 1 88.2 35 14.6 9.6 507.9 507.7 -13.21 1.00 0.197 1 00 0.4 98.7 32.0 -7.47 493.3 0.20 5205 1150 1 87.7 35 15.8 9.6 675.0 674.8 -13.06 1.00 0.196 1 00 0.4 131.0 42.7 -10.03 655.2 0.20 5222 2905 0 87.6 35 15.4 9.9 295.7 295.5 -11.81 1.00 0.196 1 00 0 4 57.3 18.7 -4.85 286.6 0.20 5261 1170 1 86.8 • 35 16.6 9.3 493 5 493.4 -14.54 1.00 0.196 1 00 0.4 96.5 31.8 -6.63 482.5 0.20 5264 3655 0 87.6 35 14.6 8.6 577.0 564.3 -13.41 1.00 0.194 1 00 0.4 110 4 36.0 -8.23 552.0 0.20 5266 1775 0 88.5 35 15.8 10.1 402.3 402.1 -13.43 1.00 0.199 1 00 0 4 80.0 25 8 -5.96 399.9 0.20 5304 3090 0 87.4 35 15.3 10.5 299 0 298.8 - 1 2 3 5 1.00 0.195 1 00 0.4 57.8 18.9 -4.68 288.8 0 20 5352 3130 0 88.4 35 15.2 8.6 284.1 284.0 -9.9 1.00 0.186 1 00 0.4 49.1 15.9 -4.95 245.3 0.20 5430 1 88.0 35 315.0 315.0 -12.425 1.00 0.197 1 00 0.4 61.0 19.8 -4.91 305.0 0.20 5451 1540 0 87.9 35 17.1 9.8 516.4 516.2 -15.31 1.00 0.194 1 00 0 4 100.5 32.6 -6.56 502.4 0.20 5455 1815 0 87.3 35 15.8 9 515.7 515.5 - 1 4 0 2 1.00 0.196 1 00 0.4 101.8 33.3 -7.26 508.9 0.20 8003 945 1 88.1 35 18 9.3 704.3 703.4 -17.72 0.99 0.201 1 00 0.4 141.5 45.9 -7.98 707.3 0.20 8046 1505 0 88.4 35 15.8 9.3 354.2 349.0 -13.97 1.00 0.196 1 00 0.4 69.6 22.5 -4.98 348.1 0.20 8060 1635 0 88.4 35 17.1 9.4 397.9 397.7 -14.02 1.00 0.195 1 00 0.4 77.2 24.9 -5.5 385.8 0.20 8071 2810 0 88.2 35 16.6 9.8 536.3 536.2 -13.93 1.00 0.195 1 00 0.4 104.5 3 3 9 -7.5 522.7 0.20 8091 3600 0 87.8 35 17.2 10 598.6 598.4 -15.08 1.00 0 2 0 0 1 00 0.4 117.1 38.1 -7.77 585.7 0.20 8119 2725 0 88.0 35 17.1 9.1 349.0 348.9 -13.42 1.00 0.195 1 00 0.4 67.4 21.9 -5.02 336.9 0.20 8128 1730 0 87.9 35 16.6 9.5 614.2 614.1 -16.25 1.00 0.196 1 00 0.4 120.0 39.0 -7.38 599.8 0.20 8161 3580 0 88.2 35 17.1 9.7 469.5 469.3 -14.07 1.00 0.198 1 00 0 4 91 3 29.6 -6.49 456.4 0.20 8162 4025 1 87.8 35 16.2 9.8 681.7 681.6 -14.82 1.00 0 196 1 00 0.4 134.3 43.7 -9.06 671.5 0.20 8174 995 1 88.1 35 17 9.7 560.8 560.6 -15.01 1.00 0.164 1 00 0.4 104.7 34.0 -6.98 523.7 0.20 8199 1160 1 88.3 35 16.1 8.8 2 6 6 0 256.5 -15.3 1.00 0.202 1 00 0.4 50.4 16.3 -3.3 252.2 0.20 8223 1075 1 87.5 35 16.1 9.9 493.3 493.2 -14.79 1.00 0.201 1 00 0.4 99.3 32.4 -6.72 496.6 0 20 8268 3680 1 88.5 35 16.5 10.1 406.4 406.2 -13.96 1.00 0.202 1 00 0 4 81 5 26 3 -5.84 407.5 0.20 8338 3335 0 88.1 35 17.6 9.7 619.7 619.5 -14.75 1.00 0.198 1 00 0.4 124.1 40.2 -8.41 620.4 0 2 0 8348 910 1 87.4 35 16.8 9.2 668.9 664.8 -16.98 1.00 0.199 1 00 0.4 134.3 43.9 -7.91 671.5 0.20 8385 3725 1 88.3 35 14.7 9 2 629 2 624.0 -15.53 1.00 0.197 1 00 0.4 1 2 5 8 40.7 -8.1 629.1 0.20 8390 1675 0 87.1 35 16.9 9 2 498.1 497.9 -16.5 1.00 0.196 1 00 0.4 99.8 32 7 -6.05 499.1 0.20 8402 3120 0 87.2 35 17.8 10.1 519.4 510.6 -17.11 1.00 0.197 1 00 0.4 102.4 3 3 6 -5 99 512 2 0.20 8405 3060 0 88.2 35 16.5 9.7 589.1 589.0 -15.43 1.00 0.197 1 00 0.4 115.6 37.5 -7.49 578.1 0.20 8419 2600 0 87.3 35 16.8 9.5 477.1 477.0 -15.27 1.00 0.197 1 00 0.4 92.8 30.4 -6.08 464.0 0.20 8431 1360 0 88.4 35 18.3 9.4 715.6 715.4 -18.2 1.00 0.198 1 00 0.4 145.2 46.9 -7.98 725.8 0.20 8448 1020 1 88.1 35 17.2 9.5 573.5 573.3 -14.59 1.00 0.197 1 00 0.4 112.8 36.6 -7.73 563.9 0.20 avg = C O V ( % ) = s u m = 20 88.0 0 .6 35 0 16.9 7.3 9.7 5.1 574.1 .30.4 572.6 30 .5 -15.63 - 1 7 . 0 4 1.00 0.3 0.20 2 . 8 1 1 1.00 0 0.4 0 113.4 3 1 . 7 36.9 3 1 . 9 -7.15 -22.08 567.2 3 1 . 7 4 Appendix II Sample Number = 005, Temperature = 20°C nominal spec failure c.c. width thickness weight meter M C T T F T T F @ stiff- coeff rate of coeff pre max U T S estimated corrected rate of number location initial final intial final initial final M C inital final max load ness deter loading deter load load deflection T T F loading (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) <%) (%) (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) (mm) (kN/s) 20 1335 0 8 8 . 7 35 18.3 10.8 848 1 839.5 -19.52 1.00 0.203 1.00 0 4 171.7 55 3 -8.8 858.7 0.20 21 4100 1 87.9 35 18.4 9.5 613.5 613.3 -18.77 1.00 0.203 1 00 0.4 122.1 39.7 -6.51 610.6 0.20 37 880 1 87.8 35 17.4 10.3 912.9 912.7 - 1 8 3 7 1.00 0.204 1 00 0.4 185.8 60 4 -10.12 928.9 0.20 50 68 1400 0 88.8 35 16.4 10.3 491 9 491.7 -16.16 1.00 0.204 1 00 0.4 100.2 3 2 2 -6.2 500.9 0.20 1460 0 88.4 35 18.9 11.1 696.7 696.5 -19.45 1.00 0.205 1 00 0.4 141.5 45.8 -7.28 707.7 0.20 69 3705 1 88 4 35 18.7 10.6 729.4 729.3 -19.35 1.00 0.192 1 00 0.4 144.3 46.7 -7.46 721.4 0.20 80 2195 1 87.7 35 22.1 10.6 1098.6 1098.4 -23 42 0.99 0.201 1 00 0.4 220.5 71.9 -9.41 1102.7 0.20 84 910 1 88 5 35 18.6 9.4 732.8 732.6 -16.74 1.00 0.202 1 00 0.4 146.0 47.1 -8.72 730.1 0.20 87 1880 0 87.8 35 18 10.4 729.0 728.8 -19.58 0.99 0.209 1 00 0.4 145.2 47.2 -7.41 725.8 0.20 97 3565 0 88.5 35 18 1 0 7 458.4 458.2 -16.51 1.00 0.180 1 00 0.4 85 8 27.7 -5.2 429.2 0.20 117 1590 0 88.4 35 18 10.5 644.1 643.9 -19.04 1.00 0.202 1 00 0.4 130.3 42.1 -6.84 651.6 0.20 151 1885 0 89.1 35 17.6 9.4 404.3 404.1 -17.96 1.00 0.201 1 00 0.4 81.5 26.1 -4.54 407.5 0.20 192 1810 0 88.4 35 16.5 9.9 742 2 742.0 -17.44 1.00 0.200 1 00 0.4 149.3 48.3 -8.56 746.4 0.20 220 1720 0 87.9 35 18.7 10.7 847.0 846.8 -17.56 1.00 0.190 1 00 0.4 163.4 53.1 -9.31 817.0 0.20 222 1220 0 87.5 35 18.8 10.7 769.6 769.5 -19.04 0.99 0.200 1 00 0.4 154.9 50.6 -8.14 774.7 0.20 232 1260 0 86.7 35 17.1 9.6 786.2 786.1 -18.01 1.00 0.205 1 00 0.4 158.8 52.4 -8 82 794.2 0.20 237 1090 1 88.1 35 17.3 10.6 724 8 683.6 -16.2 0.99 0.178 1 00 0.4 131.0 42.5 -8.09 655.2 0.20 253 1225 0 87.2 35 17.7 9 3 5 8 9 0 588.8 -16.74 1.00 0.197 1 00 0.4 116.5 38.1 -6.96 582.4 0.20 301 1155 1 86.9 35 18 9 8 637.6 637.4 -18.56 1.00 0.198 1 00 0.4 126.7 41.7 -6.83 633.5 0.20 359 900 1 88.9 35 18.3 9.7 790.6 790.5 -18.17 1.00 0.196 1 00 0.4 157.5 50.7 -8.67 787.7 0.20 417 1940 0 87.3 35 17.8 9.6 1238.1 1237.9 -19 77 0.99 0.194 1 00 0.4 243.3 79 6 -12.31 1216.7 0.20 430 1325 0 88.9 35 18.8 9 5 812.2 812.1 -19.5 1.00 0.205 1 00 0.4 163.2 52 5 - 8 3 7 815.9 0.20 488 2640 0 88.2 35 19.4 9.8 633.8 630 8 -18.72 0.99 0.198 1 00 0.4 126.7 41.0 -6.77 633.5 0.20 5043 2795 0 87.6 35 15 10.2 542.8 542.7 -11.56 1.00 0.198 1 00 0.4 107.1 34.9 -9.26 535.7 0.20 5144 1310 0 88.0 35 17.1 10.3 407.3 407.2 -12.52 1.00 0.195 1 00 0.4 79.8 25.9 -6.37 398.8 0.20 5166 2310 0 88.0 35 15.4 10.2 293.8 2 9 3 6 -11.69 1.00 0.200 1 00 0.4 57.0 18.5 -4.87 284.8 0.20 5177 1655 0 87.5 35 15.4 9 6 502.3 502.1 -11.9 1.00 0.191 1 00 0.4 95.4 31.2 -8.02 477.0 0.20 5183 3420 0 88.1 35 15.2 10 432.9 432.7 -11.62 1.00 0.198 1 00 0.4 84.5 27.4 -7.27 422.7 0.20 5188 3280 0 88.3 35 14.9 9 573.1 565.0 -14.27 1.00 0.202 1 00 0.4 114.1 3 6 9 -7.99 570.5 0.20 5191 910 1 87.7 35 16.7 9.6 545.1 544.9 -14.15 1.00 0.200 1 00 0.4 109.3 35.6 -7.72 546.6 0 20 5206 1375 0 88.5 35 15.4 9.7 275.5 275.3 -8.84 1.00 0.193 1 00 0.4 52.4 16.9 -5.93 262 0 0.20 5280 2760 0 8 8 2 35 15.1 9.4 521.6 521.5 -13.06 1.00 0.199 1 00 0.4 103.7 33.6 -7.94 518.3 0.20 5305 3090 0 88.3 35 16.8 10.1 443 6 443.5 -13.86 1.00 0.204 1 00 0.4 88.7 28.7 -6.4 443.4 0.20 5320 900 1 87.0 35 17.3 9 5 701.9 691.9 -14.99 1.00 0.199 1 00 0.4 138.2 45.4 -9.22 691.0 0 20 5347 1210 1 86.7 35 15.8 9 4 302 2 302.1 -13.96 1.00 0.199 1 00 0.4 58.3 19.2 -4.17 291.3 0.20 5367 3285 0 88.6 35 14.9 9 4 380.2 380.0 -13.26 1.00 0.198 1 00 0 4 7 5 2 24.2 -5.67 376.0 0.20 5386 3330 0 88 2 35 16.8 9.7 315 5 315.3 -11.62 1.00 0.192 1 00 0.4 61.1 19.8 -5.26 305.4 0 2 0 5390 3895 1 87.0 35 15.5 9.1 482.9 482.7 -15.52 1.00 0.194 1 00 0.4 94.1 30.9 -6.06 470.5 0.20 5398 2155 0 88.6 35 15.6 9.5 397.9 393.3 -12.53 1.00 0.194 1 00 0.4 76.7 24.7 -6.12 383.3 0.20 5417 3245 0 88.3 35 15.4 9.7 431.0 430.9 -13.5 1.00 0.201 1 00 0.4 85.8 27.8 -6.36 429.2 0 2 0 5419 2320 0 87.9 35 15.1 9.2 226 1 225.9 -12.63 1.00 0.197 1 00 0.4 42.9 14.0 -3.4 214.7 0.20 5474 3180 0 87.9 35 15 8 9 260.9 260.7 -11.47 1.00 0.197 1 00 0 4 51.1 16.6 -4.45 255.5 0.20 8004 1540 0 88.2 35 16.9 9 603.3 581.5 -16.51 1.00 0.202 1 00 0.4 117.6 38.1 -7.12 587.8 0.20 8009 1635 0 88.5 35 16.4 9.3 482.5 482.4 -13.72 1.00 0.190 1 00 0.4 91.6 29.6 -6.68 458.2 0.20 8074 1605 0 88.5 35 17 9.7 483.7 471.6 -13.52 1.00 0.202 1 00 0.4 95.6 30.9 -7.07 478.1 0.20 8097 1545 0 87.3 35 17.6 10.2 613.7 601.9 -15.25 1.00 0.204 1 00 0.4 123.0 40.3 -8.06 615.0 0.20 8102 1170 1 86.8 35 16.4 9.9 492 2 483.6 -15.18 1.00 0.202 1 00 0.4 98.2 32.3 -6.47 490.8 0.20 8157 2710 0 88.3 35 17.1 9.7 481.2 473.7 -16.89 1.00 0.197 1 00 0 4 93.7 30.3 -5.55 468.4 0.20 8179 1185 1 86 8 35 17.4 9.6 616.1 615.9 -18.17 1.00 0.200 1 00 0.4 121.3 39.9 -6.67 606.3 0 20 8186 2080 0 87.9 35 17 9.8 500.2 500.0 -15.17 1.00 0.205 1 00 0.4 100.6 32.7 -6.63 503.1 0.20 8226 2540 0 89.3 35 15.8 9.2 521.0 520.8 -15.57 1.00 0.200 1 00 0.4 103.8 33.2 -6.67 519.0 0.20 8238 2530 0 88.8 35 15.6 9.6 272.6 272.5 -14.6 1.00 0.199 1 00 0.4 54.1 17.4 -3.71 270.7 0 20 8285 3070 0 87.9 35 16 9.8 680.4 680.2 -15.09 1.00 0.194 1 00 0.4 134.5 43.7 -8.91 672.6 0.20 8297 3205 0 87.9 35 16.8 9.9 421.7 421.6 -14.35 1.00 0.202 1 00 0.4 85.2 27.7 -5.94 426 0 0 20 8317 3225 0 88.3 35 18.8 9.9 905.8 905.7 -18.18 1.00 0.198 1 00 0.4 181.8 58.8 -10 909.0 0.20 8320 1185 1 86.3 35 17.4 10.3 836.5 836.3 -18.32 1.00 0.205 1 00 0.4 169 3 56.0 -9.24 846.3 0.20 8363 1035 1 87.6 35 17.3 9.3 772.9 772.7 -16.52 1.00 0.200 1 00 0.4 155.7 50 8 -9.43 778.6 0.20 8371 2795 0 87.8 35 . 18.2 9.5 702.0 688.6 -15.41 1.00 0.203 1 00 0.4 134.1 43.7 -8.7 670.7 0.20 8437 3530 0 87.5 35 17 9 2 610.6 610.4 -16.37 1.00 0.206 1 00 0.4 122 3 39.9 -7.47 611.4 0.20 8446 3875 1 88.1 35 17.2 9.4 319.5 319.4 -17.63 1.00 0.205 1 00 0.4 64.1 20.8 -3.64 320.6 0.20 avg = 88.0 35 17.1 9.8 588.0 585.4 -15.90. 1.00 0.20 1.00 0.4 116.5 37.9 -7.20 582.3 C O V ( % ) = 0 .7 0 8.2 5 .3 35 .3 35 .4 -17 .78 0.3 2 .856 0 0 36 36.1 -24 .60 3 5 . 9 6 s u m = 17 Appendix II Sample Number = 006, Temperature = 20°C spec number failure location (mm) c c . width initial final (mm) (mm) thickness intiai final (mm) (mm) . weiqht initial final (lb) (lb) meter M C (%) M C inital final (%) (%) T T F (s) T T F ® max load (s) stiff-ness (kN/mm) coeff deter rate of coeff pre loading deter load (kN/s) (kN) max load (kN) U T S (MPa) estimated deflection (mm) corrected T T F (mm) nominal rate of loading (kN/s) 23 88 1810 0 88 .8 35 17.5 10.1 327.2 321.5 -16 1.00 0.200 1.00 0.4 65.4 21.0 -4.08 326.8 0.20 1950 0 88.8 35 16.3 9.9 535.6 530.1 -16.21 1.00 0.196 1 00 0.4 107.1 34.5 -6.6 535.3 0.20 135 1795 0 88 6 35 18.2 10.5 641.0 640.9 -17.12 1.00 0.201 1 00 0.4 128.4 41.4 -7.5 642.1 0.20 141 3710 1 87.9 35 1 7 8 10.1 615.8 610.6 -18.54 1.00 0.199 1 00 0.4 124.2 40.4 -6.7 621.1 0 20 1 4 3 3310 0 87.7 35 18.2 10.5 1047.2 1047.1 -20.09 1.00 0.200 1 00 0.4 212.9 69.4 -10.6 1064.7 0.20 149 3215 0 88 4 35 17.2 10 5 1013.0 1009.9 -18.75 0.99 0.200 1 00 0.4 196.9 63.6 -10.5 984.3 0.20 177 1740 0 88.5 35 18.9 10.1 761.6 761.4 -17.15 1.00 0.201 1 00 0.4 153.0 49.4 -8:92 764.9 0 2 0 1 7 8 1690 0 89 5 35 17.2 9.6 425.6 425 5 -16.47 1.00 0.199 1 00 0.4 85.4 27.3 -5.19 427.1 0.20 247 1230 0 87.5 35 17.1 9.5 744.5 744.4 -17.9 1.00 0.201 1 00 0.4 1 5 1 . 0 49.3 -8.43 755.1 0.20 290 1490 0 86.9 35 18.6 10.1 8B6.9 886 7 -19.19 1.00 0.200 1 00 0.4 180.0 59.2 -9.38 899.9 0.20 308 3945 1 87.3 35 16.8 10.3 418.6 418.4 -18.4 1.00 0.199 1 00 0.4 84.8 27.7 -4.61 423.8 0.20 361 1325 0 88.2 35 19 9.4 782.0 7 8 1 . 8 -18.89 1.00 0.202 1 00 0.4 159.5 51.6 -8.44 797.5 0.20 371 1315 0 87.4 35 18.8 9.4 972.7 963.7 -17.79 1.00 0.199 1 00 0.4 196 6 64.3 -11.05 983.2 0.20 373 1500 0 87.3 35 18.2 9.4 775.5 775.3 -17.33 1.00 0.202 1 00 0.4 157.5 51.5 -9.09 787.7 0.20 389 1300 0 86.8 35 17.8 9.8 917.8 917.6 -17.48 1.00 0.195 1 00 0.4 178.0 58.6 - 1 0 . 1 8 889.8 0.20 395 2515 0 88.2 35 19.3 10.6 1024.9 1020.5 -19.93 1.00 0.204 1 00 0.4 208.2 67.5 -10.45 1041.1 0.20 397 3940 1 87.5 35 18.4 10 819.0 818.8 -19.63 1 00 0.203 1 00 0.4 165.3 54.0 -8.42 826.4 0.20 432 2075 0 88.7 35 17.5 9.9 681.3 678.5 -18.76 1.00 0.194 1 00 0.4 132.8 42.8 -7.08 663.9 0.20 447 1610 0 88.3 35 17.9 9.5 926.1 9 1 9 8 -19.6 1.00 0 202 1 00 0.4 188.4 60.9 -9.61 941.9 0.20 474 3020 0 88.0 35 19 10.5 967.6 967.5 -21 0.99 0.204 1 00 0.4 196.4 63.8 -9.35 982.1 0.20 5017 3085 0 88.3 35 15.2 9.9 346.3 346.1 -12.04 1.00 0.201 1 00 0.4 65.4 21.2 -5.43 327.1 0.20 5024 1505 0 88.5 35 14.3 9.2 236.7 236.5 -11.9 1.00 0.198 1 00 0.4 46.3 14.9 -3.89 231.6 0.20 5044 910 1 87.8 35 17.2 9.9 575.1 574.9 -13.93 1.00 0.198 1 00 0.4 114.2 37.2 -8.2 5 7 1 . 2 0.20 5119 1755 0 87.9 35 16 10 312.9 307.9 -13.22 1.00 0.198 1 00 0.4 6 2 0 20.2 -4.69 310.1 0.20 5132 3790 1 88.7 35 15.5 9.8 317.8 312.9 -12.39 1.00 0.197 1 00 0.4 62.2 20.0 -5.02 310.9 0.20 5160 2750 0 88.9 35 14.5 9.4 224.0 217.7 -9.48 1.00 0.194 1 00 0.4 42.6 1 3 . 7 -4.5 213 2 0.20 5184 3335 1 87.4 35 14.9 8.8 345.9 345.8 -11.3 1.00 0.196 1 00 0.4 68.0 22.2 -6.02 340.2 0.20 5185 1770 0 88.3 35 15.9 9.2 549.0 548.8 -14.1 1.00 0.198 1 00 0.4 109.7 35.5 -7.79 548.7 0 20 5231 3705 1 87.3 35 15.7 10 403.5 403.4 -12.92 1.00 0.197 1 00 0.4 80.2 26.3 -6.21 401.0 0.20 5254 3715 1 87.0 35 16.8 9.5 547.4 547.2 -14.45 1.00 0.200 1 00 0.4 110.0 36.1 -7.61 549.8 0.20 5263 3305 0 88.2 35 16 9.6 377.5 377.3 -12.83 1 .00 0.202 1 00 0.4 74.6 24.1 -5.81 372.8 0.20 5321 1610 0 88.0 35 16 9.9 348.0 347.8 -12.29 1 .00 0.197 1 00 0.4 69.2 22.5 -5.63 346.0 0.20 5348 2570 0 87.7 35 16.4 8 9 373.7 373.5 -13.56 1.00 0.200 1 00 0.4 74.3 24.2 -5.48 371.7 0.20 5373 3525 0 87.1 35 1 7 . 1 9.3 658.8 658.6 -14 .73 1.00 0.202 1 00 0.4 131.7 43.2 -8.94 658.4 0.20 5376 1040 1 87.5 35 15.4 9.3 591.8 591.6 -13.49 1.00 0.192 1 00 0.4 114.1 37.3 -8.46 570.5 0.20 5448 3230 0 88.2 35 14 9.2 254.1 254.0 -10.12 1.00 0.195 1 00 0.4 49.4 16.0 -4.87 246.8 0.20 5469 3005 0 88.1 35 16 9.4 320.9 320.7 -12.14 1.00 0.197 1 00 0.4 63.7 20.7 -5.25 318.5 0.20 8002 3640 0 87.2 35 17 9.1 424.0 423.8 -13.77 1.00 0.192 1 00 0.4 81.1 26.6 -5.89 405.4 0.20 8035 2055 0 87.8 35 14.8 9 1 509.7 509.6 -14.49 1.00 0.195 1 00 0.4 98.9 32.2 -6.82 494.4 0.20 8040 2520 0 87.6 35 1 6 8 10 554.6 554.4 -16.06 1.00 0.194 1 00 0.4 108.6 35.4 -6.76 542.9 0.20 8042 960 1 86.8 35 16.1 9.5 803.7 803.5 -16.79 1.00 0.197 1 00 0.4 159.5 52.5 -9.5 797.5 0.20 8043 2860 0 87.9 35 15.6 9.1 2 8 3 5 283.3 -14.91 1.00 0.195 1 00 0.4 55.2 17.9 -3.7 276.1 0.20 8048 2210 0 87.6 35 17 10.5 808.6 808.4 -15.24 1.00 0.198 1 00 0.4 160.1 52.2 -10.51 800.7 0.20 8 1 1 3 1720 0 88.0 35 17.5 10.5 577.0 576.8 -17.57 1.00 0.209 1 00 0.4 116.5 37.8 -6.63 582.4 0.20 8116 3320 0 87.1 35 17.5 10.6 791.5 784.2 -16.95 1.00 0.195 1 00 0.4 154.9 50.8 -9.14 774.7 0.20 8147 2200 0 88.3 35 15.4 11.1 793.4 787.6 -13.07 1.00 0.202 1 00 0 4 156.9 50.8 -12.01 784.4 0.20 8184 1800 0 88.5 35 18.6 9.7 447.3 447.2 -16.67 1.00 0.197 1 00 0.4 86.7 28.0 -5.2 433 6 0.20 8210 3090 0 88.1 35 16.6 9.7 517.2 517.0 -13.51 1.00 0.195 1 00 0.4 100.8 32.7 -7.46 503.8 0.20 8216 3095 0 88.4 35 16.4 9.8 315.9 315.7 -14.18 1.00 0.199 1 00 0.4 62.8 20.3 -4.43 314.1 0.20 8232 2960 0 88.3 35 16.8 10.1 662.4 662.3 -15.17 1.00 0.197 1 00 0.4 130.7 42.3 -8.62 653.4 0.20 8251 1235 0 88.4 35 17.4 10.1 4 1 1 . 7 402.3 -17 .36 1.00 0.197 1 00 0.4 79.8 25.8 -4.59 398.8 0.20 8276 1895 0 88.3 35 15.6 10.1 535.2 535.0 -15.31 1.00 0.199 1 00 0.4 108.0 34.9 -7.05 540.0 0.20 8302 2465 0 88.4 35 17 9.9 557.7 557.5 -15.04 1.00 0.184 1 00 0.4 109.1 35.3 -7.25 545.5 0.20 8347 3955 1 87.2 35 16.4 9.6 5 1 7 . 2 517.0 -13.57 1.00 0.195 1 00 0.4 100.9 33.1 -7.44 504.6 0 20 8351 3335 0 88.0 35 15.8 9.1 507.2 507.0 -14.58 1.00 0.193 1 00 0.4 98.1 31.8 -6.73 490.4 0.20 8364 3040 0 87.6 35 16.6 9.2 433.4 433.3 -15.76 1.00 0.201 1 00 0.4 87.1 28.4 -5.53 435.4 0.20 8366 2195 0 87.0 35 17.7 8.9 650.2 650.0 -17.41 1.00 0.173 1 00 0.4 123.0 40.4 -7.06 615.0 0.20 8400 2275 0 87.2 35 1 6 7 8.9 653.3 644.8 -16.71 1.00 0.202 1 00 0.4 127.6 41.8 -7.64 638.2 0.20 8460 3680 1 88.3 35 17 9 8 631.4 631.2 -15.61 1.00 0 196 1 00 0.4 126.3 40.9 -8.09 631.3 0.20 8464 2790 0 87.8 35 17 9.7 646.4 646.2 -15.32 1.00 0 193 1 00 0.4 126.3 41.1 -8.24 631.3 0 20 avg = C O V ( % ) = s u m = 12 87.9 0.7 35 0 16.8 7.4 9.8 5 . 3 585.0 37 .9 583.4 3 7 . 9 -15.60 -16 .79 1.00 0.2 0.20 2 . 5 2 8 1.00 0 0.4 0 116.1 38 .7 37.8 3 8 . 9 -7.27 -28.02 580.7 38 .71 Appendix II Sample Number = 007, Temperature = 20°C nominal spec failure c.c. width thickness weight meter M C T T F T T F @ stiff- coeff rate of coeff pre max U T S estimated corrected rate of number location initial final intial final initial final M C inital final max load ness deter loading deter load load deflection T T F loading (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) (mm) (kN/s) 10 1120 1 8 8 . 4 35 17.7 9 2953.4 2953.2 -19.34 1.00 0.066 1.00 0.4 193.7 6 2 7 -10.02 2891.6 0.07 31 2095 0 87.0 35 17.9 9.5 2687.0 2682.8 -18.05 1.00 0.071 1.00 0.4 1 8 2 7 60.0 -10.12 2727.3 0.07 66 2470 0 87.9 35 16 9.3 1882.0 1881.8 -18.35 1.00 0.068 1.00 0.4 123.8 40.2 -6.75 1847.6 0.07 74 86 995 1 88.8 35 17.2 9.5 1593.7 1593 6 -17.11 0.99 0.062 1.00 0.4 92.7 29.8 -5 42 1383.9 0.07 2355 0 88.2 35 17 9.5 1786.4 1786.2 -16.85 1.00 0.069 1.00 0.4 120.2 38.9 -7.13 1793.6 0.07 106 1410 0 88.6 35 18.6 10 2561 2 2561.1 -20.19 0.99 0.071 1.00 0.4 174.3 56.2 -8.63 2600.9 0.07 138 1175 1 88.3 35 17.6 10.3 1679.9 1679.7 -15.58 1.00 0.073 1.00 0.4 113.0 36.6 -7.25 1686.6 0.07 157 1070 1 87.6 35 16.8 9 8 1709.1 1708.9 -17.65 1.00 0.070 1.00 0.4 115.8 37.8 -6.56 1727.6 0.07 174 2945 0 88.3 35 18.5 10.5 2791.6 2791.5 -18.41 1.00 0.070 1.00 0.4 188.1 60.9 -10.22 2807.3 0.07 185 2795 0 87.4 35 16 8 9.1 2890 6 2890.5 -18.75 0.99 0.068 1.00 0.4 196.9 64.4 -10.5 2938.1 0.07 189 880 1 86.8 35 19.9 9.2 2822 1 2821.9 -20.89 1.00 0.071 1.00 0.4 192.5 63.4 -9.22 2873.3 0.07 209 1340 0 87.5 35 16 3 9.3 3179.7 3179.5 -18.3 1.00 0.070 1.00 0.4 214.9 70.2 -11.74 3207.3 0.07 231 3880 1 86.6 35 18.8 9.1 2026.9 2026.8 -22.42 0.99 0.069 1.00 0.4 135.7 44.8 -6.05 2024.8 0.07 284 2710 0 86.6 35 18.5 9.3 2839.1 2838.9 -20.32 1.00 0.069 1.00 0.4 188.8 62.3 -9.29 2818.2 0.07 291 2120 0 87.9 35 17 9 9.3 1406.7 1406.5 -16.77 1.00 0.070 1.00 0.4 95.0 30.9 -5.67 1418.5 0.07 315 3020 0 87.5 35 19 4 9.1 2353.5 2353.3 -18.9 1.00 0.071 1.00 0.4 159.8 52.2 -8.45 2384.8 0.07 321 2475 1 88.3 35 18 9 9 2232.9 2225.4 -16.58 1.00 0.069 1.00 0.4 151.2 48.9 -9.12 2257.2 0.07 402 2850 0 88.7 35 17.2 10.4 2332 5 2332.3 -16.75 1.00 0.070 1.00 0.4 157.0 50.6 -9.37 2342.5 0.07 438 1175 1 89.2 35 1 7 8 9.1 2474.9 2474.7 -16.42 1.00 0.067 1.00 0 4 164.1 52.6 -9.99 2449.6 0.07 469 3425 0 89.0 35 17.8 1 1 3 1956.6 1956.5 -20.22 0.99 0.066 1.00 0.4 129.3 41.5 -6.39 1929.7 0.07 482 1165 1 87.4 35 18.4 10.8 2053 2 2053.0 -18.04 0.99 0.070 1.00 0.4 140.0 45 8 -7.76 2089.7 0.07 5085 1410 0 88.4 35 14.4 9.7 973.8 973.6 - 1 0 7 2 1.00 0.068 1.00 0.4 64.8 20.9 -6.04 966.7 0.07 5092 3930 1 88.5 35 15.4 9.8 1417.7 1417 6 - 1 2 7 3 1.00 0.068 1.00 0.4 92.7 29.9 -7.28 1383.9 0.07 5101 2900 1 88.5 35 15.4 9.9 1197.1 1179.0 -13.88 1.00 0.067 1 00 0.4 77.2 24.9 -5.56 1151.5 0.07 5114 1445 0 88.0 35 16.7 9.3 1377.2 1373.7 -13.44 1.00 0.068 1.00 0 4 91.8 29.8 -6.83 1369.9 0.07 5170 1310 0 88.4 35 14.6 9.6 1201.4 1201.3 -11.46 1.00 0.068 1.00 0.4 79.2 25.6 -6.91 1181.8 0.07 '5207 2325 0 88.5 35 13.8 9 4 524.1 518.5 -10.02 1.00 0.068 1.00 0.4 3 4 7 11.2 -3 46 517.2 0.07 5234 985 1 87.8 35 15 6 9.3 1310.9 1310.7 -13.32 1.00 0.060 1.00 0.4 76.7 25.0 -5.76 1145.1 0.07 5256 1280 0 88.0 35 15 8.9 1299.8 1299.6 -13.91 1 00 0.059 1.00 0.4 75.9 24.6 -5.45 1132.1 0.07 5293 2575 0 87.2 35 17.8 9.8 1702.0 1701.8 -13.24 1.00 0.057 1.00 0.4 96.8 31.7 -7.31 1444.5 0.07 5306 2570 0 88.4 35 15.7 9.4 1555.0 1554.9 -12.12 1 00 0 059 1.00 0.4 90.0 29.1 -7.42 1342.8 0.07 5307 3020 0 87.1 35 17.8 9.9 1410.4 1410.2 -14.67 1.00 0 0 6 1 1.00 0.4 82.8 27.2 -5.65 1235.8 0.07 5311 1070 1 88.4 35 15.9 9.5 1438.4 1426.7 -13.34 1 00 0.060 1.00 0.4 82.1 26.5 -6.15 1225.1 0.07 5354 2980 0 88.1 35 15 8.2 1284.0 1284.0 -14.046 1.00 0.066 1.00 0.4 87.0 28.2 -6.19 1298.8 0.07 5369 3895 1 88.8 35 15.5 8.7 1284.7 1284.7 -13 36 1.00 0.067 1.00 0.4 85.1 27.4 -6.37 1269.9 0.07 5395 1620 0 87.8 35 14.6 8.3 1140.4 1085 2 -12 19 1.00 0 0 6 8 1.00 0.4 7 4 0 24.1 -6.08 1105.1 0.07 5396 1395 0 87.6 35 15.9 8.4 1212.5 1212.4 -12.79 1.00 0.069 1.00 0.4 83.7 27.3 -6.55 1249.9 0.07 5401 2385 0 87.8 35 15.2 9.1 1225.8 1149.0 -12.34 1.00 0.068 1.00 0.4 78.5 25.5 -6.36 1171.0 0 0 7 5406 3720 1 88.7 35 15.6 8.9 1012.9 1012.7 -12.96 1.00 0.069 1.00 0.4 69.9 22.5 -5.4 1043.4 0 0 7 5412 2475 0 87.8 35 16.5 10.2 1101.4 1101.2 -13.57 1.00 0.067 1.00 0.4 72.9 23.7 -5.37 1087.8 0.07 5414 1120 1 88.5 35 16.4 10.1 928.8 928.6 -12.72 1.00 0.069 1.00 0.4 62.0 20.0 -4.87 924.6 0.07 8006 950 1 88.6 35 16.6 8.9 2139.8 2139 8 -18.08 1.00 0.067 1.00 0.4 147.8 47.7 -8.175 2206.0 0.07 8045 3515 0 88.1 35 17.5 9.1 1301.3 1301.3 -16.87 1.00 0.068 1.00 0.4 90.0 29.2 -5.336 1343.4 0.07 8061 1840 0 87.3 35 17.2 9.2 1757.2 1757.1 -15.82 1.00 0.069 1.00 0.4 119.3 39.1 -7.54 1780.6 0.07 8083 2415 0 88.0 35 15.6 9.4 2618.4 2618.3 -15.05 1.00 0.068 1.00 0.4 172.6 56.0 -11.47 2576.1 0.07 8087 2830 0 88.6 35 16.7 9.1 1815.1 1815.0 -15.05 1.00 0.069 1.00 0.4 121.5 39.2 -8.08 1814.0 0.07 8132 2320 0 87.6 35 18.4 9.4 1662.6 1662.5 -15.31 1.00 0.069 1.00 0 4 112.4 36.7 -7.34 1677.9 0.07 8241 3155 0 88.4 35 16.9 9.4 2261.8 2261.6 -17.67 1.00 0.068 1.00 0.4 156.4 50.5 -8.85 2334.0 0.07 8261 2995 0 88.4 35 16.4 9.6 930.9 930.7 -13.94 1.00 0.068 1.00 0.4 63.6 2 0 6 -4.56 949.4 0.07 8269 930 1 88.5 35 15.5 9.9 1197.6 1197.4 -15.59 1.00 0.094 1.00 0.4 107.4 3 4 6 -6.89 1602.2 0.07 8270 3510 0 87.1 35 17 9 6 1323.7 1323.6 -15.11 1.00 0.068 1.00 0.4 89.1 29.2 -5.9 1329.9 0.07 8290 3020 0 88.3 35 16.6 10.1 1289 2 1289.1 -16.52 0.99 0.061 1.00 0.4 76.7 24.8 -4.64 1144.0 0.07 8293 2600 0 88.5 35 17 9.3 1731.7 1731 5 -16.82 1.00 0.068 1.00 0.4 109.3 35.3 -6.5 1631 5 0.07 8308 2715 0 88.1 35 16.4 8 5 2419 6 2419.4 -16.13 1.00 0.071 1.00 0.4 166.9 54.1 -10.35 2490.7 0.07 8332 2155 0 87.1 35 16.6 8.8 2483.6 2483.4 -17.71 1.00 0.068 1.00 0.4 169.6 55.6 -9.58 2530.6 0.07 8368 1045 1 87 2 35 16.8 9.3 1391.9 1391.7 -16.96 1.00 0.069 1.00 0.4 93.7 30.7 -5.52 . 1398.1 0.07 8379 1765 0 88.2 35 16.9 10 2025.8 2025.6 -15.7 1.00 0.067 1.00 0.4 133.4 43.2 -8.5 1991.3 0.07 8436 1730 0 88.7 35 15.5 9.9 1472.2 1472.1 -14.34 1.00 0.072 1.00 0.4 98.2 31.6 -6.84 1464.9 0.07 8445 1075 1 88.2 35 18.2 10.1 1697 2 1697.0 -15.34 1.00 0.069 1.00 0.4 114.5 37.1 -7.47 1709.3 0.07 8449 2170 0 8 8 2 35 16.2 9.2 2069.5 2064.3 -15.98 1.00 0.065 1.00 0.4 134.9 43.7 -8.44 2014.0 0.07 avg = 2177 88.0 35 16.7 9.5 1773.3 1770.1 -15.78 1.00 0.07 1.00 0.4 117.7 38.2 -7.31 1757.2 0.07 COV<%) = 0 .7 0 7 .7 6.2 3 4 . 7 34 .9 -16 .96 0.3 7 . 0 9 2 0 0 36 .2 3 6 . 4 -25 .19 3 6 . 1 7 s u m = 20 Appendix II Sample Number = 008, Temperature = 20°C spec failure c c . width thickness weiqht meter M C number location initial final intial final initial final M C inital final (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) 8 3175 0 8 7 . 6 35 17.8 8.9 11 915 1 88.8 35 16.8 9.5 27 2375 0 35.0 88.6 17 9.3 41 1375 0 88.6 35 17.6 10.1 55 1465 0 88.9 35 19.2 10.4 100 2320 0 87.4 35 18 9.7 108 2240 0 87.4 35 19.2 9.9 198 3520 0 87.6 35 18 9.5 283 1670 0 88.2 35 19 9.3 287 1410 0 87.7 35 18.6 9.8 313 1305 0 87.6 35 19.3 9.7 317 1535 0 87.7 35 17.5 9.4 319 2585 0 87.3 35 18.3 9.7 353 1560 0 87.2 35 18.4 9.4 365 3320 0 88 3 35 17.6 8.9 396 950 1 89.1 35 16.6 8 412 1085 1 86.9 35 18.4 8.7 424 2290 0 88.0 35 20 9.4 453 2610 0 87.7 35 19.9 8.8 476 855 1 87.5 35 17.5 8.4 484 2410 0 86.5 35 18.7 9.4 5038 3460 0 88.5 35 15.8 8.8 5130 1735 0 88.5 35 15.5 9.6 5155 2600 0 89.0 35 16.8 9.1 5156 1605 0 88.6 35 15.5 9.7 5169 1750 0 88.5 35 17.2 9.3 5221 1210 1 88.3 35 16.6 8.4 5245 1030 1 88.1 35 16.7 8.8 5272 2160 0 88.5 35 15.2 8.6 5282 1180 1 88.3 35 15.7 8.9 5287 3670 1 88.2 35 15.8 9.5 5312 3970 1 88.4 35 15.4 9.3 5314 3580 0 86.5 35 16.9 8.4 5337 1690 0 87.7 35 1 7 3 8.7 5361 2600 0 88.1 35 16.7 8.3 5415 3945 1 87.3 35 16.1 8.8 5452 1055 1 87.8 35 14.9 8.8 5454 2140 0 87.8 35 16.9 9.1 5456 2955 0 87.8 35 14.7 9 5463 1945 0 87.6 35 15.6 9.7 8011 3800 1 87.4 35 1 6 7 8.7 8016 1950 0 87.7 35 17.8 9 3 8033 2150 0 88.0 35 17.7 9 8068 2075 0 88.1 35 16.6 9.8 8084 2870 0 87.3 35 17 9 8086 3700 1 87.7 35 17.9 9.2 8117 2810 0 88.4 35 16.4 9.5 8131 3710 1 8 8 2 35 16.7 9.5 8181 1330 0 88.1 35 16.8 8.2 8193 1900 0 89.0 35 15.7 8.9 8209 2160 0 88.6 35 18 9.7 8263 1620 0 88.2 35 16.4 9.7 8281 2070 0 87.5 35 17 . 9.7 8333 2290 0 87.9 35 15.6 8.4 8342 3715 1 88.5 35 16 8.6 8381 2615 0 87.8 35 16.9 8.8 8399 2490 0 88.4 35 16.2 8.7 8415 2290 0 87.1 35 17.2 9 8439 2695 0 87.8 35 16.5 8.8 8475 1665 0 88.5 35 15.5 8.7 mean 87 1 36 17.1 9.1 OV(%) = 7 .9 19 .3 7.3 5.6 T T F T T F @ max load stiff-ness (kN/mm) coeff deter rate of loading (kN/s) coeff pre deter load max load U T S (MPa) estimated deflection corrected T T F nominal rate of loading 1497.9 2296.7 1825.2 2299.9 2326.7 1 7 7 6 2 3108.8 2357.3 1775.0 2556.2 1970.7 2702.7 1894.3 1991.3 2845.7 1871.7 2503.0 3462.1 1858 5 2618.5 1804.2 1325.9 1174.3 1071.6 1262.7 1341.5 1608.3 1461.9 868.2 1604.3 956.1 1407.2 1239.3 721.4 1392.0 803.1 1442.6 943.6 522 9 5 7 9 7 2214.9 2189.0 1807.4 1435.6 1564.7 1908.8 1211.2 2519.2 1684.3 1521.0 1597.2 1657.0 1049.1 1855.8 1990.4 1480.3 1054.8 1368.5 1408.7 1711.8 1459.4 2261.5 1779.7 2263.1 2289.2 1739.4 3068.4 2320.1 1738.2 2 5 5 6 0 1947.2 2663.1 1857.9 1967.9 2845.5 1871.6 2468.8 3424.3 1828.2 2585.2 1781.4 1292.8 1140.5 1043.7 1226.5 1 3 1 0 0 1590.4 1421.8 827.6 1604.1 921.3 1373.4 1204.4 721.3 1358.0 761.8 1407.3 899.9 522.7 533.6 2181.8 2188.9 1807.2 1435.4 1564.6 1883.9 1173.6 2472.8 1630.9 1478.5 1560.3 1612.0 1002.3 1855.7 1950.5 1480.1 1015.9 1 3 3 9 4 1362.6 1675.2 -15.64 -18.68 -18.49 -19.64 -19.88 -17.92 -20.85 -19.56 -17.38 -16.76 -19.97 -18.46 -17.27 -18.18 -19.54 -17.41 -18.85 -22.27 -21.64 -19.93 -19.5 -11.01 -10.96 -12.8 -12.38 -13.66 -14.42 -12.73 -10.29 -14.09 -11.73 -14.79 -13.55 -11.5 -14.21 -13.81 -14.08 -12.7 -11.3 -13.18 -17.44 -17.92 -17.67 -14.34 -17 -13.69 -15.8 -17.04 -16.37 -13.9 -17.15 -15.72 -16.23 -16.1 -15.33 -14.5 -15.42 -14.55 -14.23 -14.74 1.00 1.00 1.00 1.00 1.00 1.00 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00 0.99 1.00 0.99 0.99 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1 00 1.00 1.00 1.00 1.00 1.00 1.00 too 0.99 1.00 1.00 0.99 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 0.068 0.068 0.068 0.068 0.068 0.068 0.069 0.069 0.069 0.068 0.068 0.068 0.068 0.068 0.069 0.063 0.068 0.069 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.067 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.071 0.070 0.070 0.069 0.068 0.068 0.068 0.068 0.068 0.069 1705.0 36 1675.8 36 .6 -15.94 -18 .18 1.00 0.3 0.07 1 .337 1.00 0.4 101.8 33 2 -6.51 1519.1 0.07 1.00 0.4 156.6 50.4 -8.38 2337.2 0.07 1.00 0.4 121.8 39.3 -6.59 1818.4 0.07 1.00 0.4 156.7 50.5 -7.98 2338.2 0.07 1.00 0.4 159.2 51.2 -8.01 2376.1 0.07 1.00 0.4 120.4 39.4 -6.72 1796.9 0 0 7 1.00 0.4 211.2 69.1 -10.13 3152.1 0.07 1.00 0.4 160.4 52.3 -8.2 2394.5 0.07 1.00 0.4 121.5 39.4 -6.99 1813.0 0.07 1.00 0.4 176.2 57.4 -10.51 2630.1 0.07 1.00 0.4 136.6 44.6 -6.84 2039.0 0.07 1.00 0.4 184.2 60.0 -9.98 2749.0 0.07 1.00 0.4 129.4 42.3 -7.49 1930.9 0.07 1.00 0.4 135.4 44.4 -7.45 2020.6 0.07 1.00 0.4 193.2 62.5 -9.89 2883.0 0.07 1.00 0.4 125.6 40.3 -7.21 1874.6 0.07 1.00 0.4 1 7 2 2 56.6 -9.13 2569.6 0.07 1.00 0.4 236.8 76.9 -10.63 3534.8 0.07 1.00 0.4 128.4 41.9 -5.93 1916.7 0.07 1.00 0.4 179.6 58.7 -9.01 2680.9 0.07 1.00 0.4 1 2 5 0 41.3 -6.41 1866.0 0.07 1.00 0.4 88.9 28.7 -8.08 1326.7 0.07 1.00 0.4 78.2 25.2 -7.13 1166.7 0.07 1.00 0.4 71.4 22.9 -5.58 1066.1 0.07 1.00 0.4 83.7 27.0 -6.76 1248.8 0.07 1.00 0.4 89.3 28.8 -6.54 1333.1 0.07 1.00 0.4 110.2 35.6 -7.64 1644.5 0.07 1.00 0.4 96.8 31.4 -7.6 1444.5 0 07 1.00 0.4 56.9 18.4 -5.53 849.0 0.07 1.00 0.4 107.3 34.7 -7.62 1601.2 0.07 1.00 0.4 62.9 20.4 -5.36 938.7 0.07 1.00 0.4 94.0 30.4 -6.36 1403.4 0.07 1.00 0.4 82.7 27.3 -6.1 1234.8 0.07 too 0.4 47.1 15.3 -4.1 703.0 0.07 1.00 0.4 93.0 30.2 -6.55 1388.2 0.07 1 00 0.4 52.4 17.2 - 3 7 9 7B1.9 0.07 1.00 0.4 97.0 31.6 -6.89 1447.8 0.07 1.00 0.4 61.5 20.0 -4.84 918.1 0.07 1.00 0.4 38.8 12.6 -3 43 578.7 0.07 1.00 0.4 36.4 11.9 -2.77 543.9 0.07 1.00 0.4 150.3 49.1 -8.62 2243.1 0.07 1.00 0.4 150.8 49.1 -8.41 2250.7 0.07 1.00 0.4 121.0 39.3 -6.85 1806.6 0.07 1.00 0.4 96.1 31.2 -6.7 1434.8 0.07 1.00 0.4 102.9 33.7 -6.05 1535.2 0.07 1.00 0.4 128.5 41.9 -9.39 1917.9 0.07 1.00 0.4 83.2 26.9 -5.27 1242.4 0 0 7 1.00 0.4 171.5 55.6 -10.07 2559.9 0.07 1.00 0.4 111.7 36.2 -6.82 1667.2 0.07 1.00 0.4 101.3 32.5 -7.28 1511.5 0.07 1.00 0.4 110.6 35.7 -6 45 1650.9 0.07 1.00 0.4 114.1 37.0 -7.26 1702.8 0.07 1.00 0.4 70.9 23.1 -4.37 1057.5 0.07 1.00 0.4 127.2 41.4 -7.9 1898.4 0 07 1.00 0.4 133.3 43.1 -8.69 1989.3 0.07 1.00 0.4 98.1 31.9 -6.76 1463.9 0.07 1.00 0.4 69 3 22.4 -4.49 1033.7 0 0 7 1.00 0.4 91.1 29.9 -6.26 1360.1 0.07 1.00 0.4 93.0 30.3 -6.54 1388 2 0 0 7 too 0.4 116.4 37.6 -7.9 1737.3 0.07 1.00 0.4 115.4 37.5 -7.08 1721.8 0.07 0 0 3 6 . 9 37 -24.41 3 6 . 8 7 15 Appendix II Sample Number = 009, Temperature = 20°C nominal spec failure c.c. width thickness weight meter M C T T F T T F @ stiff- coeff rate of coeff pre max U T S estimated corrected rate of number location initial final intial final initial final M C inital final max load ness deter loading deter load load deflection T T F loading (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) (mm) (kN/s) 3 2410 0 8 8 . 3 '35 18.3 9.2 1621.1 1584.7 -18.1 0.99 0.068 1.00 0.4 109.2 35.4 -6.04 1630.3 0.07 42 2600 0 88.4 35 19.5 9.9 2371.6 2355.9 -18 22 1.00 0.069 1.00 0.4 163.3 52.8 -8.96 2436.6 0.07 98 3615 0 88.0 35 18.7 9.4 2787.6 2787.4 -18.58 0.99 0.069 1.00 0.4 192.2 62.4 -10.34 2867.9 0.07 107 3470 0 88.1 35 18.3 9.4 2351.8 2351.6 -17.18 1.00 0.068 1.00 0.4 160.7 52.2 -9.35 2398.8 0.07 146 1555 0 88.4 35 18.8 9.4 2618.9 2600.1 -19.96 0.99 0.068 1.00 0.4 179.8 58.1 -9 2683.0 0.07 206 3130 0 86.3 35 19.5 9.8 3381.2 3364.1 -22 46 0.99 0.068 1.00 0.4 233.1 77.2 -10.38 3478.5 0.07 300 2180 0 87.6 35 17.4 9.2 1578.1 1578.0 -16.96 1.00 0.068 1.00 0.4 106.2 34.6 -6.26 1584.9 0.07 310 3450 0 87 6 35 19.3 8.9 2436.1 2435.9 -17.25 0.99 0.068 1.00 0.4 168.4 54.9 -9.76 2513.4 0 0 7 327 1090 1 87.4 35 16.9 9 2180.8 2180.6 -16.89 0.99 0.069 1.00 0.4 149.4 48.8 -8.84 2230.1 0.07 334 1470 0 87.1 35 18.5 8.6 1978.3 1978.2 -19.49 0.99 0.068 1.00 0.4 137.7 45.2 -7.06 2055.1 0.07 349 945 1 87.1 35 14.6 8.5 1902.6 1902.5 -1668 1.00 0.068 1.00 0.4 130.6 42.8 -7.83 1949.3 0.07 354 3065 0 88.0 35 17.3 8.5 2245.2 2245.0 -17.25 1.00 0.068 1.00 0.4 155.4 50.5 -9 2318.8 0.07 366 3965 1 88.3 35 19.3 9.5 2104.2 2086.6 -18.64 0.99 0.068 1.00 0.4 144.3 46.7 -7.74 2153.4 0.07 367 1840 0 88.8 35 18.4 8.2 2100.4 2066.8 -20.62 0.99 0 0 6 8 1.00 0.4 142.0 45.7 -6.89 2118.8 0.07 379 1280 0 88.8 35 16.8 8.8 1672.7 1656.7 -17.67 1.00 0.068 1.00 0.4 116.3 37.4 -6.58 1735.2 0.07 391 1075 1 87.9 35 19.2 9.8 2571.6 2571.5 -20.44 0.99 0.064 1.00 0.4 175.6 57.1 -8.59 2620.3 0.07 460 2270 0 88.4 35 17.6 9.2 2550.7 2550.5 -18.82 0.99 0.068 1.00 0.4 176.9 57.2 -9.4 2640.9 0.07 473 3710 1 88.9 35 19.1 9.4 1633.1 1633.0 -1792 0.99 0.068 1.00 0.4 111.0 35.7 -6.19 1656.3 0.07 5016 2950 0 88.4 35 15.8 8.8 1610.5 1610.4 -13.6 1.00 0.068 1.00 0.4 108.9 35.2 -8 1624.9 0.07 5036 1638 0 88.0 35 16.3 9.3 1432.9 1432.7 -14.43 1.00 0 0 6 2 1.00 0.4 97 4 31.6 -6.75 1453.1 0.07 5040 3925 1 87.2 35 16.6 9.4 1849.0 1848.8 -15.23 1.00 0.068 1.00 0.4 127.1 41 6 -8.35 1897.3 0.07 5042 3470 0 87.7 35 16.7 8.8 824.5 794.5 -11.49 1.00 0.068 1.00 0.4 54.5 17.8 -4.74 813.3 0.07 5077 3060 0 87.3 35 15.3 9.2 693.4 693.3 -12.84 1.00 0.069 1.00 0.4 49.4 16.1 -3 84 736.6 0.07 5082 3632 0 88.3 35 15.8 9.1 1184.2 1184.0 -11.23 1.00 0.068 1.00 0.4 82.8 26.8 -7.37 1235.8 0.07 5098 1067 1 87.7 35 15.3 9 1213.0 1212.8 -11.75 1.00 0.066 1.00 0.4 81.7 26.6 -6.95 1219.7 0.07 5189 2580 0 88.6 35 . 14.3 8.4 1333.5 1333.3 -11.8 1.00 0.062 1.00 0.4 90.8 29.3 -7.69 1354.8 0.07 5192 1050 1 88.3 35 15.9 9.2 1023.1 996.7 -13.99 1.00 0.068 1.00 0.4 68.7 22.2 -4.91 1025.1 0.07 5238 1945 0 88.4 35 16.7 9.2 1099.9 1070.4 -12.66 1.00 0.068 1.00 0.4 73.2 23.7 -5.78 1093.1 0.07 5242 2435 0 87.8 35 16.2 8.6 925.5 902.0 -13.2 1.00 0.068 1.00 0.4 62.0 20.2 -4.69 924.6 0.07 5252 2125 0 88.3 35 15.4 8.8 1788.0 1759.1 -14.99 1.00 0.068 1.00 0.4 120.9 39.1 -8.06 1804.3 0.07 5295 2655 0 88.6 35 15.4 8 3 1750.3 1717.1 - 1 3 8 3 1.00 0.069 1.00 0.4 117.9 38.0 -8.53 1760.0 0.07 5308 1210 1 87.2 35 16 8.1 1445.9 1439.8 -12.26 1.00 0.066 1.00 0.4 96.9 31.7 -7.9 1445.5 0.07 5316 2105 0 86.9 35 14.8 8.7 599.3 562.5 -10.32 1.00 0.068 1.00 0.4 38.4 12.6 -3.72 573.0 0.07 5342 3525 0 87.3 35 17 8.4 967.4 930.0 -13.33 1.00 0.068 1.00 0.4 63.8 20.9 -4.79 952.7 0.07 5350 2905 0 86.5 35 17.4 8.5 1480.9 1450.1 -15.56 1.00 0.068 1:00 0.4 100.0 33.0 -6.42 1492.1 0.07 5357 2445 0 87.9 35 16.6 8.1 1347.4 1347.3 -14.01 1.00 0.068 1.00 0.4 90.7 29.5 -6.48 1353.7 0.07 5371 3560 0 88.3 35 16.7 9.4 1348.9 1322.1 -13.12 1.00 0.068 1.00 0.4 90.6 29.3 -6.91 1352.5 0.07 5405 2285 0 88.3 35 15 9.2 1422 9 1410.4 -12 3 1.00 0.069 1.00 0.4 96.3 31.1 -7.83 1436.9 0 0 7 5468 2575 0 88.3 35 15.3 8.9 1527.1 1496.5 -13.81 1.00 0.068 1.00 0.4 102.0 33.0 -7.39 1522.2 0.07 8018 1370 0 87.9 35 16.5 9.1 1783.5 1758.9 -15.63 1.00 0.068 1.00 0.4 122.8 39.9 -7.86 1832.5 0.07 8044 1070 1 87.8 35 17.4 8.5 1530.2 1530.0 -14.88 1.00 0.069 1.00 0.4 103.2 33.6 -6.94 1540.6 0.07 8082 2275 0 86.8 35 19.4 8.8 1927.4 1927.2 -18.96 0.99 0.069 1.00 0.4 131.0 43.1 -6.91 1955.7 0.07 8095 2175 0 87.7 35 16.6 8.3 1394.8 1394.6 -16.39 0.99 0.068 1.00 0.4 94.0 30.6 -5.74 1403.4 0.07 8107 2940 0 88.1 35 17 8.8 1315.6 1315.4 -14.57 1.00 0.068 1.00 0.4 88.2 28.6 -6.06 1316.9 0.07 8149 1100 1 88.1 35 17.9 8.7 1085.1 1085.0 -1422 1.00 0.066 1.00 0.4 7 2 8 23.6 -5.12 1086.7 0.07 8166 3035 0 87.8 35 16 5 8.3 1601.2 1601.0 -15.16 1.00 0.069 1.00 0.4 108.8 35.4 -7.17 1623.9 0.07 8195 3930 1 88.8 35 16.4 9.3 1773.8 1737.3 -15.56 0.97 0.068 1.00 0.4 119.8 38.5 -7.7 1788.2 0.07 8201 3650 0 88.6 35 17 8.9 1392.3 1369.9 -15.49 1.00 0.068 1.00 0.4 93.5 30.1 -6.03 1394.8 0.07 8206 3365 0 88.5 35 16.1 8.8 2001.9 1984.9 -17.05 0.99 0.068 1.00 0.4 1 3 5 6 43.8 -7.95 2023.7 0.07 8208 1935 0 88.3 35 16.6 8.7 1 7 4 4 3 1744.1 -17.36 0.99 0.068 1.00 0.4 117.6 38.1 -6.78 1755.7 0.07 8221 950 1 87.8 35 17.5 8.6 1935.8 1905.2 -17.61 1.00 0.068 1.00 0.4 130.5 42.5 -7.41 1948 1 0.07 8282 3000 0 88.4 35 15.8 8 1 933.5 909.0 -14.39 1.00 0.068 1.00 0.4 6 2 0 20.0 -4.3 924.6 0.07 8296 1175 1 88.1 35 17.9 8.7 1740 0 1 7 0 8 8 -17.99 1.00 0.068 1.00 0 4 118.0 38.3 -6.56 1761.2 0.07 8323 2945 0 88.1 35 16 8.3 1755.0 1723.1 -16.14 1.00 0.068 1.00 0.4 118.6 38.4 -7.34 1769.9 0.07 8326 3715 1 88.3 35 19.4 8.4 1933.5 1899.7 -18.5 0.99 0.068 1.00 0.4 1 3 0 2 42.1 -7.03 1942.7 0.07 8353 915 1 87.7 35 16.6 7.7 1621.1 1621.0 -17.22 0.99 0.068 1.00 0.4 111.7 36.4 -6.48 1667.2 0.07 8389 3632 0 86.6 35 18.6 9.7 1894.4 1 8 7 9 2 -17.08 1.00 0.068 1.00 0 4 129.5 42.7 -7.58 1933.0 0.07 8458 2870 0 88.4 35 16.6 9.1 1842.0 1841 8 -18.07 1.00 0.068 1.00 0.4 128.2 41.5 -7.09 1 9 1 3 6 0.07 8469 1155 1 87.8 35 16.6 8.9 1847.4 1847.2 -16.15 0.99 0.068 1.00 0.4 1 2 4 2 40.4 -7.69 1854.0 0.07 8495 965 1 88.5 35 16.2 8.6 1092 6 1064.1 -15.37 1.00 0.068 1.00 0.4 72.8 23.5 -4.74 1086.7 0.07 avg = 87.9 35 17.0 8.9 1685.0 1671.5 -15.88 1.00 0.07 1.00 0.4 114.6 37.3 -7.10 1711.1 0.07 C O V ( % ) = 0 .7 0 8.1 5.4 31 .8 32 .3 -16 .54 0.6 1 .979 0 0 32 .7 3 2 . 8 -21.44 3 2 . 6 7 18 Appendix II Sample Number = 010, Temperature - 150*C spec failure cc. width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500s ©end of loading ness deter loading deter load deflection (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) cc) CC) C O fC) CC) CC) (s) (s) (kN/mm) (kN/s) (KN) (UN) (MPa) (mm) 65 3240 0 88.4 87.5 35.1 35.0 19.6 19.4 10.1 10.4 7.5 150.3 151.8 114.8 111.5 125.3 125.8 1563.3 56.49 -13.80 1 00 1.930 1.00 0.4 109.3 35.2 -9.35 76 3575 0 88.4 87.7 35.1 34 9 20.4 20.1 9.5 11.1 8.9 150.3 151.8 112.7 113.2 124.7 125.6 1594.3 86.41 -15.90 1.00 1.980 1.00 0.4 166.9 53.9 -12.10 81 1160 1 88.7 88.0 35.2 35.0 18.0 17.8 9.3 10.8 8.3 150.4 151.9 113.4 113.8 124.9 126.1 1594.0 84.97 -13.90 1.00 1.940 1.00 0.4 163.7 52.4 -13.84 203 1240 0 87.9 86.8 35.0 35.0 17.8 17.5 9.6 11.0 8.7 150.4 151.8 113.6 112.0 124.7 125.6 1543.5 33.18 -12.82 1.00 1.920 1.00 0.4 63.7 20.7 -5.31 226 2590 0 87.4 86.9 35.3 35.1 18.9 18.7 9.8 10.8 9.3 150.1 152.0 119.1 118.0 128 8 129.4 1562.3 49.17 -12.21 1.00 1.920 1.00 0.4 94.7 30.7 -8.91 244 2780 0 88.2 87.7 35.2 35.2 17.6 17.5 9.2 10 0 8.5 150.3 151.8 114.8 117.3 126.6 127.7 1560 0 51.72 -11.78 1.00 1.970 1.00 0.4 98.6 31.7 -9.76 255 1920 0 87.0 86.7 35.2 34.9 17.7 17.5 9.6 10.1 7.5 150.3 151.9 111.8 109.1 1233 124 0 1577.7 70.28 -14.98 1.00 1.940 1.00 0.4 136.7 44.7 -10.06 265 2205 0 88.4 88.0 35.2 35.2 17.9 17.8 9.0 9.8 7.8 150.1 151.5 116.1 113.5 126.3 126.8 1569.9 63.29 -14.17 1.00 1.940 1.00 0.4 122.8 39.5 -9.91 267 1895 0 86.6 85.6 35.2 35.2 18.3 18.1 9.3 10.6 86 150.0 152.0 117.7 116.4 127 5 128.4 1567.5 58.34 -13.75 1.00 1.910 1.00 0.4 113.2 37.2 -9.03 268 2440 0 88.1 88.1 35.3 35.1 18.1 17.9 9 3 10.1 7.7 150.6 151.5 111.8 110.2 124.0 124.3 1554.6 49.30 -12.34 1.00 1.920 1.00 0.4 95.4 30.7 -8.82 306 3265 0 88.0 87.6 35.1 35.1 18.5 18.4 9.5 10.9 8.7 150.6 152.1 114.1 115.1 125.7 126.9 1546.7 38.30 -13.14 1.00 1.940 1.00 0.4 74.1 24.0 -6.32 318 2545 0 88.0 87.9 35.1 35.0 18.5 18.4 9.2 10.4 8.2 150.6 151.9 116.0 114.5 126.5 127.2 1566.0 53.74 -13.47 1.00 1.960 1.00 0.4 104.5 33 a -8.63 345 2285 0 87.3 87.0 34.8 34.8 16.5 16.4 9.2 10.4 7.7 - 150.3 151.4 115.8 115.0 126.6 127.2 1554.1 47.87 -12.27 1.00 1.940 1.00 0.4 92.1 30.3 -8.70 381 2555 0 88.9 88.5 35.2 34.9 18.2 18.1 8.9 9.4 6.9 150.3 151 9 117.0 113.6 126.4 127.2 1579.2 72.07 -17.48 1.00 1.980 1.00 0.4 138.1 44.2 -9.37 420 1420 0 88.0 87.1 35.1 35.1 17.9 17.7 8.9 10.0 7.9 150.1 151.4 120.1 115.2 128.0 128.7 1566.4 57.09 -14.52 1.00 1.970 1.00 0.4 110.8 35.8 -8.21 440 2705 0 88.9 88.1 35.2 35.2 18.1 17.9 8.7 9.8 7.6 150.2 151.8 116.4 113.3 126.2 126.9 1562.8 52.81 -13.57 1.00 1.960 1.00 0.4 102.1 32.6 -8 66 441 1560 0 87.5 87.1 35.1 35.0 18.6 18.5 9 1 10.1 8.3 150.0 151 4 115.6 113.6 1257 126.6 1571.3 57.05 -14.85 1.00 1.970 1.00 0.4 110.6 36.0 -8.14 451 1440 0 sa.4 87.7 35.1 35.1 17.4 17.2 8.5 100 6.9 150.5 151.9 117.4 115.2 126.8 127.9 1568 0 57.21 -14.08 1.00 1.930 1.00 0.4 110.2 35.5 -8.54 458 2105 0 87.0 86.4 34.8 34.9 18.4 18.3 8.7 10.6 8 8 150.0 151.7 120.1 115.6 12S.1 128.9 1574.5 66.99 -12.64 1.00 1.970 1.00 0.4 129.3 42.6 -12.29 5006 2355 0 87.8 87.6 35.0 34.9 17.0 16.9 9.2 10.2 7.9 150.1 151 4 112.7 118.1 126.8 127.2 1545.8 38.02 -8.93 1.00 1.960 1.00 0.4 72.4 23.6 -10.51 5014 2305 0 87.3 86.9 35.1 34.9 15.3 15.2 8.6 10.7 7.9 150.0 151.4 114.7 115.0 126.6 126.8 1547.1 38.80 -10.22 1.00 1.940 1.00 0.4 75.0 24.5 -7.75 5019 3360 0 88.0 87.8 35.2 34.9 16.8 16.7 9.1 10.7 8 9 150.4 151.4 113.4 116 8 126.4 127.0 1548.3 37.74 -8.69 1.00 1.970 1.00 0.4 71.3 23.0 -9.61 5021 1535 0 88.6 88.4 35.1 34.7 16 0 15.9 9.0 10.1 7.9 150.5 151.5 120.8 115.6 128.7 129.1 1535.6 27.59 -8.10 1.00 1.950 1.00 0.4 53.5 17.2 -7.18 5025 2980 0 88.2 88.1 35.2 35.0 15.9 15.8 9.4 10.5 8.8 150.6 151.4 119.4 117.0 128.7 129.1 1547.8 38.58 -8.63 1.00 1.970 1.00 0.4 74.3 24.0 -9.55 5052 2680 0 87.9 87.7 34.9 34.9 15.3 15.1 8.5 9.6 7.1 150.6 151.4 117.4 116.8 127.5 128.4 1552.1 41.43 -8.95 1.00 1.920 1.00 0.4 78.5 25.6 -10.27 5064 1240 0 87.5 87.4 35.2 34.9 16.9 16.8 8.6 10.5 8.8 150.0 151.7 119.6 1177 129,3 129.4 1544.4 37.33 -8.90 1.00 1.990 1.00 0.4 71.9 23.4 -9.19 5066 3240 0 87.9 87.7 35.0 34.9 15.2 15.1 8.2 10.2 7.8 150.0 151.4 121.2 118.2 129.7 130.0 1533.5 23.16 -7.74 1.00 1.980 1.00 0.4 43.3 14.1 -6.71 5099 3100 0 87.4 87.0 35.1 34.9 15.6 15.5 8.9 10.6 9.1 150.1 151.4 118.7 118.5 129.0 129.3 1551.8 41.64 -8.70 1.00 1.940 1 00 0.4 79.5 26.0 -10.02 5131 3165 0 87 9 87.2 35.2 35.0 15.6 15.4 9.2 10.3 7.7 149.9 151.6 117.5 116.2 128.1 128.2 1544.8 38.59 -9.75 1.00 2.010 1.00 0.4 75.0 24.2 -8 50 5284 2400 0 88.3 88.1 35.2 35.1 17.1 17.0 8.9 10.2 8.2 150.5 151.4 121.4 117.4 129.3 129.9 1542.7 32.46 -8.52 1 00 1.990 1.00 0.4 62.8 20.2 -8.42 5313 1985 0 87.5 87.3 34.9 34.9 16.0 15.9 8.9 10.2 8.2 150.5 151.4 123.7 119.7 130.8 131.5 1540.6 31.00 -7.85 1.00 1.980 1.00 0.4 58.5 19.2 -8.28 5318 1220 0 87.8 87.1 35.1 35.1 15.4 15.2 8.3 10.1 7.0 150.3 151.9 115.4 114.0 126.5 126.8 1546.2 36.73 -10.90 1.00 1.980 1.00 0.4 71.1 23.1 -6.93 5340 2565 0 88.0 87.4 35.0 35.0 16.2 16.0 8.1 10.3 7.5 150.3 151.8 118.6 117.3 128.5 129.0 1539.0 30.86 -10.57 1.00 2.030 1.00 0.4 59.8 19.4 -6.20 5366 1720 0 87.3 87.0 35.1 34.8 17.9 17.8 8.6 10.3 7.8 150.5' 151.4 114.9 113.4 125.8 126.4 1573.4 64.70 -13.94 1.00 1.930 1.00 0.4 124.1 40.6 -10.28 5408 1820 0 86.6 86.4 35.1 34.8 15.9 15.8 8.8 10.3 8.6 150.6 151.9 119.5 118.8 129.5 129.8 1528.2 19.58 -6.18 1.00 1.950 1.00 0.4 35.3 11.6 -8.53 5440 2790 0 88.4 88.1 34.9 349 15.4 15.3 8.4 9.7 8.0 150.0 151.4 121.2 118.2 130.0 130.0 1535.7 27.58 -6.34 1.00 1.900 1.00 0.4 51.3 16.6 -10.58 8005 3255 0 88.2 87.8 35.0 34.7 17.0 16.9 83 10.2 8.2 150.1 151.6 119.0 118.1 128.0 129.3 1570.5 50.45 -10.53 1.00 1.900 1.00 0.4 97.8 31.7 -10.78 8064 2275 0 88.6 88.2 35.2 34.9 17.2 17.0 8.5 10.2 8.9 150.3 151.9 117.3 116.3 127.2 1282 1566.5 46.81 -11.56 1.00 1.940 1.00 0.4 91.9 29.5 -9.21 8078 985 1 87.8 86.8 35.1 35.0 16.2 16.1 8.2 10.0 8.1 150.1 151.6 116.7 117.3 127.5 128.3 1571.5 45.85 -11.31 1 00 1.970 1.00 0.4 68.9 28.9 -8.54 8092 3370 0 87.3 34.9 35.0 35.0 168 16.6 8.6 10.2 77 150.5 151.4 115.9 113.8 126.0 126.9 1575.0 45.17 -11.76 1.00 1.910 1.00 0.4 87.2 28.5 -7.98 8110 3035 0 87.9 87.1 35.0 35.0 16.2 16.1 9.1 11.0 8.7 150.6 151.4 115.8 112.5 125.9 126.4 1553.6 45.76 -11.22 1.00 1.980 1.00 0.4 88.5 28.7 -8.91 8129 2565 0 87.8 87.7 35.0 35.0 16.9 16.6 9.2 10.4 7.4 150.1 151.9 111.5 111.7 124.0 124.7 1563.5 57.27 -14.47 1.00 1.890 1.00 0.4 111.9 36.4 -8.55 8133 2255 0 88.4 88.2 35.2 34.9 17.8 17.6 9.6 10.1 8.1 150.6 151.4 119.2 115 9 127.6 128.7 1586.0 61.92 -24.23 1.00 1.920 1.00 0.4 119.1 38.3 -6.47 8154 1840 0 88.5 88 1 35.0 35.1 162 16.0 9.6 10.4 7.9 150.2 152.0 114.0 111.6 125.0 125.5 1537.8 30.83 -9.96 1.00 1.960 LOO 0.4 59.3 19.2 -6.51 8170 2740 0 87.9 87.7 35.0 34.9 15.1 14.8 9.2 10.1 8.1 150.6 151.8 116.1 113.1 126.6 126.8 1565.1 58.03 -12.16 1.00 1.960 1.00 0.4 114.3 37.2 -10.22 8182 1880 0 88.6 88.3 35 1 35.0 15.3 15.1 82 8.4 5.9 150.1 151.6 120.0 115.6 128.3 128.6 1558.7 51.06 -11.71 1.00 1.960 1.00 0.4 98.5 31.7 -9.59 8198 2165 0 88.0 87.5 35.1 35.0 16.6 16.5 8.6 10.4 8.3 150.4 151.8 117.6 117.0 128 2 128.6 1536.3 29.39 -9.80 1.00 1.940 1.00 0.4 56.5 18.3 -6.51 8203 3255 0 88.4 87.7 35.0 34.9 15.0 14.3 8.9 9.9 7.6 150.0 151.4 118.1 115.6 128.0 128.1 1544.8 38.14 -11.45 1.00 1.900 1.00 0.4 74.1 24.0 -7.07 8229 1960 0 883 87.8 35.3 35.0 16.2 16.1 9.6 10.3 8.5 150.5 151.8 113.3 114.6 124.9 1264 1548.4 38.97 -11.68 1 00 1.980 1.00 0.4 75.6 24.3 -7.35 8231 1580 0 875 87.1 35.1 35.0 17.8 17.6 9.3 10.6 9.2 150.1 151.4 118.1 114.9 126.3 127.9 1579.0 71.69 -13.79 1.00 1.950 1.00 0.4 139.3 45.4 -11.23 8265 2860 0 87.5 86.8 35.1 35.0 16.8 16.7 9.3 10.5 8.5 150.1 151.9 112.9 117.4 126.3 127.1 1560.5 52.15 -11.40 1.00 1.930 1.00 0.4 100.8 32.9 ' -10.37 8309 2885 0 87.4 87.1 35.0 34.9 17.0 16.8 9.5 0.6 6.8 150.3 151.4 110.0 114.2 124.6 125.0 1547.5 38 62 -11.48 1.00 1.940 1.00 0.4 74.6 24.4 -7.76 8314 2235 0 88.2 88.0 35.1 349 16.6 16.4 8.6 10.1 8 0 150.6 152.0 117.1 1151 126.7 127.9 1582.2 59.75 -10.90 1.00 2.000 1.00 0.4 115.6 37.4 -12.52 .8355 1005 1 88.7 88.5 35.0 35.0 15.9 15.7 8.4 9.7 7.2 150.2 151.8 117.6 117.0 127.5 128.5 1546.7 29.59 -10.13 1.00 1.930 1.00 0.4 58.5 18.8 -6.63 8362 3090 0 87.0 86.5 34.9 34.9 16.8 16.6 8,1 9.9 7.6 150.6 151.8 116.1 114.2 126.4 127.2 1574.6 67.01 -13.29 1.00 1.910 1.00 0.4 125.5 41.3 -14.68 8374 1515 0 87.4 86.4 34.8 34.8 16.7 16.6 8.2 9.9 7.5 150.4 151.9 116.8 115.1 126.1 1277 1553.6 47.19 -12.39 1.00 1.970 1.00 0.4 91.5 30.0 -8.42 8376 1950 0 87.0 86.6 34.B 35.0 16.2 16.0 8.1 9.8 7.6 150.6 151.4 116.5 113.0 126.6 126.9 1551.8 4352 -12.47 1.00 1.930 1.00 0.4 84.3 27.9 -7.50 8404 2520 0 88.3 88.2 34.9 34.8 15.8 157 8.8 9.8 7.8 150.6 151.4 122.2 120.4 130.8 131 2 1546.7 37.83 -8.99 1.00 2.000 1.00 0.4 73.2 23.7 -10.00 8428 2440 0 87.2 87.1 34.8 34.8 15.6 155 8.4 10.1 8.1 150.3 149.6 116.8 114.5 126.4 127.1 1558.3 46.24 -10.69 1.00 1.950 1.00 0.4 88.0 29.0 -9.48 8470 1600 0 87.9 87.5 34.9 34.9 15.7 15.5 8.5 10.1 7.1 150.6 151.4 117.0 114.0 126.8 1273 1559.1 50.29 -11.89 1 00 1.920 1.00 0.4 97.1 31.7 -a.97 avg = 2310.75 87.9 86.6 35.1 35.0 16.9 167 8.9 10.1 8 0 150.3 151.6 116.7 115.3 127.0 127.7 1557.8 47.59 -11.73 1.00 1.950 1.00 0.4 91 8 29.8 -9.00 COV <%)= 0.6 7.9 0.4 0.3 7.2 7.2 5.5 13.0 8.4 0.2 0.2 2.5 2.0 1.3 1.2 1.0 30.39 -24.46 0.00 1.537 0.00 0.0 30.6 30.5 sum = 3 Appendix fl Sample Number = 011, Temperature = 200 aC spec failure c.c. width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC initaj final 1 2 1 2 ©1500 s @end of loading ness deter loading deter load deflection (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) C O CC) C O co C O co <s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) 2 2545 0 86.6 86 9 35.1 35.0 17.4 17.0 9.0 10.3 4 2 200.1 199.9 138.5 135.2 156.5 157.9 1557.6 47.55 -12.34 1.00 1.940 1.00 0.4 91.9 29.5 -8.11 5 1330 0 88.8 68.5 35.2 35.1 18.3 17.9 9.2 9.9 4.7 200.2 199.4 137.1 135.3 154.7 157.4 1571.6 60.37 -13.10 1.00 1.910 1.00 0.4 117.3 37.5 -9 88 40 1740 0 88.3 87.8 35.3 35.2 18.2 17.9 9.5 10.8 7.0 200.6 199.1 145.1 141.0 160.8 162.0 1553.8 44.08 -11.57 1.00 1.940 1.00 0.4 85 0 27.2 -791 71 2155 0 88.1 66.8 35.3 34.9 18.3 18.0 9.5 11.1 6.7 200.2 199.8 143.3 131.2 159.8 158.2 1564.9 55.01 -11.68 1.00 1.950 1.00 0.4 105.4 33.9 -9.95 130 2465 0 87.0 87.0 35.0 34.9 17.9 17,6 9.6 10.6 5.6 200.1 199.3 146.2 145.9 162.5 163.9 1558.3 48.83 -11.47 1.00 1.970 1.00 0.4 94.1 30.9 -9.79 139 1670 0 s e a 88.1 35.2 35.1 17.5 17.2 9.4 9.9 5.8 200.5 199.4 141.0 139.9 158.7 160.3 1563.3 53.06 -12.33 1.00 1.950 1.00 0.4 103.0 32.9 -9.01 172 1395 0 88.0 88.1 35.2 35.3 19.4 19.1 9.3 10.5 5.8 200.5 199.4 141.8 139.3 158.6 160.4 1559.7 47.88 -12.14 1.00 1.900 1.00 0.4 90.6 29.3 -9.39 207 2225 0 87.2 86.6 35.1 35.3 18.2 17.9 9.9 11.1 8.2 200.1 199.6 149.8 142.7 162.3 164.1 1562.8 52.89 -11.19 1.00 1.930 1.00 0.4 102.6 33.5 -10.42 249 2030 0 87.2 86.4 35.1 35.3 17.6 17.3 9.7 11.2 7.4 200.5 199.4 149.9 143.3 163.4 164.4 1551.9 42.27 -10.37 1.00 1.940 1.00 0.4 81.3 26.6 -8.79 254 .2145 0 88.6 88.7 35.1 35.0 17.0 16.7 9.2 10.1 7.0 200.5 201.3 149.3 142.9 163.1 164.4 1575.8 67.50 -12.22 1.00 1.960 1.00 0.4 129.3 41.5 -11.63 261 2805 0 85.7 85.7 35.2 35.4 21.1 20 9 9.9 10.8 6.7 200.6 199.0 139.3 138.7 157.8 159.3 1557.0 47.05 -13.46 1.00 1.980 1.00 0.4 89.3 29.6 -8.94 266 1295 0 86.9 86.6 35.0 34.9 17.8 174 9.5 11.0 5.7 200.5 199.4 136.8 133.4 156.0 156.7 1551.1 39.37 -12.16 1.00 1.930 1.00 0.4 76.3 25.0 -7.18 298 1640 0 87.7 87.0 35.1 35.2 18.6 18.3 9.2 10.9 6.7 200.1 199.8 150.3 137.8 161.1 162.7 1553.4 42.03 -11.29 1.00 1.920 1.00 0.4 80.4 26.1 -8.34 309 2965 0 87.4 86.5 35.0 34.9 19.8 19.5 9.0 10.4 5.5 200.1 199.1 140.1 137.2 157.9 159.0 1554.1 44.71 -14.64 1.00 1 940 1.00 0.4 86.7 28.4 -6.29 330 1310 0 88.1 87.7 35.2 35.1 16.3 160 8.3 10.0 5.7 200.2 199.5 149.0 144.1 162.2 164.3 1560.4 48.48 -12.11 1.00 1.930 1.00 0.4 93.7 30.3 -8 43 342 1745 0 86.8 65.8 35.0 35.1 18.2 17.6 8.9 10.5 5.8 200.6 199.3 138.0 145.4 160.0 161.1 1557.6 48.85 -14.01 1.00 1.950 1.00 0.4 94.5 31.1 -7.47 409 2310 0 88.1 87.6 35.2 35.0 17.7 17.4 8.6 9.7 5.6 200.2 199.7 135.3 130.5 154.2 155.2 1550.6 42.42 -12.89 1.00 1.930 1.00 0.4 81.7 26.4 -6.86 446 1420 0 88.3 87.6 35.3 35.0 18.8 185 8.8 10.2 5.6 200.6 199.4 147.6 140.9 160.7 162.8 1566.1 56.30 -11.72 1.00 1.920 1.00 0.4 108.2 34.8 -10.94 446 1490 0 88.9 88.0 35.2 35.3 19.4 19.1 9.1 10.1 5.6 200.4 199.3 140.9 145.5 162.0 162.1 1570.6 63.04 -12.89 1.00 1.930 1.00 0.4 121 0 38.7 -10.73 6062 2650 0 88.9 38.4 35.1 35.6 15.6 15.3 8.8 10.0 6.4 200.5 199.8 151.5 149.8 166.5 167.1 1539.3 26 as -7.22 1.00 1.920 1.00 0.4 51.3 16.5 -7.86 5078 3395 0 83.4 87.9 35.0 34.8 16.5 16.1 9.0 9.9 7.0 200.3 199.2 156.0 150.8 168.2 168.9 1525.3 1421 -5.57 0.99 1.820 1.00 0.4 25.9 8.4 -5.81 5095 1165 1 874 87.2 35.0 34.7 16.6 16.3 8.1 9.7 5.2 200.1 199.1 149.6 149.7 164.6 166.3 1554.7 42.69 -8.73 1.00 1.920 1.00 0.4 82.8 27.0 -10.25 5112 1950 0 87.7 66.8 35.0 35.0 15.8 15.5 9.0 10.4 4.7 200.3 199.0 129.2 143.7 156.1 157.5 1535.3 27.62 -9.45 1.00 1.910 1.00 0.4 52.2 17.0 -5.98 5158 3525 0 87.9 87.6 35.1 35.5 15.7 15.4 8.1 10.1 7.1 200.1 199.7 152.4 151.1 167.3 167.8 1531.4 21.81 -6.44 1.00 1.940 1.00 0.4 41.2 13.3 -7.27 5159 2655 0 88.4 87.9 35.1 34.7 15.6 15.2 8.3 10.1 4.4 200.1 199.6 146.8 139.9 161.6 162.2 1529.1 20.83 -7.72 1.00 1.930 1.00 0.4 38.6 12.5 -7.04 5190 1365 0 88.3 97.4 35.3 34.8 14.8 14.4 8.5 9.6 37 200.1 199.6 131.4 129.2 153.1 1535 1538.8 29.69 -9.68 1.00 1.910 1.00 0.4 57.2 18.3 -6.60 5217 1825 0 87.4 87.3 35.1 35.8 15.8 15.5 S3 10.4 62 200.6 199.4 154.1 152.0 168.0 168.7 1537.7 28.12 -7.90 1.00 1.940 1.00 0.4 53.5 17.4 -7.83 5279 3455 0 87 6 87.2 35.2 35.6 15.2 14.9 8.2 10.2 6.0 200.1 199.4 147.9 149.2 167.1 165.6 1541.1 30.95 -6.54 1.00 1.980 1.00 0.4 59.1 19.2 -10.48 5303 ' 1725 0 88.5 87.9 35.3 35.1 16.2 15.8 8.6 10.3 5.8 200.1 199.2 152.1 147.2 165.9 166.3 1532.7 20.08 -5.80 1.00 1.960 1.00 0.4 37.3 11.9 -7.97 5344 2920 0 67.1 87.0 34.9 34 8 16.0 15.8 8.4 10.2 5.5 200.2 199.0 150.3 147.8 164.7 165.9 1539.1 28.92 -8.02 1.00 1.920 1.00 0.4 55.3 18.2 -7.60 5353 2890 0 88.3 87.8 35.3 35.1 16.4 16.2 8.1 9.3 5.2 200.1 199.3 150.5 146.0 165.0 165.4 1533.9 23.79 -7.68 1.00 1.980 1.00 0.4 44.4 14.3 -6.87 5360 3110 0 88.5 88.4 35.1 35.3 14.2 13.9 8 1 10.5 5.8 200.5 199.6 155.4 154.5 169.0 170.0 1529.4 17.19 -5.38 1.00 1.930 1.00 0.4 32.9 10.6 -6.66 5383 2545 0 87.4 87 6 35.0 35.1 15.9 15.6 8.1 .10.3 5.4 200.3 199.3 153.5 149.5 166.8 167.6 1536.1 26.89 -7.90 1.00 1.940 1.00 0.4 51.3 16.8 -7.36 5394 2400 0 88.3 87.3 35.1 34.6 15.0 14.6 8.2 9.9 3.3 200.1 199.2 134.0 140.0 157.1 157.9 1541.3 32.76 -9.75 1.00 1.920 1.00 •0.4 63.7 20.5 -6.81 5416 2230 0 88.1 87.3 35.1 34.4 17.2 16.8 65 10.1 6.3 200.2 199.6 138.6 146.8 160.9 161.8 1535.5 27.15 -8.27 1.00 1.950 1.00 0.4 52.6 17.0 -7.25 5420 3410 0 87.9 86.7 35.1 35.1 15.6 15.4 8.2 10.1 5.1 200.0 199.4 140.5 141.1 159.5 160.4 1541.8 32.71 -8.66 1.00 1.950 1.00 0.4 633 20.5 -7.72 5423 1925 0 87.5 66.8 35.0 347 17.0 16.6 8.0 10.1 5.5 200.6 1999 147.2 144.1 162.9 163.9 1544.4 36.40 -8.95 1.00 1.940 1.00 0.4 69.3 22 6 -9.00 5429 1715 0 87.7 87.7 35.1 35.5 17.8 17.5 87 10.2 6.0 198.9 201.6 151.0 154.2 167.4 168.5 1540.4 27.84 -8.83 1.00 1.960 1.00 0.4 53.5 17.3 -7.34 5441 2610 0 86.5 86.4 34.9 35.0 15.8 15.6 8.5 10.1 6.3 199.0 199.3 145.3 145.7 162.8 163.4 1534.1 22.99 -7.25 1.00 1.930 1.00 0.4 43.6 14.4 -6.68 5442 2330 0 88.0 87.1 35.1 34.9 15.4 15.1 8.3 10.3 5.0 198.9 199.3 152.1 142.8 163.8 164.7 1537.2 27.20 -7.83 1.00 1.930 1.00 0.4 52.0 16.8 -7.15 8031 3395 0 88.5 87.2 35.2 34.8 16.6 16.2 8.9 10.5 5.4 198.3 199.4 133.0 129.9 153.1 153.9 1543.1 31.93 -9.64 1.00 1.940 1.00 0.4 60.2 19.3 -7.40 8032 2495 0 88.6 87.8 35.2 348 16.2 15.8 9.4 10.1 5.5 198.9 199.7 133.8 133.5 155.0 155.5 1544.4 34.46 -10.62 1.00 1.910 1.00 0.4 66.3 21.2 -667 8034 2790 0 87.9 86.2 35.2 34.8 17.8 17.4 9.3 10.8 53 198.9 199.9 134.9 131.0 153.9 155.1 1545.1 33 72 -12.47 1.00 1.920 1.00 0.4 65.4 21.1 -5.63 8053 2100 0 88.3 872 35.2 35.2 16.4 16.0 9.2 10.2 5.7 200.1 199.2 144.2 141.6 160.2 161.8 1546.6 37.91 -11.53 1.00 1.940 1.00 0.4 73.2 23.6 -6.62 8108 2880 0 87.5 87.1 35.0 35.2 17.3 17.0 9.2 11.1 7.1 200.1 199.8 152.9 151.1 166.4 168.0 1542.9 33.22 -9.61 1.00 1.930 1.00 0.4 64.5 21.1 -7.13 8192 1160 1 88.5 87.5 35.3 34.9 16.6 16.3 8.9 9.0 4.6 200.3 199.3 140.1 135.9 157.6 158.6 1546.5 39.20 -11.94 1.00 1.950 1.00 0.4 75.0 24.0 -6.89 8234 3070 0 87.6 86.7 35.2 34.8 16.1 15.8 8.7 9.1 5.3 198.9 199.8 143.0 142.2 160.4 161.5 1549.7 40.63 -10.97 1.00 1.930 1.00 0.4 78.0 25.3 -7.95 8258 1600 0 88.7 88.0 35.0 35.0 17.0 16.8 9.1 10.2 5.8 198.6 199.1 151.5 138.0 161.7 162.8 1543.9 25.61 -7.81 1.00 1.940 1.00 0.4 47.4 15.3 -7.65 8277 2920 0 88.5 87.3 35.1 35.1 15.9 15.7 8.3 9.3 5.2 198.4 199.7 142.1 148.1 162.8 163.1 1533.5 22.86 -9.05 1.00 1.940 1.00 0.4 43.7 14.1 -5.78 8279 2555 0 88.8 68.1 35.0 35.0 16.6 16.3 8.5 9.8 4.5 196.7 199.5 137.9 136.1 157.1 157.7 1547.8 39.18 -1068 1.00 1.910 1.00 0.4 74.6 24.0 -7.63 8307 1867 0 88.9 88.9 34.9 34.5 17.4 17.1 8.8 9.4 5.6 199.0 199.4 144.9 141.7 160.9 161.9 1545.9 35.29 -9.47 1.00 1.920 1.00 0.4 68.5 22.0 -7.76 8325 2495 0 87.6 66.4 35.0 34.9 16.6 16.4 8.3 10.0 5.5 199.0 199.4 137.2 138.4 157.7 158.3 1542.0 32.55 -9.80 1.00 1.940 1.00 04 62.8 20.5 -6.90 8409 3075 0 87:4 S7.1 35.0 35.0 16.0 15.8 8.5 10.0 5.9 198.9 199.3 144.3 143.7 161.4 162.4 1531.5 19.69 -9.55 1.00 1.970 1.00 0.4 38.1 12.5 -4.31 8432 1400 0 87.9 87.7 35.0 34.9 16.6 16.4 7.8 9.8 5.9 198.6 199.4 149.6 148.7 164.2 165.8 1549.5 38.71 -9.54 1.00 1 930 1.00 0.4 74.7 24.3 -8.57 8440 1290 0 87.8 87.7 34.9 34.8 16.4 16.1 8.2 10.0 7.2 199.0 199.7 146.0 138.9 160.2 161.4 1550.9 39.32 -10.90 1.00 1.930 1.00 0.4 76.3 24.9 -7.72 8465 1600 0 88.0 87.4 35.1 35.2 17.0 16.8 83 10.5 5.5 198.5 199.1 141.7 139.6 159.0 160.0 1540.6 28.97 -10.82 1.00 1.950 1.00 0.4 56.1 , 18.1 -5.45 8463 3095 0 88.1 87.7 35.2 34.9 16.8 16.5 9.1 10.3 5.8 198.7 199.2 141.3 145.7 161.2 162.0 1544.9 34.67 -9.11 1.00 1.930 1.00 0.4 65.0 21.0 -8.95 8469 2290 1 88.5 87.6 35.2 34.7 17.0 16.7 9.0 9.2 6.1 199.0 199.7 147.2 132.5 158.4 159.7 1537.9 5.88 — — ***» 52.0 16.7 8491 1610 0 88.1 86.8 35.1 34.9 15.6 15.2 8.0 10.0 3.8 198.3 199.9 131.4 130.9 152.6 153.8 1552.3 43.22 1 9 9 1 GO 1 940 1 00 0.4 83.7 27.1 -7 64 8494 1375 0 87.9 87.5 35.0 34.9 16.3 16.0 8.2 ' 10.0 6.7 200.2 199.4 151.1 148.3 165.4 166.4 1546.5 37.74 -9.44 1.00 1.920 1.00 0.4 72.8 23.6 -6.57 M6AN= 2232.95 88.0 86.7 35.1 35.0 16.9 16.6 8.8 10.2 5.7 199.8 199.5 144.3 142.0 161.0 162.0 1546.7 36.22 -10.04 1.00 1.935 1.00 0.4 70.2 22.7 -7.64 COV (%)= 0.7 7.5 0.3 0.8 7.7 7.9 6.1 4.8 16.2 0.4 0.2 4.7 4.6 2.6 2.6 0.7 34.13 -21.98 0.13 1.219 0.00 0.0 32.7 32.5 0\ ON sum = 3 Appendix II Sample Number = 012, Temperature = 250°C spec failure cc. width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500 s @end of loading ness deter loading deter load deflection (mm) fmm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) C O C O C O CC) CC) co (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) 95 1435 0 87.9 88.5 35.0 35.9 19.3 18 6 9.3 10.7 4.1 2482 249.7 153.0 151.8 185.0 1846 1543.7 34.70 -1021 1.00 1.950 1.00 0.4 66.5 21.7 -7.31 104 1330 0 88.3 88.7 35.0 34.3 16.7 16.1 95 10.6 2.7 248.2 251.3 158.5 155.6 187.2 187.9 15427 32.03 -11.69 1.00 1.910 1.00 0.4 62.2 20.1 -5.61 120 2630 0 88.6 88.9 35.0 34.7 19.2 18.5 9.6 10.6 4.0 2485 250.0 158.7 160.1 189.3 1B9.4 1550.3 39.35 -13.29 1.00 1.930 1.00 0.4 76.7 24.7 -6.67 121 2060 0 87.2 86.7 35.0 35.1 18.8 18.1 97 10.7 3 1 248.6 251 0 157.9 157.0 188.5 188.3 1539.7 29.53 -10.08 1.00 1.910 1.00 0.4 56.5 18.5 -6.51 163 3220 0 88.6 87.1 . 35.0 34.2 19.4 18.8 10.0 12.3 2.7 248.7 251.6 149.7 144.8 180.8 181.5 15503 41 04 -13.28 1.00 1.900 1.00 0.4 79.7 25.7 -642 166 2440 0 88.8 89.1 35.2 345 17.9 17.2 9.3 10.5 32 2489 250.8 166.8 161.6 191.6 192.7 1542.3 32 13 -10.15 1.00 1.940 1.00 0.4 61.7 19.8 -6.84 166 2940 0 87.7 86.7 35.1 34.8 16.6 18.0 9.1 9.8 2.4 250.5 251.0 157.9 161.6 190.2 190.1 1545.9 37.23 -11.57 1.00 1.970 1.00 0.4 71.9 23.4 -7.93 204 1430 0 87.0 68.4 35.1 35.0 18.1 17.4 9.1 10.7 3.3 248.7 251.3 164.8 158.8 189.7 191.2 1537.0 25.38 -10.72 1.00 1.940 1.00 0.4 48.7 16.0 -5.17 208 1530 0 87.4 88.1 35.1 35.5 19.1 18.5 9.2 10.8 3.3 249.1 249.7 158.3 151.7 186.2 186.4 1547.4 37.31 -11.81 1.00 1.940 1.00 0.4 71.9 23.4 -6.70 221 1590 0 87.7 86.7 35.1 34.4 18.2 17.6 8.9 10.5 3.1 248.5 251.7 153.5 145.6 181.1 183.0 1549.4 39.90 -11.69 1.00 1.940 1.00 04 77.2 25.1 -7.05 272 2400 0 89.0 88.4 35.4 34.5 17.9 17.3 9.2 9.9 18 248.9 249.7 154.2 153.6 184.7 185.7 1565.3 58.05 -13.57 1.00 1.910 1.00 0.4 111.3 35.3 -9.22 314 2040 0 88.1 88.2 35.0 34.8 17.8 17.1 9.2 10.6 2.7 248.6 250.1 167.3 153.0 189.7 189.9 1532.0 21.39 -11.90 1.00 1.900 1.00 0.4 42.3 13.7 -3.63 356 2340 0 87.9 86.1 35.2 34.8 18.1 17.5 8.9 10.9 3.1 248.6 249.7 171.2 162.1 193.0 194.2 1532.4 21.89 -11.46 1.00 1.940 1.00 0.4 41.7 13.5 -4.55 384 1650 0 87.1 87.5 34.9 34.5 18.7 18.1 8.6 10.3 3.0 249.2 249.5 160.5 168.6 190.6 192.8 1553.5 45.68 -11.92 1.00 1.920 1.00 0.4 88 7 29.2 -8.20 386 2835 0 88.8 69.8 35.2 35.5 18.1 17.5 9.3 9.8 32 248.5 249.5 166 0 157.2 189.9 190.7 1539.9 29.96 -10.76 1.00 1.910 1.00 0.4 57.4 18.4 -6.41 39S 1980 0 87.3 87.7 35.0 34.7 20.1 19.4 9.2 10.5 27 248.9 251.3 160.0 152.2 188.6 187.4 1548.2 38.74 -13.90 1.00 1.910 1.00 04 76.1 24.9 -7.03 414 2065 0 88.5 88.0 35.0 34.6 17.2 16.6 84 10.1 3.4 249.0 251.5 152.9 158.9 186.0 187.4 1548.0 39.00 -11.99 1.00 1.930 1.00 0.4 75.0 24.2 -6.95 419 2230 0 87.3 68.0 35.1 34.5 18.0 17.4 8 3 103 30 248.5 249.0 162.4 163.9 190.2 191.7 1560.0 49.65 -12.49 1.00 1.910 1.00 0.4 96.9 31.6 -8.31 497 3450 0 88.6 86.6 35.1 34 6 17.2 16.6 8.1 9.4 1.9 248.6 248 9 148.5 149.3 181.1 182.2 1533.4 25.03 -11.45 1.00 1.930 1.00 0.4 48.0 15.4 -4.86 5001 2795 0 87.2 87.9 35.0 35.0 16.5 15 9 8.8 10.2 2.5 248.7 249.7 154.0 160.5 186 9 187.9 1529.9 20.48 -8.94 1.00 1.940 1.00 0.4 39.3 12 9 -4.7a 5020 2040 0 87.7 87.8 35.1 35.2 16.9 16.3 9.3 10.9 2.9 248 6 249.3 155.2 153.6 186.1 185.9 1539.3 28.32 -S 13 1.00 1.940 1.00 0.4 53.9 17.5 -7.62 5031 2565 0 880 87.1 35.0 35.3 15.9 15.3 9.7 10.4 2.1 248.9 249.7 154.1 157.0 166.1 186.8 1537.3 27.37 -7.75 1.00 1.970 1.00 0.4 52.6 17.1 -7.57 5047 2090 0 87.7 87.4 35.1 35.4 16.3 15.7 8.7 10.4 3.0 248.6 249.5 157.0 154.2 186.0 186.7 1531.2 22.99 -7.03 1.00 1.930 1.00 0.4 439 143 -6.92 5090 3410 0 880 87.3 35.2 35.5 16.8 18.1 96 10.8 4.0 248.5 249.7 152.0 151.6 184.0 184.3 1536.2 27.05 -8.61 1.00 1.930 1.00 0.4 51.4 16.6 -6.79 5105 1490 0 S7.7 86.7 35.0 35.9 15.8 15.2 8.5 99 24 2486 249.4 164.4 156.5 188.8 190.0 1533.5 2333 -7.04 1.00 1.930 1.00 0.4 44.1 14.4 -7.61 5161 1560 0 87.9 87.7 35.0 35.2 15.3 14.7 86 10.0 2.0 249.1 248.9 163 1 160.0 190.1 190.7 1534.9 25.59 -7.81 1.00 1.900 1.00 0.4 49.1 16.0 -7.39 5196 1575 0 88.2 87.7 35.2 34.4 14.9 143 8.1 10.1 23 248.7 2488 165.0 159.1 190.2 190.9 1528.0 17.05 -6.04 1.00 1.920 1.00 0.4 31.5 10.2 -6.16 5197 3220 0 87 4 88.3 35.1 35.2 16.2 15.6 84 10.1 3.2 249.2 249.2 160.8 161.4 189.2 190.5 1526.2 15.84 -8.66 1.00 1.920 1.00 0.4 30.5 9.9 -3.92 5210 3415 0 88.1 87.4 35.1 35.6 16.2 15.6 84 9.7 2.8 248.5 249.8 162.2 162.0 191.1 191.1 1529.8 18.61 -6.55 1.00 1.930 1.00 0.4 34.9 11.3 -6.52 5225 3485 0 88.0 86.6 35.1 34.3 14.6 14.0 8.8 10.5 23 248.6 249.3 143.3 162.9 183.7 185.0 1529.5 18.75 -6.41 1.00 1.950 1.00 0.4 36.4 11.8 -5.96 5240 2020 0 68.1 87.0 35.1 34.4 17.1 16.4 9.0 10.4 2.0 2479 249.3 162.3 152.0 187.7 187.6 1535.0 26.08 -823 1.00 1.910 1.00 0.4 50.7 16.4 -6.52 5244 3010 0 87.8 67.7 35.2 34.7 15.5 14.9 9.4 10.2 22 248.3 2499 156.5 158.0 186.7 187.8 1533.1 26.67 -8.87 1.00 1.930 1.00 0.4 487 15.8 -8.35 5300 2810 0 87.8 86.9 35.1 34.9 16.3 15.7 88 10.8 23 249.1 249.0 155.3 154.5 185.6 186.3 1527.2 17.90 -7.26 1.00 1.910 1.00 0.4 34.4 11.2 -5.48 5301 2925 0 87.6 85.8 35.2 34.4 16.2 15.6 88 12.3 13 248.7 248.9 144.1 157.2 1B2.3 183.4 1531.1 22.63 -8.92 1.00 1.900 1.00 0.4 434 14.1 -5.34 5326 3120 0 87.7 87.2 35.0 35.6 15.9 15.3 8.4 98 26 248.7 249.3 159.5 154.5 189.6 187.6 1534.0 24.09 -7.92 1.00 1.920 1.00 0.4 44.8 14.6 -6.98 5330 2480 0 87.5 86.9 35.2 35.6 16.6 16.0 8.4 9.9 22 250.3 249.4 159.2 156.5 187.8 188.5 1529.9 21.11 -7.61 1.00 1.960 1.00 0.4 40.7 132 -5.B0 5409 1570 0 88.0 88.0 35.0 36.0 14.7 14.1 8.5 10.2 2.2 248.8 249.1 155.4 149.8 184.3 184.7 1535.2 25.48 -B.46 1.00 1.940 1.00 0.4 48.8 15.8 -6.59 5432 3520 0 877 88.6 35.0 34 3 16.2 15.6 89 105 3.1 248.6 251.0 157.6 155.2 186.7 187.5 1528.2 17.95 -7 16 1.00 1.920 1.00 0.4 34.5 11.3 -5.24 5439 2365 0 88.3 89.4 35.0 34.8 15.2 14.6 9.0 10.6 2.2 248.6 249.4 157.1 161.4 18B.2 189.2 1525.2 15.57 -6.23 1.00 1.930 1.00 0.4 29.3 9.5 -5.32 8023 1540 0 87.7 85.6 35.0 34.5 16.9 16.3 8.6 13.0 1.6 250.3 249.0 146.8 145.3 180.0 180.6 1544.4 33.63 -10.94 1.00 1.920 1.00 0.4 65.4 21.3 -6.29 8028 2510 0 87.8 88.5 34.9 35.0 17.8 17.2 8.6 10.3 2.3 250.2 249.8 155.7 158.0 188.2 187.9 1532.2 24.13 -10.93 1.00 1.930 1.00 0.4 47.0 15.3 -4.75 8058 1585 0 87.8 88.9 34.9 34.8 17.2 16.6 8.7 10.2 2.8 250.2 249.6 159.4 155.2 188.6 188.2 1545.7 36 03 -10.70 1.00 1.950 1.00 04 69.7 22.7 -7.09 8100 1605 0 87.7 89 2 35.1 35.1 16.6 16.0 8.6 10.4 2.6 248.4 249.6 148.2 151.5 1822 182.9 1539.7 31.04 -10.6B 1.00 1.990 1.00 0.4 60.2 19.6 -6.17 8115 1660 0 88.5 86.5 35.1 34.7 16.4 15.7 9.3 10.0 1.5 248.2 249.8 141.5 141.4 174.9 177.3 1549.2 38.91 -12.20 1.00 1.940 1.00 0.4 75.9 24.5 -6.46 8126 1585 0 88.0 87.5 35.1 35.4 174 16.7 8.6 102 2.6 248.6 249.1 155.5 151.3 185.1 185.2 1531.1 21.96 -9.71 1.00 1.970 1.00 0.4 42.6 13.8 -4.77 8153 1970 0 88.2 86.8 35.2 34.9 17.6 17.0 9.4 10.1 26 248.2 249.3 154.4 152.4 184.8 185.2 1539.9 30.12 -9.37 1.00 1.930 1.00 0.4 57.6 18.6 -7.14 8160 3285 0 88.2 87.5 34.9 35.3 17.1 16.4 9 5 10 8 3.0 248.5 248.8 156.1 157.8 187.5 1543.9 33.99 -9.38 1.00 1.950 1.00 0.4 67.5 21.9 -7.68 8187 3540 0 88.2 87.5 35.0 34.7 16.5 15.9 8.5 11.7 2.6 248.8 248.9 156.1 156.1 ',66 3 187.0 1543.9 34.60 -11.39 1.00 1.920 1.00 0.4 67.5 21.9 -6.21 8213 3175 0 88.1 87.1 35.0 35.3 17.6 16.9 9.0 10.2 2.5 248.3 250.0 161.9 158.2 189.1 189.8 1542.3 33.49 -9.13 1.00 1.930 1.00 0.4 64.1 20.8 -8.53 8249 2675 0 876 86.5 35.1 34.5 16.1 15.4 8.4 9.7 2.0 249.2 248.9 168.8 159.8 191.6 192.5 1556.2 43 39 -10.71 1.00 1.930 1.00 0.4 84.1 27.4 -8,56 8253 1965 0 8S.3 86.5 35.1 34.6 15.8 15.1 84 10.0 2.4 249.1 249.4 172.0 160.4 192.9 193.9 1533.4 23.15 -9.79 1.00 1.950 1.00 0.4 45.2 14.6 -4.89 8255 2200 0 87.9 87.7 35.1 35.0 174 16.7 8 6 10.2 2.2 249.0 250.0 158.1 163.5 190.4 190.4 15400 30.61 -10.56 1.00 1.910 1.00 0.4 58.9 19.1 -6.41 8275 2790 0 88.4 87.1 34.9 34.8 16.5 15.9 8.5 97 2.5 250.4 249.1 168.5 153.9 190.6 190.7 1532.1 24.36 -8.23 1.00 1.940 1.00 0.4 46.5 15.1 -6.39 8350 1865 0 87 3 85.5 35.0 34.6 16.2 15.6 9.2 9.8 1.9 250.3 249.1 138.5 141.9 176.0 176.7 1558.3 50.68 -10.86 1.00 1.930 1.00 0.4 98.2 322 -10.10 8361 3580 0 87.1 86.4 348 352 17.4 16.8 8.5 10.3 42 248.5 249.0 156.0 155.7 187.8 186.9 1535.3 25.45 -9.05 1.00 1.940 1.00 0.4 49.1 16.2 -6.00 8378 1985 0 87.4 88.3 35.0 34.8 15.8 15.2 8.8 10.3 3.2 249.0 2492 164.4 163.6 192.8 192.4 1549.3 37.19 -11.60 1.00 1.930 1.00 0.4 71.9 235 -7.12 8393 2255 0 87.9 87.6 35.2 35.0 173 16.6 85 10.3 26 248.0 249.5 164.1 162.5 191.3 191.8 1543.0 33.01 -9.15 1.00 1.950 1.00 0.4 64.0 20.7 -7,57 8417 1860 0 88.0 67.8 35.2 34.4 15.8 15.2 8.7 10.3 2.6 248.9 249.4 142.9 165.9 184.6 186.0 1543.0 34.14 -9.56 1.00 1.920 1.00 0.4 66.1 21.4 -7,20 8426 2150 0 88.2 89.4 35.0 34.9 17.2 16.7 8.5 9.8 2.7 248.6 249.2 163.0 168.5 192.7 193 5 1534.2 24.29 -992 1.00 1.930 1.00 . 0.4 45.4 14.7 -5,59 8484 1240 0 88.3 87.0 35.0 34.5 16.2 15.6 8.6 9.2 3.0 250 5 249.0 157.8 147.8 184.7 185.1 1536.5 . 29.34 -9.98 1.00 1.970 1.00 0.4 55.7 18.0 -6 B0 MEAN= 87.9 87.6 35.1 34.9 17.0 16.4 89 10.4 2.7 248.9 249.7 157.5 156.3 187.1 187.7 1539.5 29.91 -9.86 1.00 1.932 1.00 0.4 57.6 18.7 -6.57 COV (%)= 0.5 1.1 0.3 1.3 7.2 7.4 5.0 6.3 22.9 0.3 0.3 4.6 3.8 2.1 2.0 0.6 30.36 -19.89 0.00 1.005 0.00 0.0 30.9 30.9 0\ V) sum - 0 Appendix II Sample Number = 013, Temperature = 150°C spec failure c.c width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500s @end of loading ness deter loading deter bad deflection (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) C O C O C O C O C O C O (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) 17 3080 0 87.8 87.4 35.1 35.0 17.8 17.6 9.2 10.5 8.1 150.5 151.9 124.9 122.7 127.8 132.9 1885.2 360.01 -12.30 1.00 0.204 1.00 0.4 74.9 24.3 -7.36 51 3075 0 87.7 86.5 35.2 34.9 18.8 18.6 9.5 10.2 68 150.6 149.3 126.7 124.5 128.8 133.7 2027.0 503.73 -12.41 1.00 0.204 1.00 0.4 106.3 34.4 -10.07 83 2420 0 88.9 88.3 35.1 35.0 18.1 17.9 9.2 9.9 7.8 150.3 151.9 127.1 125.3 127.0 134.5 2044.7 517.96 -12.36 1.00 0.203 1.00 0.4 107.7 34.5 -10.98 173 2835 0 87.8 B6.7 34.9 34.8 18.0 178 9.4 10.6 6.7 150.3 151.8 121 3 123.4 125.9 131.9 2108.6 580.78 -14.21 1.00 0.201 1.00 0.4 1208 39.4 -9.38 187 1930 0 86.4 85.9 35.0 34.8 18.4 18.1 9.7 10.7 6.6 150.6 151.8 124.7 122.2 128.6 132.7 1971 1 441.87 -12.49 1.00 0.206 1.00 0.4 92.1 30.4 -7.93 190 2715 0 87.6 87.3 35.0 34.9 19.1 18.9 9.2 10.7 9.1 150.6 151.9 126.6 124.2 128.6 134.0 1925.4 396.55 -11.76 1.00 0.203 1.00 0.4 82.5 26.9 -787 202 1975 0 88.7 88.1 35.1 35.0 16.5 16.2 9.9 9.2 6.1 150.7 151.4 126.9 123.5 127.3 133.8 2076.1 559.57 -14.01 1.00 0.208 1.00 0.4 116.9 37.5 -9.93 213 1670 0 87.3 86.9 35.0 34.8 18.8 18.6 9.5 10.B 8.2 150.7 151.3 127.2 125.8 129.6 134.7 1917.5 384.60 -11.13 1.00 0.198 1.00 0.4 79.7 26.1 -8.76 258 1780 0 87.2 86.2 34.9 34.7 18.0 17.8 90 11.0 7.1 150.6 149.5 124.3 121.6 127.9 132.0 1934.5 417.47 -11.51 1.00 0.205 1.00 0.4 87.5 28.8 -8.95 292 1290 0 87.4 86.5 35 1 34.7 19.8 19.6 9.5 10.9 7.4 150.6 149.7 122.2 121.1 125.7 131.2 2064.4 525.78 -14.68 1.00 0.210 1.00 04 1119 36.4 -9.05 307 3335 0 87.4 86.3 35.0 34.9 18.4 18.2 9.1 10.9 7.5 150.3 149.8 127.5 120.7 128.5 132.7 2026.4 489.10 -14.18 1.00 0.214 1.00 0.4 103.4 33.8 -7.89 335 2125 0 88.5 87.8 35.0 34.7 18.6 18.4 9.7 10.6 7.4 150.1 149.7 125.5 122.4 128.2 132.6 2110.0 585.54 -13.11 1.00 0.205 1.00 0.4 122.5 39.5 -10.77 347 3465 0 88.3 87.7 35.0 34.7 18.8 18.6 9.7 10.6 8.1 150.1 149.7 125.5 121.9 129.7 132.4 1974.6 438.35 -11.70 1.00 0.213 1.00 0.4 91.7 29.7 -9.30 357 2135 0 87.7 86.7 34.9 34.8 18.3 18.1 9.1 10.6 7.4 150.5 149.5 1303 122.3 128.9 134.2 2027.3 511.86 -11.33 1:00 0.209 1.00 0.4 106.9 35.0 -11.21 369 1300 0 88.9 88.0 34.9 34.9 17.2 17.0 86 9.9 6.9 150.0 151.5 123.9 122.9 126.5 132.5 1983.5 437.23 -13.01 1.00 0.208 1.00 0.4 91.7 29.6 -8.82 450 2120 0 86.6 86.0 34.9 348 18.1 18.0 9.1 10.4 8.0 150.6 151.8 126.0 125.7 1262 134.3 2159.1 622.45 -15.34 1.00 0.206 1.00 0.4 1308 43.3 -9.78 467 2420 0 66.4 85.4 34.9 34.8 18.4 18.2 9.8 106 7.1 150.0 151.6 119.7 120.7 126.1 130.4 19968 461.37 -11.96 1.00 0.211 1.00 04 96.5 32.0 -9.19 475 2185 0 87.8 87.5 34.8 34.4 18.6 18.4 9.3 10.5 7.5 150.2 149.8 126.0 120.9 127.5 132.3 2017.3 494.07 -12.84 1.00 0.206 1.00 0.4 103.4 33.9 -9.43 479 1420 0 87.2 85.9 34.9 34.8 17.8 17.6 9.1 103 7.6 150.1 151.7 125.6 124.6 127.2 133.7 2088.2 557.81 -13.77 1.00 0.204 1.00 0.4 116.6 38.3 -9.67 480 1695 0 88.1 87.6 34.9 34.8 17.4 17.2 8.7 10.6 8.0 150 5 149.3 131.2 125.6 131.0 135.6 1859.7 323.71 -10.06 1.00 0.210 1.00 0.4 67.7 22.0 -7.97 5034 1340 0 88.2 87.9 35.0 348 16.3 16.1 9.5 10.6 8.7 150.2 149.6 129.3 125.0 131.1 134.7 1832.6 316.46 -7.28 1.00 0203 1.00 0.4 65.6 21.3 -10.79 5045 1295 0 88.2 87.4 35.0 34.8 15.8 15.6 9.3 10.2 65 150.1 151.4 1264 123.1 128.3 133.4 2011O 475.38 -10.45 1.00 0.205 1.00 0.4 99.3 32.2 -10.78 5061 2960 0 88.2 87.2 34.9 34.7 15.6 154 8.5 9.4 6 1 150.6 149.8 120.1 121.7 127.2 130.7 1868.9 34560 -10.72 1.00 0205 1.00 0.4 72.2 23.5 -8.20 5093 1435 0 87.6 87.2 34.9 34.7 16.8 16.7 89 10.6 7.1 150.1 149.5 130.7 124.2 131.3 134.9 1827.0 310.82 -8.18 1.00 0.205 1.00 04 64.2 21.0 -9.41 5124 2750 0 87.2 87.1 34.9 34.5 16.1 15.9 8.9 10.5 8.5 150.5 149.8 127.5 120.6 129.3 132.8 17822 267.97 -8.73 1.00 0.202 1.00 0.4 55.6 18.3 -7.52 5127 2505 0 88.9 B8.7 35.2 34.9 14.2 14.0 9.0 9.5 7.7 150.5 149.7 130.1 125.9 133.0 135.4 1720.7 202.28 -5.70 1.00 0.205 1.00 0.4 41.8 13.4 -8.09 5141 1840 0 88.3 880 35.0 34.8 14.6 14.4 85 10.6 8.1 150.5 149.5 129.0 1268 132.4 135.3 1737.1 22090 -6.88 1.00 0.211 1.00 0.4 46.5 15.1 -7.15 5143 3145 0 87.5 869 34.9 34.5 15.2 15.0 8.8 10.5 7.0 150.6 151.4 126.2 119.8 129.1 132.3 1781.0 267.15 -8.88 1.00 0.202 1.00 0.4 55.7 18.2 -7.02 5178 2000 0 88.0 87.9 35.0 34.9 149 148 85 10.1 7.5 150.5 149.8 129.3 126.7 131.3 135.4 1750.0 230.55 -7.20 1.00 0.199 1.00 0.4 47.4 15.4 -7.29 5194 1410 0 88.6 87.9 35 1 34.8 13.6 13.4 8.9 10.0 6.0 150.2 149.3 122.7 1203 128.1 130.9 1855.1 322.05 -8.11 1.00 0.202 1.00 0.4 66.3 21.3 -8.71 5223 1995 0 87.9 87.2 35.2 35.0 16.5 16.3 8.9 10.6 7.6 150.3 149.8 127.2 127.4 130.7 134.9 1830.9 311.03 -8.88 1.00 0.211 1.00 0.4 64.2 20.8 -882 5224 2595 0 87.8 87.4 35.0 35.0 15.9 15.7 8.4 10.3 7.4 150.6 151.5 126.7 124.3 130.5 134.0 1745.6 209.72 -7.38 1.00 0.207 100 0.4 43.3 14.1 -7.52 5253 3390 0 87.8 87.3 35.2 35.1 16.1 15.9 8.5 10.5 7.9 150.2 149.3 126.7 126.3 130.6 134.2 1849.9 334.29 -8.98 1.00 0.206 1.00 0.4 69.9 22.7 -8.85 5298 3265 0 87.8 87.6 35.1 34.7 17.1 17.0 9.0 10.2 7.7 150.5 149.6 124.5 121.2 129.8 131.9 1692.3 168.48 -6.27 1.00 0.204 1.00 0.4 34.1 11.1 -7.60 5380 2170 0 88.4 88.3 35.1 349 16.9 16.8 8.9 10.1 7.9 150.3 149.3 129.2 126.4 130.7 135.1 1843.0 319.91 -7.96 1.00 0.205 1.00 0.4 66.2 21.3 -9.37 5384 2160 0 87.9 87.6 35.0 34.7 16.1 15.9 8.7 10.3 7.3 150.5 149.3 127.9 124.5 129.9 134.1 1839 3 313.48 -8.64 1.00 0.212 1.00 0.4 65.6 21.4 -8.77 5400 2590 0 88.1 87.2 34.8 34.6 15.4 15.3 8.5 10.2 6.9 150.3 149.5 123.4 124.2 129.0 132.5 1867.8 349.83 -9.15 1.00 0.214 1.00 0.4 72.8 23.7 -9.14 5403 3045 0 88.1 87.9 34.9 34.7 15.5 15.4 8.2 9.9 7.9 150.1 149.9 129.0 125.7 131.2 134.9 1753.2 221.68 -7.24 1.00 0.202 1.00 0.4 45.4 14.7 -6.97 5450 2350 0 88.2 88.2 35.0 34.8 14.4 142 8.4 9.9 7.8 150.2 149.8 131 0 127.6 132.8 136.2 1776.7 262.71 -6.70 1.00 0.213 1.00 0.4 57.8 18.7 -9.88 5453 2545 0 86.7 86.2 34.9 34.9 15.9 15.7 8.7 10.2 8.0 150.1 151.8 126.6 122.3 129.7 133.3 1784.1 272.04 -8.72 1.00 0.214 1.00 0.4 59.3 19.6 -7.59 8037 2025 0 88.0 87.5 35.0 35.0 17.0 16.8 8.2 10.1 7.6 150.1 149.5 124.8 120.3 128.6 131.6 1796.0 278.53 -9.82 1.00 0.210 1.00 0.4 58.6 19.0 -7.26 8051 2430 0 88.1 87.1 35.0 35.0 16.0 15.8 8.7 10.2 8.0 150.6 149.8 128.2 124.9 1290 134.4 1913.0 398.47 -9.56 1.00 0.220 1.00 04 87.6 28.4 -10.43 8072 2175 0 88.4 87.8 350 34.8 17.2 17.0 8.6 10.4 7.8 150.6 151.8 127.8 126.5 130.5 135.2 1841.5 327.78 -10.40 1.00 0.218 1.00 0.4 71.9 23.3 -8.72 8090 1510 0 87.8 86.9 35.1 34.7 17.2 16.9 8.7 9.8 6.1 150.6 151.8 119.5 118.0 127.7 129.6 1992.6 465.00 -11.03 1.00 0.203 1.00 0.4 100.5 32.6 -10.22 8112 1600 0 88.0 87.5 352 35.0 17.0 16.7 9.4 10.3 6.3 150.2 149.8 1230 120.4 127.7 131.2 1947.7 426.54 -11.64 1.00 0.223 1.00 0.4 94.3 30.5 -9.61 8118 2580 0 87.7 87.0 35.2 34.8 16.1 15.8 9.0 10.1 6.7 150.6 151.4 124.8 115.1 129.0 130.3 1891.9 375.25 -11.39 1.00 0.222 1.00 0.4 83.0 26.9 -8.32 • 8134 2580 0 88.6 87.7 349 35.1 16.9 16.7 8.7 9.9 6.9 150.6 149.3 121.4 117.6 127.5 129.7 1805.3 288.89 -11.14 1.00 0.220 1.00 0.4 63.9 20.7 -6.82 8138 3025 0 88.5 87.5 35.0 34 8 15.8 15.6 9.2 10.3 6.8 150.6 151.5 123.7 129.2 126.8 134.7 1921.6 384.00 -10.03 1.00 0.210 1.00 0.4 80.5 26.0 -9.02 8143 2520 0 87.5 87.4 350 34.9 17.1 16.9 9.4 10.8 7.9 150.7 151.4 125.9 124.6 128.4 133.8 1974.1 454.92 -11.10 1.00 0.213 1.00 0.4 94.3 30.8 -10.26 8168 3360 0 87.9 87.4 34.9 35.1 15.4 15.2 9.3 10.5 7.5 150.5 149.5 126.8 121.6 129.8 1328 1761.3 235.49 -9.79 1.00 0.207 1.00 0.4 49.1 16.0 -5.42 8173 2420 0 88.2 87.8 35.1 34.7 17.0 16.9 9.2 10.6 7.9 150.2 149.3 130.3 128 6 131.4 136.2 1890.2 376.06 -9.03 1.00 0.214 1.00 0.4 78.5 25.4 -10.03 8200 1975 0 87.7 86.7 34.9 34.7 15.8 15.6 8.3 98 5.6 150.3 151.8 118.1 120.5 127.2 129.9 1960.7 445.29 -13.21 1.00 0.220 1.00 0.4 97.5 31.9 -7.87 8202 1830 0 886 88.2 35.0 34.9 18.1 18.0 8.2 8.8 7.1 150.1 151.3 128.1 125.0 131.0 134.6 1766.3 241.90 -10.14 1.00 0.224 1.00 0.4 52.5 17.0 -5.85 8204 2070 0 88.7 88.6 35.1 34.9 15.6 15.5 9.1 9.4 6.8 150.1 151.3 129.0 126.4 131.1 135.4 1819.8 295.35 -9.04 1.00 0.218 1.00 0.4 64.1 20.6 -8.23 8233 1575 0 87.1 865 35.0 35.1 18.0 17.9 9.6 10.6 7.8 150.6 149.3 126.0 121.8 127.3 132.6 1911.6 399.50 -10.20 1.00 0.206 1.00 0.4 83.6 27.4 -9.53 8247 3195 0 88.7 88.1 35.0 35.0 16.2 16.0 9.1 10.0 6.6 150.1 151.8 126.9 121.9 128.7 1332 1867.6 350.92 -11.11 1.00 0.212 1.00 0.4 74.3 24.0 -7.26 8274 1650 0 880 87.6 34.9 34.8 17.4 17.2 8.7 10.1 8.3 150.6 149.8 129.9 120.1 128.8 133.4 1850.4 334.21 -8.53 1.00 0.212 1.00 0.4 70.5 23.0 -9.56 8322 1815 0 87.8 87.0 35.1 34.7 17.4 17.1 9.1 10.2 6.6 150.2 149.4 122.9 121.4 128.3 131.4 1885.8 367.70 -11.16 1.00 0.211 1.00 0.4 77.8 25.3 -7.96 8344 3315 0 87.7 87.2 34.9 34.7 17.4 17.2 9.0 10.5 8.4 150.6 149.7 128.1 127.1 131.3 135.1 1820.2 303.57 -8.76 1.00 0.209 1.00 0.4 64.0 20.9 -8.40 8433 3085 0 88.1 88.0 34.7 34.6 15.4 15.2 8.6 10.3 7.4 150.5 151.6 127.4 122.7 128.5 133.7 1959.1 438.90 -11.52 1.00 0.211 1.00 0.4 95.3 31.2 -10.10 avg = 87.9 87.3 35.0 34.8 16.9 16.7 9.0 10.3 7.4 150.4 150.4 126.1 1233 1290 133.3 1898.7 375.34 -10.41 1.00 0.209 1.00 0.4 79.1 25.7 -8.74 COV(%)= sum = 0 0.7 0.8 0.3 0.4 8.0 8.1 4.8 4.2 9.8 0.2 0.7 2.4 2.3 1.4 1.3 5.9 28.86 -21.79 0.00 2930 0.00 0.0 28.9 29.1 Appendix II Sample Number = 014, Temperature = 200°C spec failure cc width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500s ©end of loading ness deter loading deter load deflection (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) CO CO CO (*C) CO CO (s) (s) (kN/mm) (kN/s) (kN) (kN) (MPa) (mm) 25 2545 0 889 87.4 35.1 34.7 17 2 16.7 9.7 9.6 29 200.3 199.4 144.0 139.0 157.9 161.0 1817.3 287 26 -11.26 1.00 0219 1.00 0.4 63.2 20.2 -5.93 48 3285 0 87.7 87.3 35.0 34.7 19.6 19.2 9.2 10.1 5.2 200.1 199.4 163.4 160.2 161.8 174.4 2086.1 560.26 -12.58 1.00 0.218 1.00 0.4 123.4 40.2 -10.83 62 2115 0 87.4 86.6 35.0 34.8 18.8 18.4 9.2 10.6 4.6 200.6 199.7 154.9 149.2 159.0 168.1 1928.0 411.18 -11.95 1.00 0.208 1.00 0.4 88.4 28.9 -8.31 79 1965 0 87.2 87.0 34.9 35.2 18.6 18.3 9.4 10.7 6.6 200.6 199.4 1523 148.1 160.6 166.8 1781.4 256.62 -9.75 1.00 0.217 1.00 0.4 55.9 18.3 -7.24 85 2485 0 88.1 86.8 35.0 34.7 18.5 18.1 9.3 10.3 4.5 200.5 199.4 148.0 143.0 158.8 163.7 1877.7 351.70 -10.43 1.00 0.216 1.00 0.4 76.5 24.8 -8.24 89 1810 0 88.4 87.0 35.1 35.0 18.0 17.6 9.4 10.4 4.5 200.3 199.4 148 5 148.5 157.1 165.6 1856.1 323.36 -12.62 1.00 0.218 1.00 0.4 70.4 22.7 -6 40 101 2025 0 88.2 88 6 35.1 34.9 18.4 18.0 9.2 10.9 5.6 200.5 199.8 161.8 160.4 165.4 174.1 1897.0 373 11 -10.02 1.00 0.211 1.00 0.4 81.5 26.4 -9.40 153 2020 0 88.0 87.8 35.1 34.9 16.0 15.7 9.2 10.1 4.7 200.6 199.6 153.7 153.8 161.6 169.2 1823.3 309.65 -10.24 1.00 0.218 1.00 0.4 68.4 22.1 -7.41 169 2910 0 87.0 86.5 35.1 34.9 18.6 18.1 9.2 11.0 5.2 200.1 199.3 137.7 143.0 156.5 160.1 1905.4 382.45 -10.61 1.00 0.217 1.00 0.4 836 27.4 -9.37 181 1870 0 87.8 86.5 35.1 35.2 17.5 17.2 8.8 10.3 6.3 200.2 199.8 1569 156.5 163.2 171.2 1913.1 384.33 -10.28 1.00 0.211 1.00 0.4 82.8 26.9 -8.89 196 1500 0 867 86.9 35.1 35.0 17.9 17.6 9.5 10.7 7.1 200.5 199.5 158.6 1530 163.8 1705 1785.9 253.05 -10.57 1.00 0.222 1.00 0.4 55.0 18.1 -6.89 212 1905 0 66.9 85.8 349 34.9 18.8 18.4 9.2 10.8 6.1 200.2 199.8 143.2 147.6 155.4 163.6 1860.1 331.12 -12.66 1.00 0.211 1.00 04 72.4 23.9 -6.40 273 1660 0 87.9 86.7 35.1 34.8 19.3 18.9 95 10.7 6.0 200.5 199.4 165.2 146.6 161.5 170.6 1885.2 357.67 -11.02 1.00 0.216 1.00 0.4 780 25.3 -9.11 276 1515 0 863 86.6 35.0 34.0 18.9 18.5 8.8 10.5 5.8 200.1 199.6 160.0 156.0 164.5 171.9 1874.9 345.23 -10.10 1.00 0.222 1.00 0.4 75.9 25.1 -10.44 282 1990 0 87.5 86.7 34.9 34.6 18.4 18.1 8.9 10.8 6.8 200.7 199.9 153 5 151.4 162.0 168.4 1768.7 233.84 -11.04 1.00 0.216 1.00 0.4 50.4 16.5 -4.83 302 2210 0 87.4 86.0 35.0 34.9 19.0 18.6 93 10.7 4.2 200.2 199.4 141.5 145.5 156.3 162.3 1825.0 292.50 -10.99 1.00 0.220 1.00 0.4 61 7 20.2 -6.57 333 1660 0 87.6 86.1 35.0 35.0 18.3 17.9 94 11.4 5.4 200.5 199.6 152.2 1529 161.4 168.4 1855.7 322.48 -9.73 1.00 0.209 1.00 0.4 67.0 21.8 -9.88 404 1940 0 88.2 87.1 35.1 34.5 17.2 16.8 9.1 9.8 5.6 200.3 199.4 149.5 152.5 162.9 167.3 1708.8 181.35 -10.55 1.00 0.203 1.00 0.4 37.5 12.1 -4.42 415 2885 0 87.5 86.4 34.9 34.6 19.4 19.0 88 10.5 5.1 2006 199.8 157.3 1572 159.7 171.6 2071.8 547.00 -13.50 1.00 0.216 1.00 0.4 120.3 39.4 -10.02 437 3695 1 87.2 85.1 34.8 34.2 17.4 16.9 9.2 10.1 3.3 200.1 199.4 139.6 138.0 153.3 159.1 2116.7 591.05 -14.06 1.00 0.216 1.00 0.4 130.8 43.1 -9.96 461 2565 0 68.5 87.3 35.0 34.8 17.0 16.7 8.6 9.9 5.3 200.2 199.8 157.2 143.9 159.2 167.0 1806.5 285.30 -9.71 1.00 0.220 1.00 04 61.1 19.7 -7.51 465 2735 0 87.6 87.4 35.0 34.9 19.7 19.3 89 10.3 6.9 200.1 199.6 149.7 147.5 161.1 165.7 1712.5 186.36 -9.18 1.00 0217 1.00 0.4 406 13.2 -4.49 495 2190 0 87.5 85.9 34.8 34.6 18.4 18.0 8.9 10.4 4.5 200.2 199.8 144.1 138.4 155.0 160.9 1857.7 335.31 -10.87 1.00 0.217 1.00 0.4 72.3 238 -7.73 496 3095 0 87.5 87.2 34.9 34.8 17.2 16.8 8.5 10.3 6.6 200.6 199.4 153.2 155.4 162.4 169.5 1868.6 352.15 -10.37 1.00 0.213 1.00 04 76.1 24.9 -8.70 5008 2960 0 88.4 87.9 35.1 35.0 15.8 15.4 8.6 10.1 5.3 200.6 199.6 150.3 159.2 167.0 169.9 1731.1 212.46 -6.55 1.00 0.213 1.00 0.4 45.8 14.8 -7.90 5010 3490 0 88.6 87.3 34.9 34.2 15.8 15.2 8.7 9.9 5.2 200.1 199.4 131.9 148.5 154.3 160.0 1785.5 266.30 -8.88 1.00 0.214 1.00 0.4 58.2 18.8 -7.06 5076 2740 0 87.2 85.8 34.8 34.4 15.7 15.3 9.3 10.7 3.9 200.6 199.4 137.8 133.0 154.5 156.9 1748.7 210.18 -8.56 1.00 0.221 1.00 0.4 46.1 15.2 -6.46 5122 2550 0 B7.2 87.2 34.9 34.6 16.1 15.8 8.3 10.3 5.9 200.1 199.4 163.0 159.0 169.4 173.9 1723.6 201.67 -6.79 1.00 0.225 1.00 0.4 43.5 14.3 -8.28 5133 2500 0 88.6. B8.2 35.0 34.3 15.7 15.4 8.7 9.9 4.5 200.5 199.4 155.0 153.8 165.5 169.6 1681.0 158.72 -6.86 1.00 0.218 1.00 0.4 34.4 11.1 -5.57 5138 3580 0 88.5 87.7 35.0 34.3 17.8 17.4 8.3 9.8 6.1 200.5 199.4 160.2 153.6 166.5 171.2 1694.9 172.43 -5.79 1.00 0.206 1.00 0.4 35.1 11.3 -7.66 5153 1420 0 87.3 87.0 348 35.0 16.0 15.7 8.2 10.4 7.2 200.1 199.4 164.0 159.0 168.7 174.2 1749.1 221.49 -7.78 1.00 0.215 1.00 0.4 48.4 15.9 -6.87 5175 2330 0 B8.4 87.3 35.3 349 14.6 14.3 8.3 10.1 4.7 200.2 199.7 152.3 145.8 162.8 166.0 1675.0 162.17 -5.62 1.00 0.215 1.00 04 33.6 10.8 -7.31 5236 1390 0 88.0 87.5 35.1 35.4 168 16.5 8.9 10.5 5.1 200.3 199.8 161.3 156.6 168.9 172.6 1770.8 240.13 -7.34 1.00 0.215 1.00 0.4 52.4 17.0 -7.88 5333 1920 0 88.3 87.6 35.0 35.2 16.6 16.2 9.0 10.2 4.2 200.1 201.2 145.8 155.9 170.4 167.5 1745.0 205.83 -7.03 1.00 0219 1.00 0.4 44.8 14.5 -7.60 5336 1335 0 88.1 87.0 35.1 34.6 150 14.7 8.5 10.1 5.7 200.1 199.6 155.1 148.3 164.0 167.8 1711.7 180.88 -6.92 1.00 0216 1.00 0.4 39.4 12.7 -5.96 5359 1490 0 878 87.5 35.1 34.8 14.4 14.0 7.6 9.9 5.4 200.1 199.7 158.2 152.7 167.1 170.3 1645.3 116.56 -5.94 1.00 0215 1.00 0.4 24.1 7.8 -4.73 5368 2085 0 88.1 87.7 35.2 35.1 15.7 15.4 8.9 9.4 4.6 200.1 199.6 164.0 163.0 171.3 175.6 1704.9 182.85 -5.15 1.00 0215 1.00 0.4 39.2 12.6 -9.10 5370 2225 0 88.2 87.4 35.1 34.5 168 16.4 8.6 10.5 5.4 200.5 199.6 156.0 155.9 166.7 170.6 1671.5 131.96 -6.59 1.00 0.221 1.00 04 29.1 9.4 -4.54 5379 2015 0 87.5 87.2 35.0 35.3 17.4 17.0 9.0 10.3 5.B 200.1 199.4 160.5 152.3 166.6 170.8 1788.6 263.35 -6.88 1.00 0.216 1.00 0.4 57.4 18.7 -9.93 5399 1495 0 88.3 87.7 35.1 35.1 16.7 16.4 8.4 10.0 6 5 200.6 199.6 164.1 163.0 171.9 175.7 1704.3 171.34 -6.03 1.00 0.216 1.00 0.4 37.3 12.1 -7.45 5413 2160 0 B7.9 87.5 35.0 34.9 14.7 14.3 8.3 10.4 4.1 200.1 199.8 156.2 159.2 169.2 171.7 1789.0 247.44 -7.35 1.00 0208 1.00 0.4 51.7 16.8 -7.94 5472 1365 0 87.9 87.6 34.9 35.2 16.4 16.0 8.6 10.0 5.8 200.4 199.8 155.0 153.1 164.8 169.4 1706.3 175.00 -6.60 1.00 0204 1.00 0.4 36.0 117 -6.37 8096 2670 0 87.2 85.8 34.7 34.5 16.2 15.6 9.3 10.4 4.4 200.6 199.8 142.6 139.8 156.3 160.9 1957.1 430.24 -10.21 1.00 0.216 1.00 0.4 95.4 31.5 -10.66 8139 2505 0 87.9 86.9 34.9 34.8 16.6 16.2 8.4 96 4.4 200.6 199.6 148.1 146.7 157.9 165.0 1807.6 254.27 -9.42 1.00 0.213 1.00 0.4 55.0 17.9 -6.83 8155 3000 0 88.4 86.9 35.1 34.8 15.5 15.0 86 10.3 36 200.6 201.3 146.7 141.8 154.0 163.2 1915.9 378.88 -10.84 1.00 0.216 1.00 0.4 82.5 26.6 -8.33 8171 2740 0 88.0 87.5 35.0 35.3 15.7 15.3 8.1 9.9 4.1 200.3 199.4 152.6 155.3 162.1 169.2 1797.2 281.99 -9.59 1.00 0.216 1.00 0.4 61.5 20.0 -7.37 8230 1610 0 88.1 87.7 35.1 34.8 15.9 15.6 8.4 9.9 6.3 200.3 199.8 160.9 155.7 167.9 172.2 1705.2 187.33 -7.28 1.00 0.225 1.00 0.4 40.7 13.2 -6.65 8246 2245 0 87.2 86.9 34.8 34.8 16.9 16.6 8.4 10.3 5.7 200.3 199.9 160.7 158.5 166.9 173.1 1856.3 321 22 -8.48 1.00 0.215 1.00 0.4 69.7 23.0 -9.66 8272 1395 0 882 87.2 350 34.9 17.9 17.6 8.8 102 5.1 200.1 199.4 155.7 158.6 161.6 171.4 1933.7 397.63 -10.52 1.00 0.221 1.00 0.4 87.7 28.4 -9.68 8291 2115 0 88.5 87.9 35.0 35.0 16.8 16.5 8.6 11.5 39 200.6 199.8 139.5 145.3 157.7 161.7 1675.7 142.74 -9.33 1.00 0.220 1.00 0.4 31.3 10.1 -4.32 8312 1980 0 86.7 85.7 34.8 34.3 17.8 17.4 8.6 10.3 4.7 200.5 199.4 145.2 146 0 157.3 163.7 1789.9 274.38 -9.36 1.00 0.215 1.00 0.4 60.2 20.0 -8.17 8319 2520 0 88 6 87.9 35.1 34.5 15.2 14.9 83 9.1 3.8 200.2 199.8 146.1 147.0 158.9 164.4 1828.2 310.95 -10.43 1.00 0.224 1.00 0.4 68.7 22.1 -7.22 8329 3280 0 88.5 87.8 34.9 34.5 159 15.5 84 10.0 4.7 200.1 199.4 156.6 153.6 165.9 170.0 1772.1 247.74 -7.83 1.00 0216 1.00 0.4 53.6 17.4 -7.43 8412 1900 0 87.8 87.6 34.9 34.4 17.4 17.0 8.4 10.0 6.1 200.5 199.4 143.6 150.2 167.4 164.6 1797.6 272.77 -7.55 1.00 0.219 1.00 0.4 59.1 19.3 -10.69 8421 3425 0 87.5 86.7' 34.6 35.0 16.9 16.5 8.4 10.1 4.5 200.4 199.4 143.9 139.6 156.9 161.1 1710.9 190.37 -9.10 1.00 0.208 1.00 0.4 41.3 13.5 -5.20 8452 2165 0 87.4 87.3 34.7 34.8 16.2 15.8 8.2 10.2 5.9 200.5 199.4 155.0 154.2 167.5 169.7 1774.6 260.31 -7.72 1.00 0.212 1.00 0.4 54.3 17.9 -7.66 8453 1875 0 67.6 88.2 35.1 34.9 168 16.5 8.1 10.0 5.4 200.5 199.6 159.1 152.1 164.0 170.4 1744.8 222.95 -8.32 1.00 0.210 1.00 0.4 47.5 15.5 -6.59 8454 1520 0 ' 87.4 87.8 . 34.8 35.2 17.2 16.9 8.3 10.3 6.5 200.3 199.8 155.7 156.9 167.2 170.9 1713.1 195.56 -8.09 1.00 0.216 1.00 0.4 41.8 13.7 -7.42 8474 2625 0 86.7 86 1 34.9 34.8 17.0 16.7 8.8 10.3 6.1 200.3 199.7 158.3 156.0 165.2 171.4 1765.3 248.10 -8.20 1.00 0.208 1.00 0.4 53.5 17.7 -7.76 8478 1855 0 87.2 87.0 34.8 35.1 18.4 18.1 87 10.4 6.3 200.6 199.8 163.4 154.6 168.6 172.7 1865.6 336.26 -8.61 1.00 0.212 1.00 0.4 73.0 24.0 -9.54 mean 2250.8 87.8 87.1 35.0 34.8 17.1 16.7 8.8 10.3 5.3 200.3 199.6 152.8 151.2 162.5 168.0 1805.3 278.81 -9.13 1.00 0.215 1.00 0.4 60.4 19.7 -7.65 COV(%)= sum = 1 0.7 0.8 0.4 0.9 7.8 7.9 5.0 4.1 18.8 0.1 0.2 5.2 4.5 3.0 2.7 5.6 36.36 -22.74 0.00 2.228 0.00 0.0 37.3 37.6 Appendix il Sample Number = 015, Temperature = 250°C spec failure c.c width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500 s @end of loading ness deter loading deter load deflection (mm) (mml (mm) (mm) (mm) (lb) (lb) (%) (%) (%) CO CO CO CO CC) CC) (s) (s) (kN/mm) (kN/s) (kN) (kN) (Mpa) (mm) 1 2150 0 88.1 87.7 34.9 34.6 168 16.2 8.7 10.1 2.0 250.4 249.1 151.4 159.7 187.5 186.9 1737.4 217.90 -10.88 1.00 0.217 1.00 0.4 47.1 15.3 -4.84 13 1325 0 880 88.6 35.1 35.2 176 16.9 96 10.4 2.2 250.3 249.6 156.9 157.7 186.3 188.2 1643.6 125.56 -9.97 1.00 0214 1.00 0.4 27.2 8.8 -2.84 36 3130 0 89.0 86.8 35.2 34.7 175 16.8 9.3 10.4 2.9 250.5 249.7 165.2 157.7 1822 191.0 1768.2 246.65 -10.55 1.00 0.221 1.00 0.4 53.9 17.2 -5.34 49 3420 0 87.3 87.1 35.1 34.6 18.9 18.2 9.6 10 6 2.3 2501 248.8 156.5 152.8 181.8 186.2 1763.0 242.53 -12.25 1.00 0.218 1.00 0.4 52.8 17.2 -4.83 116 2320 0 86.9 86.5 34.9 34.7 20.5 19.6 10.2 10.7 2.5 250.7 2493 158.8 157.6 187.9 188.8 1698.1 171.73 -10.45 1.00 0.221 1.00 0.4 37.6 12.4 -4.47 184 3415 0 86.8 85.8 34.9 34.0 19.1 18.4 89 102 22 250.2 249.3 168.0 167.1 ' 189.3 195.0 1835.3 314.38 -11.39 1.00 0213 1.00 0.4 6a:s 22.7 -7.01 188 1625 0 87.4 86.8 35.2 346 172 16.5 86 10.3 2.3 250.4 250.0 159.4 158.5 185.9 189.4 1792.3 279.25 -11.26 1.00 0.211 1.00 0.4 61.0 199 -5.83 211 3485 0 87.9 86.4 35.2 34.4 17.2 165 9.5 10.6 2.0 250.4 249.5 158.2 164.8 184.4 191.0 1766.1 255.26 -10.13 1.00 0.210 1.00 0.4 55.6 18.0 -5.79 223 2870 0 87.6 88.3 35.2 34.5 18.2 17.4 96 10.5 3.2 250.6 249.1 163.8 164.9 189.4 192.9 1836.2 323.14 -10.89 1.00 0.210 100 0.4 70.8 23.0 -7.61 250 3165 0 87.2 85.3 35.2 34.8 17.4 167 9.2 11.2 2.5 250.1 249.8 168.6 165.9 190.1 194.8 1766.7 231.52 -11.37 1.00 0 220 1.00 04 50.0 16.3 -6.62 263 1565 0 88.6 89.0 35.1 34.8 17.8 17.0 9.9 10.0 1.9 250.1 249.3 156.9 162.2 189.5 189.6 1755.2 230.59 -8.91 1.00 0.214 1.00 0.4 50.0 16.1 -6.86 286 1920 0 86.8 85.2 34.9 34.5 19 4 18.7 9.9 10.5 2.2 250.3 249.8 166.7 168.5 193.6 195.1 1747.4 223.83 -12.37 1.00 0.218 1.00 0.4 48.9 16.1 -4.67 295 1760 0 87.6 87.9 35.2 34.6 18.4 17.7 9.5 10.8 2.0 250.8 249.4 171.0 158.3 192.1 193.1 1664.7 141.43 -10.29 1.00 0.222 1.00 0.4 30.7 10.0 -4.18 296 2930 0 87.9 87.3 35.1 348 188 18.0 9.3 10.6 2.4 250.3 249.3 175.0 157.6 193.5 194.1 1837.8 322.51 -9.96 1.00 0.218 1.00 0.4 70.8 23.0 -7.51 316 3395 0 88.2 87.7 35.1 34.5 16.9 16.2 9.5 10.1 2.8 250.6 249.7 163.9 158.9 188.2 191.0 1695.5 174.70 -9.30 1.00 0.213 1.00 0.4 37.1 12.0 -5.24 368 3135 0 87.6 87.2 35.1 34.5 192 18.5 9.3 15.9 1.8 250.3 2492 160.3 155.9 189.7 188.6 1890.2 330.25 -11.87 1.00 0 221 1.00 0.4 72.6 23.6 -7.97 374 2345 0 883 88.8 35.1 34.7 18.1 17.4 9.6 10.0 2.2 250.5 249.2 156.8 160.4 187.8 1890 1788.7 26647 -10.33 1.00 0.213 100 0.4 57.8 18.7 -6.53 399 2525 0 87.6 86.8 34.9 34.8 17.8 17.0 9.0 10.7 2.3 250.1 249.2 169.1 165.8 192.9 194.8 1797.7 280.90 -11.37 1.00 0.213 1.00 0.4 61.0 20.0 -6.34 401 2865 0 87.8 87.2 34.9 34.7 17.9 17.1 8.7 102 1.8 250.3 249.4 1662 172.9 194.2 196.3 1843.1 320 98 -11.08 1.00 0.224 1.00 0.4 70.1 229 -6.87 406 1625 0 88.0 88.3 34.9 34.7 17.1 164 88 10.0 2.3 250.2 249.9 158.5 166.4 190.6 191.7 1774.2 256.22 -10.21 1.00 0214 1.00 0.4 55.8 18.2 -6.69 456 2220 0 87.2 87.9 34.8 35.0 17.4 16.7 85 10.2 2.1 250.1 249.9 161 6 156.5 187.9 189.3 1811.0 294.42 -10.23 1.00 0.221 1.00 0.4 64.1 21.1 -7.63 463 2000 0 87.0 850 34.8 34.4 17.8 17.2 86 10.6 2.4 250.1 249.5 160.4 159.0 185.3 189.8 1728.8 212.12 -11.91 1.00 0.219 1.00 0.4 46.2 15.3 -4.50 471 1965 0 87.5 88.6 35.1 34.8 18.1 17.4 9.0 10.3 2.1 250.8 2492 156.9 158.2 184.1 188.4 1758.6 238.55 -11.34 1.00 0220 1.00 0.4 51.7 16.9 -5.58 478 1685 0 87.7 86.1 34.9 34.7 179 17.2 8.8 10.3 1.7 250.8 251.3 167.2 167.9 190.B 195.4 1783.2 251.88 -11.82 1.00 0.213 1.00 0.4 54.1 17.7 -9.45 5023 3175 0 87.9 879 35.0 34.3 16.9 16.2 9.3 9.8 2.2 250.6 249.0 165.2 161.4 189.5 192.1 1691.0 174.51 -8.29 1.00 0.211 1.00 0.4 37.8 12.3 -4.B7 5073 2485 0 875 879 35.0 35.5 15.4 14.8 9.0 9.6 1.6 2508 249.5 163.0 160.8 188.1 191.3 1745.1 211.39 -7.24 1.00 0.215 100 0.4 45.2 14.7 -7.04 5079 3090 0 88.5 88.5 35.1 34.8 15.6 14.9 89 9.6 1.5 250.3 248.9 166.0 153.7 186.6 189.8 1686.3 168.09 -7.71 1.00 0.215 1.00 0.4 36.5 11.8 -5.42 5089 3130 0 88.2 88.3 35 1 35.3 14.B 14.1 87 10.0 1.7 250.3 249.6 1702 158.4 191.9 192.8 1613.5 93.86 -5.95 1.00 0223 1.00 0.4 20.1 6.5 -3.57 5106 1595 0 87.8 86.6 35.1 34.7 160 15.2 8.8 9.9 1.9 250.6 249.3 166.9 165.2 188.8 194.0 1741.9 223.59 -7.62 1.00 0.226 1.00 0.4 48.9 15.9 -7.17 5137 1935 0 87.7 86.6 35.1 35.7 17.4 16.7 9.0 10.0 1.7 250.7 2492 173.6 158.1 1906 193.9 1688.1 169.20 -5.39 1.00 0.214 1.00 0.4 36.5 11.9 -7.62 5167 2280 0 87.8 87.0 35.0 35.6 16 8 16.1 8.3 10.3 2.3 250.3 249.6 166.0 162.7 191.9 192.9 1619.6 100.74 -5.34 1.00 0.211 1.00 0.4 21.2 6.9 -4.37 5172 2865 0 88.6 88.2 35.0 349 16.2 15.6 8.5 9.6 2.5 250.2 249.5 167.1 170.2 195.2 195.7 1609.6 102.88 -6.22 1.00 0.230 1.00 0.4 26.4 8.5 -4.49 5187 2540 0 88.6 89.0 35.0 34.8 14.7 13.9 8.6 9.5 15 250.3 249.9 165.3 171.5 194.5 195.6 1735.1 214.73 -8.65 1.00 0.216 1.00 0.4 46.7 15.1 -5.66 5302 1580 0 88.2 87.6 35.1 35.0 148 14.1 8.6 10.1 2.3 250.4 249.1 173.8 167.0 192.8 196.9 1641.1 121.35 -5.52 1.00 0.212 1.00 0.4 25.6 8.3 -4.84 5322 1280 0 88.0 88.6 35.1 34.7 16.1 15.4 86 10.2 1.6 250.4 249.3 165.6 159.6 190.8 191.7 1736.5 205.92 -7.99 1.00 0212 1.00 0.4 437 14.2 -6.17 5324 2355 0 87.5 886 350 34.1 16.4 15.7 8.1 9.9 1.8 250.5 249.6 169.7 161.6 191.6 193.8 1637.9 109.01 -7.19 1.00 0.217 1.00 0.4 23.6 7.7 -3.48 5338 1485 0 883 87.2 35.0 34.8 15.8 15.1 7.8 9.9 1.7 250.1 249.0 169.5 169.0 190.9 196.0 1716.7 188.14 -7.04 1.00 0215 1 00 04 40.4 13.1 -6.37 5358 3455 0 88.2 87.5 35:0 360 15.1 14.6 8.6 9.0 2.3 250.1 249.8 1689 167.1 1939 195.3 1678.3 157.70 -6.78 1.00 0.219 1.00 0.4 34.0 11.0 -5.52 5372 2625 0 B8.0 87.3 35.0 34.1 16.4 15.6 8.5 9.9 2.1 250.7 249.1 1694 165.6 192.0 195.0 1657.9 137.98 -6.26 1.00 0.216 1.00 0.4 29.1 9.5 -5.60 5392 2700 0 88.1 87.2 35.0 35.6 16.3 15.6 86 10.0 2.1 2506 249.0 161.6 162 8 188.5 191.4 1662.4 132.18 -5.20 1.00 0.215 1.00 0.4 28.2 9.1 -623 5393 2030 0 87.1 86.1 34.8 35.5 17.3 16.7 8.4 10.3 2.5 250.6 249.2 170.3 165.6 192.9 195.3 1668.5 170.07 -7.86 1.00 0.240 0.98 0.4 41.9 13.8 -6.02 5427 3190 0 88.2 89.1 34.9 35.1 15.6 14.9 6.3 9.5 2.3 250.7 249.7 171.9 152.2 185.9 191 4 1708.2 170.59 -6.10 1.00 0.215 1.00 0.4 36.8 12.0 -6.84 5461 1720 0 87.7 87.6 350 34.5 15.1 14.5 88 10.3 2.4 250.4 249.4 167.9 165.1 189.5 194.3 1735.3 208.02 -7.50 1.00 0.202 1.00 0.4 42.7 13.9 -6.24 8017 2220 0 87.8 87.0 350 35.2 17.6 16.9 9.0 10.0 1.7 250.4 249.7 168.7 159.2 189.8 192.6 1718.3 194.26 -8.88 1.00 0212 1.00 0.4 41 2 134 -5.94 8049 1740 0 88.5 87.6 35.0 34.1 15.5 14.8 93 10.1 1.6 250 1 249.2 170.5 153.8 187.5 191.3 1721.2 193.49 -8.83 1.00 0.212 1.00 0.4 41.4 13.4 -4.90 8062 1615 0 87.5 88.0 34.9 34.4 17.6 16.8 88 10.3 2.1 250.6 249.7 174.3 168.5 192.9 197.7 1794.5 262.83 -9.66 1.00 0.211 1.00 0.4 54.7 17.9 -6.31 8080 3220 0 87.5 86.2 35.0 34.9 17.5 16.8 86 10.2 2.1 250.4 249.1 173.4 170.1 194.4 1977 1771.9 242.94 -8.55 1.00 0.203 1.00 0.4 49.8 16.3 -7.52 8098 2040 0 88.1 875 35.2 34.8 17.4 16.7 8.7 10.3 2.2 250.4 249.5 158.5 169.0 191.0 192.5 1796.1 266.87 -10.54 1.00 0.204 1.00 0.4 55.8 18.0 -6.40 8104 2705 0 86.1 86.0 34.8 35.1 17.5 16.8 8.5 10.7 2.4 250.8 249.2 163.0 163.1 189.4 192.1 1721.8 199.17 -8.27 1.00 0.209 1.00 0.4 41.1 13.7 -5.74 8125 2225 0 87.9 87.6 35.1 34.6 15.0 14.4 86 10.5 1.7 250.2 251.9 171.9 159.7 194.1 1942 1798.6 262.82 -9.56 1.00 0.217 1.00 0.4 56.5 18.3 -6.64 8163 1850 0 882 85.7 35.2 34.4 16.6 15.9 87 11.1 1.7 250.6 249.3 168.5 147.7 183.7 188.7 1741.7 21266 -8.56 1.00 0.214 1.00 0.4 46.4 15.0 -5.95 8169 2545 0 87.5 85.4 35.1 34.3 15.6 15.0 8.4 9.2 0.7 250.4 249.5 170.7 147.1 177.0 189.2 1770.6 248.62 -11.35 1.00 0.216 1.00 0.4 53.9 17.5 -5.21 8250. 1530 0 88.3 86.0 35.0 34.5 16.0 15.3 9.7 9.8 1.0 250.3 249.5 144.8 142.1 175.8 178.9 1716.9 185.35 -9.56 1.00 0.212 1.00 0.4 393 12.7 -4.58 8288 2050 0 88.4 86.3 35.0 34.3 17.0 16.2 8.3 9.0 0.5 250.1 249.6 156.9 149.5 174.5 185.4 1762.7 237.75 -10.97 1.00 0.221 1.00 0.4 51.7 16.7 -5.14 8327 2260 0 88.4 87.0 35.1 34.7 16.4 15 6 8.9 10.0 2.5 250.4 249.4 164.4 166.6 191.8 193.7 1767.0 244.32 -9.86 1.00 0.217 1.00 0.4 53.0 17.1 -5.94 8360 1595 0 87.8 88.3 35.3 34.6 15.3 14.7 8.3 9.9 1.5 250.7 250.0 165.2 165.8 193.6 193.8 1719.6 193.09 -8.27 1.00 0.202 1.00 0.4 39.6 12.8 -5.16 8373 2600 0 86.9 86.1 35.0 34.9 16.9 16.2 8.6 10.6 2.7 250.1 249.0 172.4 1625 189.1 194.8 1791.3 272.41 -8.77 1.00 0.207 1.00 0.4 56.2 18.5 -6.84 8414 1190 1 87.7 87.1 35.0 351 16.5 15 8 8.5 10.3 19 250.2 249.8 162.9 159.9 186.4 190.9 1755.4 221.20 -8.03 . 1.00 0.206 1.00 0.4 45.8 15.0 -6.02 8444 1535 0 87.8 86.2 34.9 34.5 15.8 15.2 9 1 10.0 1.5 250.3 248.9 160.9 157.3 182.7 189.2 1815.4 267.91 -8.99 1.00 0.221 1.00 0.4 56.5 18.5 -6.75 8498 3330 0 88 0 86.7 35.0 34.9 16.0 15.3 8.4 9.8 1.9 250.1 250.1 176.9 169.5 195.2 198.8 1732.1 170.99 -8.58 1.00 0.187 1.00 0.4 31.6 10.3 -4.09 mean 2294 87.8 87.3 35.0 34.8 16.5 15.9 8.7 10.2 1.9 250.4 249.5 166.0 161.5 189.3 192.5 1733.5 207.89 -8.62 1.00 0.214 1.00 0.4 44.6 14.5 -5.94 COV(%)= sum = 1 06 1.2 0.3 12 7.7 7.8 5.6 8.5 24.6 0.1 0.2 3.8 4.0 2.4 1.8 3.5 28.56 -22.65 0.00 3.469 0.26 00 29.0 29.2 1^ o Append ix II Sample Number = 016, Temperature = 150°C spec failure cc width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500s @end of loading ness deter loading deter load deflection (mm) (mm) (mm) (mm) (mm) (lb) (|b) (%) (%) (%) CO CC) CC) CO CO CC) (s) (s) fkN/mm) (kN/s) (kN) (kN) (MPa) (mm) 26 1505 0 88.9 87.9 35.2 34.6 17.2 16.9 10.6 10.7 6.1 150.1 151.7 128.8 122 1 126.4 133.9 2725.9 1162.81 -11.00 1.00 0.069 1.00 0.4 77.3 24.7 -7.63 58 3275 0 87.9 86.8 35.0 35.0 20.3 20.1 9.7 11.0 7.7 150.3 151.4 134.8 1323 127.0 139.3 2746.9 1185.54 -11.68 1.00 0.067 1.00 0.4 79.0 25.7 -7.95 94 3475 0 87.5 860 35.0 34.9 18.1 17.8 10.2 10.9 7.8 150.3 151.4 130.0 1332 125.3 138.0 2979.1 1393.37 -10.17 1.00 0.067 1.00 0.4 94.0 30.7 -10.35 119 2325 0 88.2 87.7 35.0 34.8 19.0 18.8 9.4 10.6 7.6 150.5 151.3 135.0 133.5 125.7 139.8 2889.0 1309.44 -11.48 1.00 0.068 1.00 0.4 88.2 28.5 -8.86 144 2280 0 87.9 866 35.0 34.6 19.1 18.8 9.5 10.7 6.1 150.1 151.8 127.0 1258 127.1 134.6 2902.8 1336.51 -11.10 1.00 0.066 1.00 0.4 89.1 29.0 -9.62 150 1815 0 87.6 87.0 35.0 34.9 19.2 18.9 9.9 10.9 8.2 150.1 149.7 139.9 1370 127.6 142.3 3425.0 1859.81 -12.82 1.00 0.066 1.00 0.4 125.6 40.9 -11.42 155 1720 0 88.6 87.5 35.1 34.8 18.4 18.2 10.0 10.6 7.3 150.0 151.5 125.6 129.0 126.9 135.1 2588.2 1017.52 -11.08 1.00 0.068 1.00 0.4 68.2 21.9 -7.07 175 3020 0 87.3 86.2 352 34.9 17.3 17.0 9.3 10.4 6.8 150.3 151.2 135.2 127.2 127.2 137.7 2919.8 1342.76 -11.44 1.00 0.069 1.00 0.4 90.3 29.4 -882 194 2340 0 88.6 B7.7 35.1 34.9 16.2 16.0 9.6 10.2 6.8 150.6 151.8 136.5 122.8 126.8 136.8 2584.9 1029.57 -10.43 1.00 0.065 1.00 0.4 67.7 21.8 -7.77 215 1745 0 86.9 86.2 34.9 34.8 18.0 17.7 89 10.9 5.7 150.1 151.8 1389 133.2 125.3 141.0 3618.8 2057.50 -13.50 1.00 0.068 1.00 0.4 138.9 45.8 -10.97 218 1400 0 88.3 87.5 35.0 34.8 19.3 19.0 9.7 102 6.4 150.6 151.5 137.8 133.4 127.9 140.8 3147.5 1568.63 -11.53 1.00 0.069 1.00 04 105.6 34.2 -11.11 238 2610 0 87.2 86.0 35.0 34.4 18.7 18.5 9.5 10.9 7.6 150.3 151.4 136.9 133.9 126.3 140.6 3048.9 1467.45 -11.29 1.00 0.068 1.00 0.4 98.8 32.4 -9.22 297 2300 0 87.7 87.3 35.1 34.9 16.8 16.7 9.1 10.9 7.3 150 2 151.8 136.1 132.5 127.0 139.9 2782.3 1205.34 -10.26 1.00 0.068 1.00 0.4 80.8 26.3 -8.95 351 3070 0 87.0 86.7 35 1 34.7 18.6 18.4 9.3 10.6 8.1 150.1 151.8 131.8 130.1 127.6 137.6 2585.7 1046.36 -10.29 1.00 0.067 1.00 0.4 69.1 22.7 -9.09 355 1875 0 88.4 87.1 35.1 34.8 16.6 16.3 94 10.3 6.4 150.5 151.6 119.8 119.8 124.5 130.2 2472.3 919.81 -10.76 1.00 0.067 1.00 0.4 61.0 19.7 -6.37 360 2460 0 87.9 87.2 35.0 34.7 16.8 16.6 9.3 10.4 6.0 150.2 151.6 129.9 124.4 125.9 135.1 2622.8 1060.78 -11.13 1.00 0.067 1.00 0.4 70.8 23.0 -683 372 1605 0 87.0 85.9 34.8 34.7 18.3 18.1 8.6 10.3 6.4 150.0 151.6 134.9 1323 124.4 139.4 2913.5 1340.85 -11.63 1.00 0.066 1.00 0.4 89.5 29.6 -8.64 385 1955 0 878 87.4 35.1 34.9 18.1 17.9 9.3 10.3 7.3 150.5 151.4 128.5 1298 125.8 136.4 25299 972.67 -10.43 1.00 0.067 1 00 0.4 64.2 20.8 -7.16 442 1360 0 88.7 87.7 35.2 34.7 16.9 16.6 9.8 9.9 5.7 150.5 151.3 128.3 124.6 126.4 134.6 30753 1496.84 -11.03 1.00 0.067 1.00 0.4 101.2 32.4 -10.19 452 1945 0 87.1 86.5 34.9 34.8 18.2 17.9 8.9 10.5 5.7 150.5 151.2 125.1 127.2 125.2 134.4 3132.6 1574.07 -13.75 1.00 0.067 1.00 0.4 106.7 35.2 -9.00 459 2650 0 87.8 B7.0 34.9 35.0 18.4 182 9.1 9.9 6.8 150.5 151.6 136.8 1338 126.7 140.5 3014.9 1401.98 -11.51 1.00 0.070 1.00 0.4 96.6 31.6 -9.54 489 3445 0 88.0 86.8 35.0 34.7 17.1 16.9 8.9 10.3 8.0 150.1 151.4 132.1 132.1 126.6 138.3 2594.3 1046.27 -11.36 1.00 0.066 1.00 0.4 69.0 22.4 -7.02 5007 1830 0 88.6 87.8 35.1 34.8 16.0 15.7 9.3 10.0 6.0 150.1 151.5 131.2 127.0 1280 136.3 2400.1 846.44 -8.16 1.00 0.067 1.00 0.4 56.0 18.0 -7.57 5027 3395 0 68 3 87.8 35.0 35.0 15.8 15.6 9.4 10.7 7.3 150.0 151.3 131.2 1274 1289 136.4 2359.7 819.53 -7.50 1.00 0.067 1.00 0.4 53.9 17.4 -8.10 5051 1660 0 88.6 87.5 35.1 34.9 16.0 15.8 9.5 10.4 6.8 150.1 151.4 129.3 1276 127.5 135.9 2307.3 755.03 -8.72 1.00 0.066 1.00 0.4 49.8 16.0 -7.18 5071 2245 0 87.9 87.4 34.9 34.7 15.1 14.9 9.2 10.7 7.2 150.5 151.4 133.0 129.3 131.0 137.7 2313.4 780.86 -7.55 1.00 0.069 1.00 04 51.7 16.9 -8.14 5086 1415 0 87.4 87.1 34.9 34.7 13.9 13.7 9.3 11.1 8.0 150.2 149.4 129.2 125.8 128.8 135.0 2063.3 496.76 -5.68 1.00 0.068 1.00 0.4 32.5 10.7 -6.73 5115 1375 0 87.7 86.8 34.7 34.6 14.4 14.2 9.3 10.2 6.7 150.4 151.7 130.2 120.1 126.4 133.8 2495.5 906.92 -8.49 1.00 0.068 1.00 0.4 61.4 20.2 -7.81 5216 1480 0 88.1 86.8 35.1 35.0 15.1 14.9 8.6 10.4 6.4 150.1 151.8 133.9 129.2 127.5 138.0 2654.9 1072.33 -10.20 1.00 0.069 1.00 0.4 72.6 23.5 -8.13 5220 1540 0 87.9 87.3 35.2 35.0 15.8 15.7 8.9 10.8 7.7 150.5 151.7 134.5 132.4 129.1 139.3 2531.0 996.12 -7.94 1.00 0.068 1.00 0.4 66.4 21.5 -9.20 5251 2490 0 88.2 87.8 35.2 34.8 16.4 16.2 9.3 10.4 7.4 150.5 151.8 135.1 131.9 128.1 139.4 2388.3 829.01 -7.56 1.00 0.067 1.00 0.4 54.7 17.6 -8.14 5262 1520 0 88.1 87.5 35.1 34.9 17.1 16.9 9.0 10.6 8.8 150.1 151.3 135.3 134.7 129.8 140.2 2621.1 1058.14 -7.24 1.00 0.066 1.00 0.4 70.2 22.7 -11.20 5268 2165 0 87.0 86.6 35.0 34.6 17.2 17.0 9.3 10.6 8.1 150.0 151.7 135.9 134.5 129.4 140.4 26625 1091.99 -7.80 1.00 0.067 1.00 0.4 72.6 23.8 -11.20 5285 2175 0 88.9 88.4 35.1 34.8 16.0 15.8 9.0 9.8 6.4 150.0 151.8 124.3 128.8 127.8 134.7 2279.8 708.32 -6.12 1.00 0.067 1.00 0.4 47.1 15.1 -9.85 5297 2475 0 88.3 88.3 35.0 34.8 15.0 14.8 9.1 10.3 6.9 150.3 151.8 132.7 131.8 129.9 138.5 2343.9 767.87 -6.60 1.00 0.069 1.00 04 51.0 16.5 -8.71 5309 2540 0 B7.8 87.5 35.1 35.0 16.2 16.1 9.3 10.4 7.9 150.6 151.4 134.9 132.2 129.9 139.4 2408.5 875.97 -664 1.00 0.068 1.00 0.4 58.0 18.8 -11.09 5323 2065 0 87.7 87.0 35.1 34.7 16.4 162 9.2 10.1 7.7 150.5 151.9 129.9 129.7 129.2 136.9 2387.2 851.76 -6.13 1.00 0.068 1.00 0.4 57.0 18.5 -10.45 5334 2580 0 87.7 86.7 35 1 34.5 15.9 15.6 9.2 10.2 5.4 150.5 151.3 119.4 123.8 127.6 131.4 2420.7 863.44 -9.28 1.00 0.068 1.00 0.4 57.8 18.8 -6.57 5381 3050 0 87.6 87.1 35.0 34.9 17.1 16.9 9.3 10.4 7.4 150.5 151.4 133.4 130.3 127.1 138.2 2465.3 917.25 -8.38 1.00 0067 1.00 0.4 60.9 19.9 -7.91 5389 2895 0 88.0 87.5 35.0 34.9 17.8 17.6 8.9 10.1 7.8 150.0 151.6 136.6 133.6 129.7 140.3 2513.3 981.75 -7.03 1.00 0.068 1.00 04 65.9 21.4 -11.25 5407 1240 0 88.2 87.8 34.9 34.8 15.5 15.3 8.6 10.3 7.7 150.1 151.7 131.7 133.3 130.7 138.6 2281.7 716.80 -5.80 1.00 0.067 1.00 0.4 47.5 15.5 -9.54 5411 2440 0 87.5 86.4 34.9 34.7 16.2 16.0 8.7 10.8 7.8 150.5 151.7 133.8 131.4 130.1 138.8 2431.0 860.85 -7.11 1.00 0.067 1.00 0.4 57.7 18.9 -8.91 8015 3535 0 68.2 87.7 35.2 35.0 17.1 16.9 9.0 10.3 7.4 150.0 151.6 133.7 129.2 128.5 137.9 2350.5 799.65 -8.45 1.00 0.067 1.00 0.4 52.7 17.0 -6.79 8027 3425 0 87.8 87.5 35.0 35.0 16.1 16.0 8.9 10.3 8.0 150.5 151.4 136.1 132.4 128.6 139.8 2508.7 900.99 -8.59 1.00 0.069 1.00 0.4 60.6 19.7 -8.26 8038 1590 0 87.4 87.0 35.1 35.2 16.6 16.5 8.6 10.6 7.8 150.6 151.7 136.9 129.7 127.7 139.2 2611.3 1015.47 -8.77 1.00 0.067 1.00 0.4 68.5 22.4 -9.19 8063 1345 0 88.2 B7.4 35.0 35.0 18.4 18.3 9.5 10.7 7.5 150.3 151.3 130.9 127.8 127.3 136.5 2339.0 789.98 -8.91 1.00 0.067 1.00 0.4 52.3 17.0 -7.38 8103 1095 1 87.5 86.0 35.0 34.5 17.8 17.5 10.1 11.1 6 1 150.6 151.3 128.3 1257 1277 135.0 3003.6 1433.34 -8.54 1.00 0.067 1.00 0.4 96.5 31.5 -1232 8242 3350 0 88.1 87.3 34.9 34.6 16.9 16.6 9.4 10.8 7.2 150.6 151.8 123.5 121.9 125.7 132.2 2483.7 916.72 -10.55 1.00 0.068 1.00 0.4 60.6 19.7 -6.61 8257 2665 0 87.8 87.1 35.1 34.8 16.6 16.4 9.2 10.2 7.6 150.5 151.5 135.7 126.4 128.0 137.7 2644.9 1074.63 -8.90 1.00 0.067 1.00 0.4 71.8 23.3 -9.05 8271 3240 0 88.8 88.0 34.8 34.7 15.6 15.4 9.7 10.2 5.8 150.3 151.4 133.7 126.4 127.9 137.0 2871.1 1347.73 -10.72 1.00 0.068 1.00 0.4 90.1 29.2 -931 8280 2590 0 875 87.2 35.0 34.7 18.0 17.7 9.1 10.7 7.4 150.1 151.5 137.6 135.7 128.4 141.4 2727.8 1167.01 -9.16 1.00 0.067 1.00 0.4 77.2 25.2 -9.49 8304 2445 0 86.5 85.8 34.8 34.6 16.9 16.7 8.6 10.9 6.6 149.9 151.3 137.0 127.7 128.9 138.4 2826.0 1267.51 -10.07 1.00 0.068 1.00 0.4 B4.9 28.2 -8.99 8357 1475 0 88.3 87.5 35 1 34.9 16.2 16.0 8.2 10.1 6.8 150.2 151.8 137.6 133.1 129.6 140.6 2639.8 1080.84 -9.01 1.00 0.068 1.00 0.4 72.S 23.5 -9.37 8382 1420 0 87.2 86.7 35.0 34.8 18 8 18.5 9.2 10.7 7.4 150.0 151.6 136.8 127.9 125.2 138.5 3060.8 1471.20 -10.54 1.00 0.068 1.00 0.4 99.1 32.5 -10.63 8391 2100 0 87.6 87.3 35.1 34.9 16.4 16.2 8.8 10.1 7.8 149.9 151.4 132.6 129.2 128.6 137.5 2303.7 730.05 -8.94 1.00 0.067 1.00 0.4 48.7 15.8 -6.54 8406 2585 0 87.5 86.6 34.9 34.8 16.7 16.6 8.9 10.2 8.0 150.2 151.5 137.5 133.8 128.7 140.7 2577.5 1006.95 -8.46 1.00 0.067 1.00 0.4 66.5 21.8 -9.71 8413 2360 0 87.6 86.9 35.0 34.7 16.6 16.4 9.0 10.7 7.4 150.5 151.7 134.7 132.4 129.7 139.4 2838.3 1290.52 -7.89 1.00 0.067 1.00 0.4 85.6 27.9 -12.97 8457 3225 0 88.5 87.8 35.0 34.7 16.8 16.5 9.6 11.0 8.1 150.3 151.7 137.0 134.2 129.7 140.8 2634.7 1071.08 -8.89 1.00 0.067 1.00 0.4 70.4 22.7 -10.26 8459 1650 0 87.4 86.4 35.0 35.0 17.5 17.3 9.0 10.4 7.2 150.5 151.7 135.8 130.9 127.4 139.2 2650.2 1080.63 -11.02 1.00 0.068 1.00 0.4 72.1 23.6 -7.29 8461 2790 0 87.9 873 35.0 35.0 16.2 16.0 9.2 10.3 7.3 150.2 151.7 139 6 138.1 128.3 142.9 2928.6 1350.68 -10.71 1.00 0.069 1.00 0.4 91.0 29.6 -8.99 avg = 87.9 87.1 35.0 34.8 17.0 16.8 9.2 10.5 7.1 150.3 151.5 132.8 129.8 127.7 137.8 . 2660.5 1096.47 -9.46 1.00 0.067 1.00 0.4 73.3 23.8 -8.91 COV(%)= sum= 1 0.6 0.7 0.3 0.4 7.6 7.6 4.7 3.0 10.8 0.1 0.3 3.5 3.2 1.2 1.9 11.2 26.83 -20.28 0.00 1.375 0.00 0.0 27.5 27.8 -17.55 Appendix II Sample Number = 017, Temperature = 200°C spec failure cc width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 @1500 s @end of loading ness deter loading deter load deflection (mm) (mm) (mm) (mm) (mm) (lb) (lb) (%) (%) (%) CO CO CC) CC) CO CC) (S) (s) (kN/rnm) (kN/s) W) (kN) (MPa) (mm) 6 1725 0 88.7 87.9 35.2 34.5 17.9 17.4 9.3 10.2 3.4 199.9 199.4 167.7 154.8 151.3 174.0 2738.9 1152.28 -11.55 1.00 0.068 1.00 0.4 78.2 25.1 -8.29 12 1640 0 88.5 87.8 35.0 34.9 19.4 18.8 9 1 10.5 3.1 199.9 199.3 164.5 157.3 164.9 173.8 2728.9 1164.37 -10.29 1.00 0.068 1.00 0.4 78.2 25.3 -8.76 18 1480 0 88.2 87.6 35.2 34.9 18.4 17.9 10.0 10.3 3.5 199.9 199.6 164.6 161.7 157.9 175.3 2812.4 1281.88 -10.66 1.00 0.068 1.00 0.4 86.2 27.8 -8.69 34 . 2645 0 87.6 87.3 35.2 35.1 18.2 17.6 10.1 11.0 4.1 200.2 199.3 1522 158.3 164.4 170.1 2300.4 752.58 -8.28 1.00 0.069 1.00 0.4 51.3 16.6 -7.15 39 2005 0 88.9 88.5 35.2 34.7 17.8 17.4 9.3 10.8 4.8 200.4 199.3 162.2 159.5 1602 173.8 2199.6 658.02 -9.25 1.00 0.069 1.00 0.4 45.2 14.5 -5.67 43 1795 0 88.5 87.2 35.1 34.9 17.8 17.2 9.8 10.5 5.0 200.3 199.5 159.3 146.0 158.2 168.4 2295.3 704.61 -9.93 1.00 0.069 1.00 0.4 48.0 15.5 -5.81 56 2510 0 88.0 88.3 35.1 35.3 18.4 17.7 9.3 10.6 4.1 200.3 199.8 163.4 150.4 160.9 171.3 2643.3 1093.70 -9.27 1.00 0.068 1.00 0.4 74.0 24.0 -9.58 70 2565 0 88.9 87.4 35.1 34.7 16.8 16.1 9.2 9.2 1.1 200.4 199.6 154.7 143.6 144.9 166.1 2682.0 1082.38 -16.15 0.97 0.069 1.00 0.4 73.7 23.6 -5.61 118 1950 0 874 85.9 34.9 34.9 200 19.4 9.7 10.8 3.8 200.4 199.2 158.6 148.9 153.3 169.1 2581.9 1010.71 -12.19 1.00 0.068 1.00 0.4 68.2 22.4 -6.74 152 1800 0 87.3 86.3 34.9 34.9 18.7 18.1 9.5 10.8 5.0 200.4 199.4 152.7 142.9 152.5 165.2 2286.3 744.86 -12.04 1.00 0.067 1.00 0.4 49.8 16.3 -4.69 183 2600 0 87.9 86.1 35.0 34.6 17.6 17.0 9.3 10.6 3.6 200.4 199.4 141.4 138.6 156.5 160.0 2535.3 1011.59 -11.37 1.00 0.069 1.00 0.4 67.8 22.1 -891 199 1860 0 87.3 87.6 35.0 34.9 19.2 18.8 9.4 10.7 3.7 199.9 199.7 153.7 163.6 161.6 172.4 2542.7 1004.82 -10.65 1.00 0.068 1.00 0.4 68.0 22.2 -7.15 217 2540 0 87.4 88.1 35.1 35.0 17.3 17.0 8.8 10.6 4.5 200.2 199.7 151.3 155.3 157.9 168.8 2083.5 558.55 -9.97 1.00 0.068 1.00 0.4 37.6 122 -5.04 262 2435 0 87.1 87.4 34.8 35.3 18.5 18.0 8.7 10.6 4.2 200.3 199.3 153.7 160.5 164.1 171.3 2552.9 1005.24 -9.48 1.00 0067 1.00 0.4 66.9 22.1 -8.28 341 2460 0 88.7 86.1 349 34.7 17.4 17.0 9.0 10.7 4.3 199.9 199.6 156.7 149.2 157.2 1685 2159.7 595.15 -11.06 1.00 0.069 1.00 0.4 40.1 12.9 -3.96 350 3420 0 87.0 87.3 34.9 34.5 18.3 17.8 8.6 10.2 62 200.3 199.6 137.6 170.1 153.9 169.2 2566.6 1029.92 -15.56 1.00 0.068 1.00 0.4 69.5 22.9 -5.42 411 3275 0 87.8 87.0 35.0 35.2 17.3 16.9 9.3 10.3 4.0 200.1 199.2 159.3 161.1 161.8 173.3 2248.7 703.49 -9.15 1.00 0.068 1.00 0.4 47.1 15.3 -5.75 428 1830 0 87.1 85.0 34.9 350 20.0 19.5 9.4 10.8 3.1 199.9 199.3 165.2 167.6 158.1 177.5 3021.8 1454.56 -13.59 1.00 0.068 1.00 0.4 98.3 32.3 -9.29 429 2120 0 86.8 86.1 34.9 35.5 180 17.6 9.4 10.8 5.0 200.1 199.8 156.7 158.3 159.9 171.7 2111.8 566.46 -9.78 1.00 0.069 1.00 0.4 38.3 12.6 -5.81 490 2280 0 88.1 86.0 34.9 344 17.8 17.1 9.8 10.7 1.4 200.0 199.6 138.9 127.8 141.0 155.5 2676.1 1143.36 -13.52 1.00 0.068 1.00 0.4 77.3 25.1 -6.39 5002 1275 0 87.2 86.6 35.0 34.1 16.8 16.4 9.4 10.6 3.8 199.9 199.4 155.5 157.2 162.6 170.8 2373.6 827.45 -6.91 1.00 0.068 1.00 0.4 55.8 183 -9.06 5013 1465 0 89.0 88 4 350 34.7 14.2 13.8 9.4 9.7 38 200.1 199.2 151.6 148.0 162.4 1664 2078.9 500.11 -5.62 1.00 0.069 1.00 0.4 33.4 10.7 -6.23 5074 3295 0 87.6 87.5 34.9 35.1 16.4 16.0 9.0 10.3 69 200.1 199.4 159.3 153.9 166.4 171.0 1924.8 358.66 -4.50 1.00 0.067 1.00 0.4 23.3 7.6 -5.73 5075 1570 0 87.9 87.2 350 35.4 15.2 14.7 9.2 10.8 3.3 200.0 199.8 155.7 148.6 161.4 168.1 2326 3 75031 -6.88 1.00 0069 1.00 0.4 50.1 16.3 -8.39 5081 1560 0 88.8 87.7 35.1 35.1 16.4 16.0 8.9 10.6 4.3 200.0 199.7 154.5 150.7 157.1 168.3 2188.7 617.91 -6.68 1.00 0.068 1.00 0.4 41.1 132 -766 5088 1635 0 87.5 86.2 34.9 34.4 15.0 14.5 6.9 10.4 2.8 199.9 199.5 154.1 145.8 154.1 166.5 2597.7 1044.12 -9.69 1.00 0.067 1.00 0.4 694 22.7 -7.64 5091 3490 0 88.2 87.1 34.9 34.8 14.5 14.0 9.2 10.0 4.6 200.1 199.8 166.6 165.9 165.0 177.5 2352.2 794.38 -6.73 1.00 0.067 1.00 0.4 53.0 17.2 -9.00 5151 3040 0 87.7 86.5 34.9 34.5 15.7 15.2 9.4 10.1 2.8 200.3 199.2 147.4 137.5 155.7 161.5 2207.3 645.91 -6.72 1.00 0.068 1.00 04 43.4 14.2 -7.72 5164 1590 0 88.6 87.9 35.0 34.7 16.1 15.6 9.1 10.6 4.7 200.3 199.3 151.3 153.4 169.0 168.2 2046.7 462.17 -5.86 1.00 0.068 1.00 0.4 31.1 10.0 -6.25 5180 1300 0 87.1 87.4 35.1 36.4 15.6 15.1 9.1 10.3 4.5 200.1 199.6 157.8 151.2 164.7 169.6 2098.2 544.72 -5.79 1.00 0.068 1.00 0.4 36.5 11.9 -7.16 5218 2020 0 88.2 68.2 35.2 35.2 14.8 14.4 8.8 10.4 4.0 200.1 199.6 163.4 157.1 164.2 173.4 2244.4 511.93 -5.97 1.00 0.067 1.00 0.4 34.1 11.0 -5.84 5233 2500 0 88.0 87.7 35.0 34.6 15.8 15.3 9.2 10.2 5.3 200.2 201.9 154.6 149.0 167.1 168.2 2013.8 463.18 -5.64 1.00 0.066 1.00 0.4 30.9 10.0 -5.76 5237 2880 0 883 88.0 35.1 34.8 14.4 14.0 9.1 10.6 3.0 200.0 199.4 160.3 154.3 156.2 171.5 2464.9 922.27 -8.69 1.00 0.068 1.00 0.4 62.6 20.2 -7.68 5274 3210 0 882 87.0 35.1 34.6 15.6 15.2 9.1 10.4 2.5 200.1 199.8 148.9 145.8 153.6 164.9 2441.9 B51.03 -8.16 1.00 0.068 1.00 0.4 57.3 18.5 -7.31 5294 1990 0 882 87.0 35.1 34.7 15.8 15.4 90 10.5 3.0 200.5 199.6 149.3 145.4 157.3 164.9 2155.3 600.00 -883 1.00 0.067 1.00 0.4 39.8 12.9 -4.67 5328 2700 0 88.3 87.6 35.3 35.2 16.8 16.4 9.0 10.0 3.8 200.2 199.9 156.9 149.5 162.8 168.8 2229.4 632.31 -6.42 1.00 0067 1.00 0.4 42.4 13.6 -7.41 5345 2200 0 88.5 87.8 35.0 35.5 179 17.4 9.2 9.8 3.3 200.2 199.2 160.6 163.0 163.4 174.4 2405.8 866.41 -899 1.00 0.069 1.00 0.4 58.9 19.0 -8.07 5475 2820 0 88.5 88.6 34.9 35.3 16.1 15.6 8.9 9.8 4.7 199.9 199.2 149.2 147.4 165.0 165.4 1987.7 446.51 -6.35 1.00 0.069 1.00 0.4 30.2 9.8 -5.20 8022 2065 0 86.7 84.7 34.9 34.7 16.4 15.9 90 10.4 3.5 200.3 199.4 163.3 152.7 153.8 171.9 2817.0 1239.46 -10.76 1.00 0.068 1.00 0.4 83.6 27.6 -8.05 8024 2335 0 88.1 88.8 34.9 34.8 16.5 16.1 8.6 9.8 4.3 200.1 199.7 161.6 159.7 159.8 173.7 2269.2 725.22 -8.83 1.00 0.069 1.00 0.4 48.1 15.6 -7.07 8050 3515 0 87.0 86.5 34.8 34.7 16.8 16.4 8.9 10.6 3.9 200.1 199.2 1605 149.1 167.8 169.7 2527.8 937.77 -8.15 1.00 0.069 1.00 0.4 63.6 21.0 -8.52 8093 1780 0 87.8 87.7 35.0 35.0 16.8 16.4 9.4 10.7 4.1 200.3 199.3 161.1 155.2 161.5 172.0 2351.7 763.89 -7.86 1.00 0.068 1.00 0.4 51.4 16.7 -7.36 8144 2665 0 88.4 86.7 35.0 34.8 15.6 15.1 9.3 10.9 4.9 200.0 199.4 161.4 153.9 1632 171.7 2145.6 606.18 -8.33 1.00 0.069 1.00 0.4 40.7 13.1 -6 43 8164 2390 0 877 86.2 35.1 34.7 16.9 16.5 89 10.7 4.7 200.1 199.7 151.8 154.7 155.7 168.8 2254.5 689.92 -9.12 1.00 0.065 1.00 0.4 45.5 14.8 -5.38 8172 2130 0 88.3 87.6 35.0 34.8 16.7 16.3 9.2 10.3 5.0 199.9 199.7 159.1 152.4 160.1 170.5 2208.7 675.27 -8.74 1.00 0069 1.00 0.4 45.4 14.7 -6.05 8180 2330 0 879 87.3 34.8 34.7 17.4 17.0 8.5 10.1 3.8 199.9 199.3 167.4 161.3 165.2 176.1 2149.1 569.11 -6.20 1.00 0.067 1.00 0.4 37.7 12.3 -7.94 8214 2270 0 88.4 86.7 35.0 34.9 14.7 14.4 9.1 10.9 5.0 200.3 1992 150.1 144.4 157.6 164.8 1978.0 421.26 -7.77 1.00 0.068 1.00 0.4 28.0 9.1 -3.75 8237 1800 0 88.5 87.8 35.1 34.5 15.8 15.3 9.1 10.3 4.6 199.9 199.8 159.1 149.5 163.5 169.5 2336.5 789.59 -7.30 1.00 0069 1.00 0.4 53.7 17.3 -8.34 8298 1860 0 88.3 86.6 34.9 346 17.0 16.5 9.1 10.2 3.1 200.4 199.2 153.4 154.9 153.7 169.4 2758.4 1207.16 -10.58 1.00 0.067 1.00 0.4 79.9 25.9 -7.89 8318 1945 0 87.5 86.9 35.0 34.8 17.6 17.1 9.4 11.0 3.5 200.2 199.7 155.8 154.8 166.7 170.2 2515.1 960.57 -8.16 1.00 0.068 1.00 0.4 63.8 20.9 -8.55 8324 1700 0 88.4 87.4 35.1 34.8 16.9 16.2 9.3 9.9 2.3 200.1 199.6 159.4 149.7 156.6 169.7 2677.3 1119.16 -10.11 1.00 0.068 1.00 0.4 74.7 24.1 -7.94 8331 2990 0 88.0 87.8 35.2 34.9 15.9 15.6 8.9 10.1 4.7 200.1 199.6 163.0 157.1 161.9 173.3 2105.6 535.20 -8.31 1.00 0.067 1.00 04 35.8 11.6 -4.73 8337 1860 0 88.5 87.8 34.8 34.7 16.5 16.2 9.2 10.0 5.5 200.0 199.4 1556 153.6 162.9 169.6 1986.8 466.81 -6.43 1.00 0.068 1.00 0.4 31.3 10.2 -6.39 8340 2015 0 87.8 87.6 35.1 34.9 16.2 15.7 9.1 10.4 4.4 • 200.1 199.7 163.7 159.5 159.0 174.4 2517.1 921.12 -8.61 1.00 0.069 1.00 0.4 63.3 20.5 -8.54 8356 1485 0 87.9 87.3 35.1 35.1 17.8 17.3 9.2 10.5 5.4 200.3 199.6 162.7 160.4 164.2 174.3 2074.2 539.55 -6.77 1.00 0.067 1.00 0.4 35.8 11.6 -6.68 8407 2910 0 87.1 87.1 35.0 34.8 166 16.1 8.7 10.3 2.8 199.9 199.8 155.2 159.8 157.9 171.6 2618.9 1019.27 -9.23 1.00 0.069 1.00 0.4 68.7 22.5 -8.25 8411 1500 0 88.2 875 35.0 34.9 17.1 16.6 90 10.5 3.7 200.2 199.8 157.3 150.7 161.9 169.3 2395.5 894.00 -7.73 1.00 0.069 1.00 0.4 60.4 19.6 -9.24 8476 2725 0 87.6 86.6 34.9 34.8 15.5 15.1 9.3 10.4 4.2 200.3 199.4 154.4 159.8 156.5 171.4 2354.4 786.68 -8.27 1.00 0.069 1.00 0.4 52.7 173 -6.86 . 8477 2355 0 88.3 87.2 35.0 34.4 17.5 17.0 9.5 10.2 2.8 199.8 199.4 149.6 143.4 151.2 164.2 2656.4 1138.33 -13.03 1.00 0.068 1.00 0.4 76.9 24.9 -6.52 8487 2760 0 87.9 87.6 34.9 34.8 17.2 16.8 9.1 10.2 3.9 200.2 199.6 156.1 148.7 161.1 168.2 2437.1 859.96 -7.24 1.00 0.069 1.00 0.4 58.4 19.1 -8.95 avg = 87.9 87.2 35.0 34.9 16.9 16.4 92 10.4 4.0 200.1 199.5 156.5 153.1 159.5 169.8 2367.3 807.06 -8.93 1.00 0.068 1.00 0.4 54.3 17.6 -7.05 COV(%)= sum= 0 0.6 0.9 0.3 1.0 7.9 7.9 3.4 3.4 25.9 0.1 0.2 4.1 5.0 3.4 2.4 10.7 31.58 -27.26 0.39 1.225 0.00 0.0 31.8 32.0 -20.66 Append ix II Sample Number» 018, Temperature = 250°C spec failure c.c width thickness weight meter MC platen temp wood temp avg temp avg temp TTF duration stiff- coeff rate of coeff preload max UTS max number location initial final initial final initial final MC inital final 1 2 1 2 ©1500 s @end of loading ness deter loading deter load deflection (mm) (mm) (mm! (mm) (mm) (lb) (lb) (^%) (%) (%) CO CC) CO CO CO (•C) (s) (s) (kN/mm) (KN/s) (kN) (kN) (MPa) (mm) 7 1990 0 88.1 89.5 35.0 35.0 18.4 17.5 9.6 10.1 1.1 250.1 249.6 181.5 177.2 185.7 202.8 24340 903.98 -11.58 1.00 0.067 1.00 0.4 60.6 19.6 -7.37 15 1500 0 88.9 87.7 35.0 35.1 17.2 16.5 99 10.5 1.5 250.2 251.8 167.2 162.7 189.8 193.6 2101.8 527.46 -8.97 1.00 0.067 1.00 0.4 35.7 11.5 -4.48 44 3220 0 890 88.4 35.2 35.1 17.8 17.1 9.2 9.5 2.1 250.2 249.0 174.9 173.7 188.1 199.4 2040.2 464.40 -8.24 1.00 0.068 1.00 0.4 32.1 10.2 -4.89 78 1800 0 88.6 88.8 35.1 35.1 17.8 17.0 9.7 10.4 0.9 250.0 251.9 167.9 161.0 186.6 193.3 2382.0 844.85 -10.24 100 0.069 1.00 0.4 57.5 18.5 -6.65 103 2420 0 87.5 88.5 35.0 35.1 18.8 17.9 9.4 10.6 1.4 250.2 251.4 173.1 159.1 186.9 194.3 2377.5 810.53 -9.44 1.00 0.066 1.00 0.4 53.9 17.6 -6.42 109 2320 0 87.4 86.5 35.1 34.9 17.8 17.1 9.2 10.9 1.8 250.3 251.7 173.2 164.2 188.5 196.1 2189.5 652.99 -10.53 1.00 0.069 1.00 0.4 43.9 143 -5.64 112 2990 0 88.6 86.0 35.2 35.0 18.5 17.5 9.6 10.7 1.2 250.5 251.6 175.2 172.4 182.7 199.6 2546.9 996.28 -10.74 1.00 0.068 1.00 0.4 67.1 21.5 -7.56 126 2400 0 88.2 87.5 35.1 34.7 17.4 16.7 10.1 10.8 1.0 250.1 251.8 174.4 163.6 180.5 196.3 2329.8 741.41 -10.62 1.00 0.068 1.00 0.4 49.7 16.1 -5.60 131 2090 0 88.0 87.8 35.2 35.2 17.8 16.9 9.3 10.4 1.0 250.4 251.3 169.7 165.2 190.4 195.2 2318.5 790.33 -10.74 1.00 0.069 1.00 0.4 53.7 17.3 -5.50 159 2290 0 87.1 90.0 34.8 34.8 18.1 17.2 9.2 10.9 1.2 250.5 251.4 173.3 169.7 187.9 198.0 2218.1 692.03 -9.46 1.00 0.066 1.00 0.4 45.8 15.1 -5.36 230 2150 0 87.9 89.9 35.0 34.9 18.8 18.1 9.5 109 1.6 250.1 251.2 176.8 169.2 190.3 198.9 2182.1 614.97 -9.50 1.00 0.067 1.00 0.4 40.6 13.2 -4.52 241 2000 0 87.7 B7.6 35.0 34.7 17.6 15.0 9.1 10.4 0.8 250.1 251.7 173.7 171.8 187.9 198.8 2599.1 70942 -9.12 1.00 0.069 1.00 0.4 47.8 15.6 -6.36 256 1440 0 87.0 86.6 34.9 34.9 18.7 16.1 9.6 10.7 1.0 248.4 248.9 168.9 164.8 183.9 194.1 2466.1 949.18 -10.31 1.00 0.069 1.00 0.4 63.6 20.9 -6.95 259 2320 0 87.8 86.9 35.1 34.2 18.9 18.0 9.9 10.7 1.0 248.5 251.3 178.1 167.6 180.1 198.5 2482.5 959.75 -11.89 1.00 0.069 1.00 0.4 643 20.9 -6.02 270 3200 0 87.5 87.5 35.1 34.8 19.0 18.1 9.4 10.6 1.3 250.1 251.4 179.1 159.4 185.3 196.4 2171.2 644.73 -9.14 1.00 0.068 1.00 0.4 438 14.2 -5.10 339 2610 0 87.3 87.8 35.0 35.2 18.8 18 0 9.2 10.8 1.7 250.1 249.1 171.0 160.3 186.3 193.6 2107.3 549.97 -10.36 1.00 0067 1.00 04 36.6 12.0 -4.83 348 1620 0 87.8 86.0 35.0 34.7 16.9 16.1 9.2 10.6 1.8 250.0 249.2 176.7 156.6 190.2 194.3 2059.5 522.97 -7.78 1.00 0.068 1.00 0.4 35.2 11.4 -5.11 382 1740 0 87.1 87.6 35.1 34.7 185 17.8 9.6 10.7 1.2 250.0 249.3 158.4 156.1 178.2 188.0 2014.0 484.29 -10.61 1.00 0.068 1.00 0.4 32.6 10.7 -3.21 434 3030 0 88.7 89.6 35.6 34.6 17.5 16.6 9.5 10.5 1.4 250.2 251.3 180.8 174.5 190.9 202.0 2582.7 1050.16 -10.65 1.00 0.068 1.00 0.4 70.8 22.4 -8.88 464 1445 0 88.0 86.9 349 34.8 15.2 16.0 9.1 10.6 1.4 250.1 251.3 179.1 163.8 189.2 197.9 2195.7 631.41 -11.05 1.00 0.068 1.00 0.4 42.3 13.8 -3.96 486 1900 0 88.6 87.4 35.0 34.7 17.7 16.9 9.7 10 1 10 250.5 251.2 184.0 171.9 195.0 202.2 2196.1 622.41 -9.85 1.00 0069 1.00 0.4 43.2 13.9 -6.50 5026 1350 0 87.8 87.0 35.0 36.1 164 15.5 92 10.6 16 250.3 251.3 170.3 161.8 187.6 194.3 2001.7 441.42 -7.56 1.00 0067 1.00 0.4 29.2 9.5 -4.56 5068 1800 0 88.4 87.8 35.2 36.2 15.1 14.4 9.3 10.2 1.3 250.1 250.7 173.4 161.0 188.2 194.9 1994.2 437.87 -6.88 1.00 0.069 1.00 0.4 29.3 94 -4.45 5087 2520 0 87.2 87.1 34.8 34.6 15.1 14.5 9.9 11.1 1.0 248.4 251.9 1685 164.6 181.0 194.4 2070.9 528.50 -8.14 1.00 0.067 1.00 0.4 34.7 11.4 -4.80 5100 2930 0 87.7 87.5 35.2 35.9 16.4 15.6 9.5 10.8 1.3 250.2 251.6 169.6 162.5 186.0 194.3 2163.0 615.89 -7.11 1.00 0.067 1.00 0.4 41.0 13.3 -6.56 5129 2050 0 87.9 87.0 35.1 35.8 16.8 160 9.4 10.5 1.8 248.9 251.1 168.0 165.6 188.8 194.5 2076.5 550.06 -7.10 1.00 0.068 1.00 0.4 36.5 11.8 -5.89 5186 2545 0 878 87.7 35.0 36.6 15.5 13.0 9.0 10.5 1.3 248.7 251.7 178.6 162.4 190.0 197.1 1930.5 375.41 -4.98 1.00 0.068 1.00 0.4 24.9 8.1 -5.42 5241 1790 0 883 88.1 35.1 352 16.0 15.3 9.1 106 1.3 250.6 251 9 168.4 166.7 193.3 195.5 1929.3 369.42 -5.70 1.00 0.069 1.00 0.4 24.9 8.0 -4.77 5243 2700 0 87.8 87.2 35.1 35.7 14.3 15.2 9.6 10.4 12 250.1 251.7 166.9 162.0 188.5 193.3 2051.4 506.22 -6.04 1.00 0.068 1.00 0.4 34.0 11.0 -6.28 5265 2100 0 88.3 87.5 35.4 35.9 15.7 14.7 9.1 10.7 0.9 250.6 249.4 175.8 165.6 181.3 197.1 2219.9 605.86 -7.16 1.00 0.068 1.00 0.4 41.1 13.1 -6.15 6275 1970 0 88.4 86.8 34.9 34.5 17.6 16.9 9.4 10.1 1.0 250.1 251.0 169.4 157.4 180.7 192.4 1942.7 395.92 -10.87 1.00 0.067 1.00 0.4 25.9 8.4 -2.56 5296 2240 0 88.4 87.6 34.9 35.8 14.6 13.8 9.5 10.7 12 250.1 249.6 171.7 162.0 188.9 194.5 2024.4 456.38 -5.97 1.00 0.068 1.00 0.4 30.5 9.9 -5.47 5365 2460 0 88.3 85.8 34.9 34.2 14.5 13.7 9.6 10.6 0.4 250.0 249.2 173.4 170.0 176.8 197.7 20505 507.04 -7.47 1.00 0.068 1.00 0.4 33.7 10.9 -4.91 5385 2840 0 87.7 86.7 35.0 35.5 156 14.9 9.1 10.8 1.3 250.3 251.7 174.9 167.6 181.4 197.8 2133.8 580.94 -6.39 1.00 0.067 1.00 0.4 38.7 12.6 -6.93 5421 1600 0 88.0 87.3 34.8 36.3 15.5 14.8 9.2 10.7 1.9 250.1 249.1 166.6 159.2 186.5 191.8 1919.0 362.63 -5.69 1.00 0.068 1.00 0.4 23.5 7.7 -4.85 5428 1300 0 87.9 88.9 35.0 36.0 15.6 14.9 9.5 10.7 1.4 250.5 249.7 172.9 169.9 184.7 197.6 2204.9 658.37 -7.27 1.00 0.068 1.00 0.4 44.1 14.3 -6.75 5437 1385 0 89.0 87.6 34 9 34.4 14.2 13.6 9.0 10.1 17 250.2 251.4 178.4 172.9 185.9 200.7 1872.1 330.65 -5.24 1.00 0.067 1.00 0.4 22 1 7.1 -4.42 5449 2350 0 889 89.7 35.0 34.8 15.4 14.7 8.6 9.4 1.6 250.1 251.1 179.9 179.3 200.8 203.3 2016.6 467.13 -6 65 1.00 0.067 1.00 0.4 30.7 9.9 -5.30 5460 2240 0 88.0 S73 34.9 35.8 14.6 14.0 9.4 10.6 1.5 250.3 250.7 167.8 165.9 189.2 194.7 1887.9 315.49 -7.14 1.00 0.069 1.00 0.4 21.3 6.9 -4.28 5462 2450 0 87.8 87.5 34.9 35.0 15.5 14.6 9.2 10.0 1.0 250.2 249.7 179.0 180.6 192.3 203.2 2116.2 577.99 -6 79 1.00 0.068 1.00 0.4 38.6 12.6 -6.46 5470 2070 0 87.9 86.8 34.9 34.4 16.2 15.4 9.0 10.1 1.4 250.0 251.2 173.8 168.8 187.3 197.7 1989.8 421.33 -5.42 1.00 0.067 1.00 0.4 27.6 9.0 -5.66 8001 1320 0 86.5 86 8 34.9 34.8 19.5 18.6 9.0 10.4 15 250.1 251.7 169.8 166.5 190.9 195.7 2243.0 690.00 -11.40 1.00 0.067 1.00 0.4 46.1 15.3 -4.95 8029 1690 0 88.2 87.8 350 34.8 17.0 16.2 9.3 9.9 1.0 250.4 248.7 184.1 169.3 189.5 201.0 2254.1 700.87 -9.76 1.00 0.068 1.00 0.4 47.8 15.5 -5.10 8041 3190 0 87.2 87.3 35.0 36.2 16.9 16.2 9.1 10.3 1.8 250.7 249.8 167.8 166.0 186.0 194.7 2079.7 514.59 -8.34 1.00 0.067 1.00 0.4 34.1 11.2 -4.36 B055 2170 0 87.4 87.6 350 36.4 16.0 15.2 9.1 10.2 0.8 250.0 249.1 177.9 170.5 188.5 • 199.3 2277.2 746.56 -7.67 1.00 0.069 1.00 0.4 50.6 16.6 -7.14 8066 1500 0 87.9 88 9 35.0 36.2 17.0 16.2 9.4 10.6 1.3 250.0 250.8 173.7 1636 183.2 195.9 2298.4 737.64 -9.47 1.00 0.067 1.00 0.4 49.0 15.9 -5.74 8122 2930 0 88.0 88.1 349 34.9 17.0 16.1 9.4 10.7 1.0 250.4 251.4 171.9 164.7 188.5 195.8 2285.5 750.67 -9.49 1.00 0.069 1.00 0.4 51.3 16.7 -5.89 8176 1500 0 88.0 87.3 34.9 35.7 16.3 15.6 9.4 10.3 1.1 250.0 251.7 168.7 166.9 185.1 195.5 2172.0 617.38 -8.01 1.00 0.067 1.00 0.4 41.3 13.5 -6.01 8266 3530 0 88.2 88.9 348 35.1 15.2 14.5 9.0 10.5 1.3 250.4 250.8 167.8 158.6 187.3 192.3 2010.7 469.25 -8.26 1.00 0.067 1.00 0.4 30.7 10.0 -4.77 8283 2700 0 88.6 86.7 34.8 34.6 16.3 15.7 9.1 102 1.2 250.4 251.8 170.2 166.4 181.4 195.9 2210.7 662.59 -8.82 1.00 0.068 1.00 0.4 43.6 14.1 -5.68 8287 3000 0 88.1 87.4 34.9 35.4 17.0 16.2 8.9 10.2 1.5 250.0 251.2 173.1 166.0 187.5 196.5 2194.7 638.08 -7.83 1.00 0.067 1.00 0.4 41.7 13.6 -6.91 8334 2700 0 87.5 87.2 34.9 35.0 17.1 16.2 8.8 10.3 1.0 250.0 251.6 168.5 165.9 185.7 195.1 2101.1 537.10 -7.28 1.00 0.067 1.00 0.4 35.5 11.6 -5.57 8372 2275 0 874 84.8 34.8 34.5 16.5 15.7 9.2 10.5 0.5 250.3 249.2 186.8 171.7 182.6 202.7 2375.7 830.27 -8.67 1.00 0.068 1.00 0.4 56.3 18.5 -7.67 8386 2130 0 88.0 86.5 35.1 34.3 17.9 17.0 9.7 10.3 0.9 250.1 249.4 169.4 157.2 176.2 192.1 2384.6 844.61 -10.01 1.00 0.067 1.00 0.4 56.1 18.2 -6.83 8420 3600 0 88.1 88.6 35.0 34.8 16.B 15.9 8.9 10.2 1.7 250.1 251.0 170.4 165.6 184.8 195.5 2177.5 636.83 -8.01 1.00 0.067 1.00 0.4 42.3 13.7 -6.78 8456 2530 0 88.1 87.4 34.9 34.8 16.3 15.6 8.8 9.2 1.4 250.7 252.0 176.3 172.5 186.7 200.1 2123.6 567.33 -7.60 1.00 0.066 1.00 0.4 37.4 12.1 -5.37 8480 1500 0 87.9 87.9 35.0 35.0 17.2 16.4 9.5 10.6 1.2 250.5 249.1 175.5 170.5 189.5 198.6 2296.5 752.62 -8.75 1.00 0.069 1.00 0.4 50.1 16.3 -6.24 8482 2460 0 87.8 88.5 35.0 34.7 16.6 15.8 9.2 10.7 1.1 250.5 251.4 174.1 157.7 187.0 194.3 2258.5 684.04 -9.71 1.00 0.068 1.00 0.4 46.1 15.0 -5.29 8490 2880 0 888 87.4 35.1 347 16.9 16.1 9.5 9.8 1.0 250.4 251.6 175.6 167.6 1B9.2 198.1 2044.5 559.47 -8.08 1.00 0.066 1.00 0.4 36.0 11.5 -5.27 8492 3550 0 885 86.9 34.9 35.0 16.4 15.7 9.9 10.0 1.2 250.1 251.3 168.9 167.2 186.9 195.6 2108.7 532.41 -8.90 1.00 0.069 1.00 0.4 36.1 11.7 -4.36 avg = 88.0 87.6 35.0 35.1 16.8 16.0 9.3 10.4 1.3 250.1 250.8 173.2 166.1 186.7 196.6 2174.8 619.01 -8.54 1.00 0.068 1.00 0.4 41.4 13.4 -5.62 COV(%)= sum= 0 0.6 1.1 0.4 1.7 7.9 7.9 3.3 3.5 26 8 0.2 0.4 3.0 3.3 2.3 1.6 8.0 27.33 -20.57 0.00 1.250 0.00 0.0 27.8 27.7 -20.04 APPENDIX III - PROGRAM STRUCTURE OF PARAFIT 174 PARAFIT RANDNUM NONPARST INITCOND OTTFPARA FRPRMN - [FUNC] -[DFUNC] LINMIN • [TTF] MNBRAK DBRENT-DERIVS RKQS -DF1DIM RKCK [FUNC] DERIVS SUBROUTINE ROLES PARAFIT Main program - sets up program variables, includes data files, and inputs program parameters and outputs program results. RANDNUM Inputs look-up random number table for generating random variables. NONPARST Inputs non-parametric short-term strength distribution and determines the values at various required percentile. INITCONC Inputs initialize the parameters of the function expressing the mean temperature as a function of the temperature of exposure and time. OTTFPARA Inputs lognormal parameters of the time-to-failure distributions of all the samples (Appendix III). FRPMN Given a starting point p that is a vector of length n, Polak-Ribiere minimization is performed on a function FUNC, using its gradient as calculated by DFUNC. The convergence tolerance on the function value is input as ftoi. Returned quantities are p (the location of the minimum), iter (the number of iterations that were performed), and fret (the minimum value of the function). The routine LINMIN is called to perform line FUNC The function implements Eqn [7.17], passes on to TTF the parameter vector p to compute a time-to-failure TTF Computes a time-to-failure value. Calls RKQS to perform the Runge-Kutta integration scheme. RKQS Fifth-order Runge-Kutta step with monitoring of local truncation error to ensure accuracy and adjust stepsize. Input are the dependent variable vector y(1 :n) and its derivative dydx(1 :n) at the starting value of the independent variable x. Also input are the stepsize to be attempted htry, the required accuracy eps, and the vector yscal(1 :n) against which the error is scaled. On output, y and x are replaced by their new values, hdid is the stepsize that was actually accomplished, and hnext is the estimated next stepsize. DERIVS is the user-supplied subroutine that computes the right-and side derivatives. RKCK Given values for n variables y and their derivatives dydx known at x, use the fifth-order Cash-Karp Runge-Kutta method to advance the solution over an interval h and return the incremented variables as yout. Also return an estimate of the local truncation error in yout using the embedded fourth-order method. The user supplies the subroutine DERIVES, which returns derivatives dydx at x. DERIVS Calculates the rate of damage in accordance with Eqn [7.13] given temperature and stress. LINMIN Given an n-dimensional point p(1:n) and an n-dimensional direction xi(1 :n), moves and resets p to where the function FUNC(p) takes on a minimum along the direction xi from p, and replaces xi by the actual vector displacement that p was moved. Also returns as fret the value of FUNC at the returned location p. This is actually accomplished by calling the routines MNBRAK and BRENT. MNBRAK Given a function FUNC, and given distinct initial points ax and bx, this routines searches in the downhill direction (defined by the function as evaluated at the initial points) and returns new points ax, bx, cx, that bracket a minimum of the function. Also returned are the function values at the three points, fa, fb, and fc. DBRENT Given a function f and its derivative df, and given a bracketing triplet of abscissas ax, bx, cx ,(such that bx is between ax and cx, and f(tox) is less than both f(ax) and f(cx)), this routine isolates the minimum to a fractional precision of about tol using a modification of Brent's method that uses derivatives. The abscissa of the minimum is returned as xmin, and the minimum function value is returned as dbrent, the returned function DF1 DIM Used by LINMIN as the function FUNC or f passed to MNBRAK or DBRENT. 175 APPENDIX III c c ,-C PROGRAM PARAFIT.FOR C C FILES USED C C (UNIT= 1 ,FILE='RANDIN.TBL',STATUS='OLD') RANDNUM.FOR C (UMT=2,FILE='RANDOUT.TBL',STATUS='UNI<NOVvrN') RANDNUM.FOR C (UNIT=3(FILE='ZVALIN.TBL',STATUS='OLD') OTTFPARA.FOR C (UNIT=4,FILE= ,ZVALOU.TBL',STATUS= ,UNI<NOWN') OTTFPARAFOR C (UNIT=5,FILE=DATIN,STATUS='OLD') PARAFIT AND OTHERS C (UMT=6,FILE=DATOUT,STATUS=UNI<NOWN') PARAFIT AND OTHERS C (UNIT=7,FILE= ,STSIN.TBL'JSTATUS= ,OLD') NONPARST.FOR C (UMT=83LE='STSOUT.TBL^STATUS='UNICNOWN ,) NONPARST.FOR C (UNIT=9,FILE='MESSAGE.OUT',STATUS='UNI<NOVvTS[') PARAFIT AND OTHERS PROGRAM MAIN INTEGER iter REAL FTOL, fret C FTOL = convergence tolerance C iter = return by frprmn, number of iteration used in the minimization C fret = the minimum value of the function COMMON TEMPVALUE COMMON /SAMPLE SIZE AND VARIABLES/ N , NPAR, NVAR, 1 NTILE, SCALLING, THRESHOLD, TO C N = SAMPLE SIZE OF SIMULATION C NPAR = NUMBER OF PARAMETER TO BE OPTIMIZED, MAXIMUM 10 C NVAR = NUMBER OF VARIABLES IN THE DAMAGE RATE EQUATION C FOR LOGNORMAL NPAR = 2 * NVAR C NPAR <= 10 C NTILE = FIT TO PERCENTILE OF (%) C SCALLING = FACTOR TO DIVIDE THE DIFFERENCE BETWEEN OBSERVED TTF AND C PREDICTED TTF C THRESHOLD = VALUE AS A FRACTION OF THE SHORT-TERM STRENGTH BELOW WHICH C NO DAMAGE IS ACCUMULATED AS A RESULT OF STRESS ONLY C TO = ROOM TEMPERATURE $INCLUDE:'RANDNUM.INC ! /TABLE OF RANDOM Z VALUES/ $INCLUDE:'LOGNORPA.lNC' ! /LOGN PARAMETERS SH TERM STRENGTH/ $INCLUDE:TNITCOND.INC ! /INITIAL CONDITIONS/ $INCLUDE:'OTTFPARA.INC ! /OBSERVED TTF PARAMETERS/ C C P() = ARRAY STORING THE INITIAL LOGNORMAL PARAMETER VALUES C C P( 1) = LOCATION PARAMETER M U of the first parameter C P(2) = SCALE PARAMETER SIGMA of the first parameter C P(3) = LOCATION PARAMETER M U of the second parameter C P(4) = SCALE PARAMETER SIGMA of the second parameter APPENDIX III C P(5) = LOCATION PARAMETER M U of the third parameter C P(6) = SCALE PARAMETER SIGMA of the third parameter C etc. REALM p(10) REALM SUBTITLE(20) CHARACTER CHAR( 10) M5 CHARACTER* 12 DATIN, DATOUT TEMPVALUE=1.0 WRITE(*,*) ' ENTER INPUT FILE NAME: ' READ(*,'(A12)') DATIN WRITE(*,*) 1 ENTER OUTPUT FILE NAME: ' READ (*,'(A12)') DATOUT OPEN(UNIT=5 ,FILE=DATIN,STATUS='OLD') OPEN(UNIT=6,FILE=DATOUT,STATUS=UNI<NOWN') OPEN(UNIT=9,FILE='MESSAGE.OUT,STATUS =UNKNOWN) READ(5,100) SUBTITLE WRITE(6,102) SUBTITLE 100 FORMAT(/20A4/) 102 FORMAT (1X.20A4) C This part reads in the sample size and number of variables to be C optimized, and their initial lognormal parameters values READ(5,103) N , NPAR, NVAR, FTOL, NTILE, SCALLING, THRESHOLD, TO WRITE(6,104) N , NPAR, NVAR, FTOL, NTILE, SCALLING, THRESHOLD, TO 103 FORMAT(45X,I12y,45X,I12y,45X,I12, 1 /,45X,E15.9y,45X>I12y,45X,E15.9y,45X,E15.9y,45X,E15.9) 104 FORMAT(/,4X;SAMPLE SIZE =',115, 1 /,4X,'NUMBER OF RANDOM PARAMETERS = ',115, 2 /,4X,'NUMBER OF VARIABLES IN DR FUNCTION =',115, 3 /,4X,'FUNCTION CONVERGENCE TOLERANCE ='.E15.9, 4 /,4X,'FIT TO PERCENTILE OF (%) =',112, 5 /,4X,'SCALLING FACTOR FOR THE MINIMIZATION = ',E15.9, 6 /,4X,THRESHOLD EXPRESSED AS FRACTION OF STS = ',E15.9, 7 /,4X,'ROOM TEMPERATURE ( K) =',E15.9, 8 /) C INPUT THE INITIAL LOGNORMAL VALUES OF EACH PARAMETER TO BE OPTIMIZED C SUBTITLE = " M U SIGMA " READ(5,100) SUBTITLE WRITE(6,102) SUBTITLE WRITE(6,*) DO 101=1 ,NPAR ! one parameter per line READ (5,43) CHAR(I), P(I) 43 FORMAT (A45, E12.6E2) 10 CONTINUE WRITE (6,44) (CHAR(I), P(I), 1=1,NPAR) 44 FORMAT(A45,E12.6E2) APPENDIX III WRITE(6,*) C A L L READ R A N D N U M (N,NVAR) C A L L R E A D ST STRENGTHS (N.NVAR) C A L L READ INITIAL CONDITIONS () C A L L READ OBSERVED TTF PARAMETERS () WRITE(6,*) WRITE(6,'(4x,a,/)') ******* Minimization Results ******' WRITE(6,*) C A L L frprmn (P,NPAR,FTOL,iter,fret) WRITE(*,'(/4x,a,i3)') 'Iterations:'.iter WRITE(*,'(4x,a,el4.6)') Tunc, value at solution',fret WRITE(6,'(4x,a)') 'solution vector' WRITE(6,44) (CHAR(I),P(I),I=1,NPAR) WRITE(6,'(lx,a,lx,a,2x,a,2x,a)') '%tile','exper';moder,'...' N=NT*NS D O 30 J=1,NP percentile = real(J)/(NP+1.) WRITE(6,105) percentile, (OTTFP(J,K), PTTFP(J,K),K= 1,N) 30 C O N T I N U E 105 FORMAT(lX,25F7.1) CLOSE (UNIT=5 .STATUS='KEEP) CLOSE (UNIT=6.STATUS='KEEP) CLOSE(UNIT=9,STATUS ='KEEP) STOP E N D C C Subroutine R A N D N U M . F O R C C This subroutine reads in a table of random standard C normal univariates C SUBROUTINE READ R A N D N U M (N.NVAR) R E A L M SUBTITLE (20) INTEGER N . N V A R $ I N C L U D E : ' R A N D N U M . I N C ! /TABLE OF R A N D O M Z V A L U E S / C RN(N,NVAR+1) = ARRAY T O STORE T H E R A N D O M N U M B E R S M A X RN( 1000,6) C N E E D O N E M O R E SET FOR G E N E R A T I N G ST S T R E N G T H C NVAL+1<6 C N V A R = N U M B E R OF VARIABLES I N T H E D A M A G E RATE E Q U A T I O N C FOR L O G N O R M A L N P A R = 2 * N V A R C N P A R <= 10 178 A P P E N D I X III OPEN(UNIT= 1 ,FILE='RANDIN.TBL',STATUS ='OLD') OPEN(UMT=2,FILE='RAM30UT.TBL',STATUS='UM^ C SUBTITLE = " **** TABLE OF RANDOM NUMBERS ****" READ( 1,100) SUBTITLE 100 FORMAT(/20A4/) WRITE(2,102) SUBTITLE 102. FORMAT(/1X,20A4/) DO 10 J=1,N READ (1,42) (RN(J,I),1=1,NVAR) WRITE (2,43) (RN(JJ),1=1,NVAR) 10 CONTINUE 42 FORMAT (6F 12.7) 43 FORMAT (IX, 6F12.7) CLOSE(UNIT= 1 ,STATUS ='KEEP') CLOSE(UNIT=2,STATUS ='KEEP') RETURN END PROGRAM NONPARST.FOR This routine reads in the the short-term strength sample data and the non parametric percentiles (censored). This data is provided by STS.XLS. The n observations of short-term strength are generated on the basis of these non-parametric test data subroutine READ ST STRENGTHS (N.NVAR) INTEGER N , NVAR REALSTS(2,540) C N = SAMPLE SIZE OF SIMULATION C NVAR = NUMBER OF VARIABLES IN THE DAMAGE RATE EQUATION $INCLUDE:'RANDNUM.INC ! /TABLE OF RANDOM NUMBERS/ C RN(N,NVAR) = ARRAY TO STORE THE RANDOM NUMBERS MAX RN( 1000,6) C NEED ONE MORE SET FOR GENERATING ST STRENGTH $INCLUDE:'LOGNORPAINC ! /LOGN PARAMETERS SH TERM STRENGTH/ C ROL = rate of loading for obtaining short-term strength C STSP(l) = THRESHOLD (NOT USED) C STSP(2) = LOCATION PARAMETER M U (NOT USED) C STSP(3) = SCALE PARAMETER SIGMA (NOT USED) C ST(1000) = array storing simulated short-terms strength at room temperature C C SUBTITLE = " **** INPUT TO LOGNORPA SHORT TERM STRENGTH LOGNORMAL PARAMETERS ****" APPENDIX III 179 C REAL*4 SUBTITLE(20) READ(5,100) SUBTITLE 100 FORMAT(/20A4/) WRITE(6,102) SUBTITLE 102 FORMAT (1X.20A4) READ(5,103) ROL, STSP(l), STSP(2), STSP(3) WRITE(6,104) ROL, STSP(l), STSP(2), STSP(3) 103 FORMAT(45X,G12.0y,45X,G12.0y,45X,G12.0y,45X,G12.0) 104 FORMAT(/,4X;RATE OF LOADING SH-TERM STRENGTHS = 'E15.9, 1 /,4X,THRESHOLD = ',E15.9, 2 /,4X,'LOCATION PARAMETER M U = \E15.9, 3 /,4X,'SCALE PARAMETER SIGMA = \E15.9, 4 I) C reads in actual test data in the following. In this C case we use a non-parametric approach to generate the values in ST(1000) C OPEN(UNrT=7,FILE='STSIN.TBL',STATUS='OLD') OPEN(UNIT=8,FILE='STSOUT.TBL',STATUS =UNKNOWN') C SUBTITLE = " **** TABLE OF SHORT-TERM STRENGTHS FROM TESTING ****" READ(7,100) SUBTITLE WRITE(8,102) SUBTITLE DO 10 J= 1,540 READ (7,42) STS(1,J), STS(2,J) WRITE (8,43) STS(IJ), STS(2,J) 10 CONTINUE 42 FORMAT (2F 10.7) 43 FORMAT (IX, 2F12.7) IC = NVAR J = 1 DO 30 1=1, N DO WHILE (J .LE. 540 .AND. RN(I,IC) .GT. STS(IJ)) J = J + 1 END DO IF (J .EQ. 1) THEN C THE RANDOM NUMBER IS LESS THAN THE PERCENTILE OF THE FIRST ELEMENT ST(I) = STS(2,1) - (STS(1,1)-RN(I,IC)) * 1 (STS(2,2) - STS(2,1))/(STS(1,2) - STS(1,1)) ELSE IF (J. EQ. 540) THEN C THE RANDOM NUMBER IS LARGER THAN THE PERCENTILE OF THE LAST ELEMENT ST(I) = STS(2,540) + (RN(I,IC)-STS(1,540)) * 1 (STS(2,540)-STS(2,539))/(STS(1,540)-STS(1,539)) ELSE C THE RANDOM NUMBER IS BETWEEN J AND J+1 PERCENTILES ST(I) = STS(2J-1) + (RN(LIC)-STS(lJ-l)) * 1 (STS(2J) - STS(2,J-1))/(STS(1,J) - STS(lJ-l)) 180 A P P E N D I X III END IF I = 1 30 CONTINUE WRITE (8,*) WRITE (8,'(lX,a/)') THE SHORT-TERM STRENGTH AS GENERATED' DO 40 1=1, N WRITE (8,43) RN(J,IC), ST(J) 40 CONTINUE CLOSE(UNIT= 7,STATUS='KEEP') CLOSE (UNIT= 8,STATUS='I<EEP') RETURN END C C PROGRAM INITCOND.FOR C C This routine reads in initial conditons of the test or simulations C and the parameters for the temperature model to predict the mean C temperature of the specimens. C C MODEL: T - TO = (P0*(T-T0)+Pl*t)(l-exp(-K*t/P0)) subroutine READ INITIAL CONDITIONS () $INCLUDE :'INITCOND.INC ! /INITIAL CONDITIONS/ C STARTDAMAGE = INITIAL DAMAGE C TPAR(l) =P0 C TPAR(2) = PI C TPAR(3) = K C SUBTITLE = "**** INPUT OT INITCOND: INITIAL CONDITIONS ****' C REAL*4 SUBTITLE(20) READ(5,100) SUBTITLE 100 FORMAT(/20A4/) WRITE(6,102) SUBTITLE 102 FORMAT (1X.20A4) READ(5,103) STARTDAMAGE, TPAR(l), TPAR(2), TPAR(3) WRITE(6,104) STARTDAMAGE, TPAR(l), TPAR(2), TPAR(3) 103 FORMAT(45X,G12.0y,45X,G12.0y,45X,G12.0y,45X,G12.0) 104 FORMAT(/,4X,'INITIAL DAMAGE =',E15.9, 1 /,4X,'PARAMETER P0 - to predict mean temp = ',E15.9, 2 /,4X;PARAMETER PI - to predict mean temp = ',E15.9, 3 /,4X,'PARAMETER K - to predict mean temp = '.E15.9, 4 I) RETURN END APPENDIX III 181 C C PROGRAM OTTFPARA.FOR C C This program reads in the ttf lognormal parameters of the C exposed samples subroutine READ OBSERVED TTF PARAMETERS () REAL Z(50) C Z() = ARRAY TO STORE THE STANDARD NORMAL VALUE UP TO 50 EQUAL-SPACED C PERCENTILES $INCLUDE:'OTTFPARA.INC C /OBSERVED TTF PARAMETERS/ C NT NUMBER OF TEMPERATURES OF EXPOSURE C NS NUMBER OF LOADING CONDITIONS, MAXIMUM 5 LOAD CONDITIONS C NP NUMBER OF PERCENTILE LEVELS FOR OPTIMIZATION C TTFPAR(:,1) = TEMPERATURE OF EXPOSURE C TTFPAR(:,2) = STARTING TIME OF TEMPERATURE EXPOSURE C TTFPAR(:,3) = MODE OF LOADING C TTFPAR(:,4) = STARTING TIME OF LOADING C TTFPAR(:,5) = STRESS VALUE (DEPENDS ON MODE OF LOADING) C TTFPAR(:,6) = THRESHOLD OF OBSERVED TTF LOGNORMALLY FITTED C TTFPAR(:,7) = LOCATION PARAMETER M U OF OBSERVED TTF LOGNORMALLY FITTED C TTFPAR(:,8) = SCALE PARAMETER SIGMA OF OBSERVED TTF LOGNORMALLY FITTED C OTTFP(50,12) = OBSERVED PERCENTILE TTF VALUES FOR UP TO 50 PERCENTILE LEVEL C AND 9 SAMPLES C PTTFP(50,12) = PERCENTILE VALUES OF PREDICTED TTF C SUBTITLE = " **** EXPOSURE AND LOADING CONDITIONS ***** " REAL*4 SUBTITLE(20) R£AD(5,100) SUBTITLE 100 FORMAT(/20A4/) WRITE(6,102) SUBTITLE 102 FORMAT (1X.20A4) R£AD(5,1031) NS, NT, NP WRITE(6,1041) NS, NT, NP 1031 FORMAT(45X,112 JA5X,112 /,45X,112) 1041 FORMAT(/,4X,'NUMBER OF LOADING CONDITIONS = ',115, 1 A4X/NUMBER OF TEMPERATURES OF EXPOSURE =',115, 2 /,4X/NUMBER OF PERCENTILE LEVELS = ',115, 3 I) READ(5,100) SUBTITLE WRITE(6,102) SUBTITLE C SUBTITLE = " —- TEMP TIME START MODE TIME START STRESS THRESH LOCATION SCALE-—" 182 A P P E N D I X III WRITE (6,*) DO 10K=1,NT*NS READ(5,103) TTFPAR(K,1), TTFPAR(K,2), TTFPAR(K,3), 1 TTFPAR(K,4), TTFPAR(IC5)>TTFPAR(IC6), TTFPAR(K,7), 2 TTFPAR(K,8) WRITE (6,104) TTFPAR(ICl), TTFPAR(K,2), TTFPAR(K,3), 1 TTFPAR(K,4), TTFPAR(IC5),TTFPAR(IC,6), TTFPAR(K,7), 2 TTFPAR(K,8) 20 CONTINUE 10 CONTINUE 103 FORMAT(1X,8G9.0) 104 FORMAT(lX,8E9.3) C calculate percentile value of observed ttf OPEN(UNIT=3 .FILE='ZVALIN.TBL'.STATUS='OLD') OPEN(UNIT=4,FILE='ZVALOU.TBL',STATUS='UNICNOWN') C C SUBTILTLE = " **** Z VALUES FOR NP PERCENT INTERVALS NP = 50 ****" C READ(3,100) SUBTITLE WRITE(4,102) SUBTITLE C C READ IN THE STANDARD NORMAL VALUE (Zi) FOR EACH PERCENTILE C WRITE (4,*) D O 3 0 J = l , N P READ (3,43) Z(J) WRITE (4,43) Z(J) 43 FORMAT (8X,F 12.7) 30 CONTINUE CLOSE(UMT=3,STATUS='KEEP') CLOSE(UNIT=4,STATUS=TCEEP') C NC = NT*NS ITOTOAL NUMBER OF SAMPLES DO 50 I = 1,NP DO 40 J = 1,NC OTTFP(IJ) =TTFPAR(J,6)-r-EXP(TTFPAR(J,7)-r-Z(I)*TTFPAR(J,8)) 40 CONTINUE 50 CONTINUE C OTTFP(IJ) CONTAINS A MATRIX OF PERCENTILE VALUES OF TTF OF ALL THE C SAMPLES INPUTED. EACH J COLUMN STORES A SAMPLE'S PERCENTILE VALUES (E.G. C FORM ZERO PERCENT TO 98 PERCENT FOR THE CASE OF NP = 50) ON THE BASED OF C THE INPUT LOGNORMAL PARAMETERS. THESE LOGNORMAL PARAMETERS WOULD HAVE TO C BE PREDETERMINED BY FITTING THE EXPERIMENTAL DATA WITH LOGNORMAL C DISTRIBUTION FUNCTION. C RETURN END A P P E N D I X III $debug SUBROUTINE frprmn(P,N,ftol,iter,fret) INTEGER iter,N,NMAX,ITMAX REAL fret,ftol,P(N),EPS,func EXTERNAL func PARAMETER (NMAX=50,ITMAX=200,EPS = l.e-10) CU USES dfunc,func,linmin INTEGER its,) REAL dgg,fp,gam,gg,g(NMAX) ,h(NMAX) ,xi(NMAX) fp=func(P) call dfunc(P,xi) do 11 j = l,n g(j)=-xi(j) h(j)=g(j) xi(j)=h(j) 11 continue do 14its=l,ITMAX iter=its call linmin(P,xi,n,fret) if(2.*abs(fret-fp).le.ftol*(abs(fret)-r-abs(fp)+EPS))return write (6,*) write (6,'(lx,a,i6,3x,a,el4.6)') 'iteration=', its, 'func=', fp d o l 9 k = l , N write(6,94) k, P(k) 19 continue 94 FORMAT(/,4X,'parameter ',I5,2x,E15.9) write (*,'(lx,a,i6,3x,a,el4.6)') 'iteration=', its, 'func=', fp fp=func(P) call dfunc(P,xi) gg=o-dgg=0. do 12 j = l,n gg=gg+g(j)**2 -C dgg=dgg+xi(j)**2 dgg = dgg +( x i(i) +g(i))* x i(i) 12 continue if(gg.eq.O.)retum gam=dgg/gg do 13 j = l,n g(j) =-»()) h(j)=g(j)+gam*h(j) xi(j)=h(j) 13 continue 14 continue pause 'frprmn maximum iterations exceeded' return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. 184 APPENDIX III $DEBUG C -C FUNCTION func.FOR C C This function calculate the sum of square of difference between C observed percentiles and predicted percentiles which are based on C Model 2 C C use ttf C REAL FUNCTION func (P) INTEGER*4 SRT$REAL4 COMMON A(10) COMMON TEMPVALUE COMMON /SAMPLE SIZE AND VARIABLES/ N , NPAR, NVAR, 1 NTILE, SCALLING, THRESHOLD, TO PARAMETER (SRT$REAL4 = #00010000) real*4 P(10), strength, PreTTF(500) $INCLUDE:'RANDNUM.INC ! /TABLE OF RANDOM STANDARD NORMAL VALUES/ C RANDNUM.INC RN(RNCOL) = ARRAY TO STORE THE RANDOM NUMBERS MAX RN( 1000,6) C NEED ONE MORE SET FOR GENERATING ST STRENGTH C N = SAMPLE SIZE < 1000 C NVAR = NUMBER OF VARIABLES IN THE DAMAGE RATE EQUATION C FOR LOGNORMAL NPAR = 2 * NVAR C NPAR <= 10 $INCLUDE:'OTTFPARA.INC C /OBSERVED TTF PARAMETERS/ C NT NUMBER OF TEMPERATURES OF EXPOSURE C NS NUMBER OF LOADING CONDITIONS, MAXIMUM 5 LOAD CONDITIONS C NP = NUMBER OF PERCENTILE LEVELS FOR OPTIMIZATION C C TTFPAR(NT*NS, 1) = TEMPERATURE OF EXPOSURE C TTFPAR(NT*NS,2) = STARTING TIME OF TEMPERATURE EXPOSURE C TTFPAR(NT*NS,3) = MODE OF LOADING C TTFPAR(NT*NS,4) = STARTING TIME OF LOADING C TTFPAR(NT*NS,5) = STRESS VALUE (DEPENDS ON MODE OF LOADING) C TTFPAR(NT*NS,6) = THRESHOLD C TTFPAR(NT*NS ,7) = LOCATION PARAMETER M U C TTFPAR(NT*NS,8) = SCALE PARAMETER SIGMA C OTTFP(50,9) = PERCENTILE VALUES OF OBSERVED TTF C PTTFP(50,9) = PERCENTILE VALUES OF PREDICTED TTF $INCLUDE:'LOGNORPA.INC C ST(I) = SAMPLE OF SHORT-TERM STRENGTH C P( 10) = ARRAY STORING THE INITIAL LOGNORMAL PARAMETER VALUES C P( 1) = LOCATION PARAMETER M U of the first parameter C P(2) = SCALE PARAMETER SIGMA of the first parameter] C P(3) = LOCATION PARAMETER M U of the second parameter 185 A P P E N D I X III C P(4) = SCALE PARAMETER SIGMA of the second parameter] C P(5) = LOCATION PARAMETER M U of the third parameter C P(6) = SCALE PARAMETER SIGMA of the third parameter] C etc. C LOOPING THROUGH ALL SAMPLES C TOTAL NUMBER OF SAMPLES = NT*NS SUMSQDIF=0.0 DO 25 11=1,NT*NS !for each sample DO 20 1= 1,N !for each simulation A(l)=P(l)*1.0E+06 !EXP(P(1)+RN(I,1)*P(2)) if (A(l) .gt. 20000.0) A(l)=20000.0 !set upper limit on al A(2)=P(3)*1.0E+10 A(3)=P(5)*1.0E+08 A(4)=P(7)*1.0E+03 if (A(4) .gt. 0.12) A(l) =0.12 !set upper limit on a4 A(5)=P(9) if (A(5) .It. 150.0) A(5) = 150.0 !set upper limit on a5 A(6)=P(10) if (A(6) .It. 0.5) A(6)=0.5 if (A(6) .gt. 1.0) A(6) = 1.0 if (A(l) .It. 0.0 .OR. A(2) .It. 0.0 .OR. A(3) .It. 0.0 .OR. * A(4) .It. 0.0) goto 15 strength=ST(I) A(5)=exp((15488.96/A(l)-0.4917)/strength)* 1 ((-1.02E-6*A(l)/A(4)+0.036)*strength + 2 (0.0034*A(l)-23.4)/A(4)) preTTF(I) =TTF(Strength,II) 20 CONTTNUE C SORT ARRAT PreTTF IN ACCENDING ORDER ICOUNT=N CALL SORTQQ(LOC(PreTTF),ICOUNT,SRT$REAL4) C DETERMINE THE NON-PARAMETRIC PERCENTILE VALUE OF SAMPLE II C AT THE SAME PERCENTILE LEVEL OF THE ARRAY PreTTF C AND STORE IT IN PreTTFP IN COLUMN II C C LET IX=THE RANK OF THE ARRAY ELEMENT CORRESPONDING TO PERCENTILE GIVEN BY IP/NP C SINCE IX/(N+1) =IP/NP THEREFORE DC=IP/NP * (N+1) C D 0 21IP=1,NP rX=(real(IP)/real(NP))*N PTTFP(IP,II)=PreTTF(rX) !find the percentile values 21 CONTINUE 25 CONTINUE A P P E N D I X III SUMSQDIF=0.0 , mp = INT(REAL(NTILE)/100.0*np) !fit to NTILE percentiles only DO30I=l,NT*NS DO 50 K=l,mp SUMSQDIF = SUMSQDIF + ((OTTFP(I<CI)-PTTFP(ICI))/SCALLING)**2 50 CONTINUE 30 CONTINUE 15 if (SUMSQDIF .EQ. 0.0) THEN func=TEMPVALUE*1.5 ELSE func=SUMSQDIF tempvalue=SUMSQDIF end if END $DEBUG C C FUNCTION TTF.FOR C -C This function calculates the time to failure given values C of the parameters of the damage function C FUNCTION ttf (strength,II) PARAMETER(ACC= 12.0,TINY= 1 .e-30) $INCLUDE:'LOGNORPA.INC ! /LOGN PARAMETERS SH TERM STRENGTH/ C ROL = rate of loading for obtaining short-term strength COMMON A( 10) COMMON /SAMPLE SIZE AND VARIABLES/ N , NPAR, NVAR, 1 NTILE, SCALLING, TIIRESIIOLD, TO COMMON T,S C A ( l ) = a l C A(2) = a2 C A(3) = a3 C A(4) = a4 C A(5) = ideal strength C A(6) = exponent of the initial ratio of short-term strength to ideal strength C strength = short-term strength C NVAR = number of variables, maximum 10 INTEGER II REAL*8 eps,hdid,hnext,htry,x,y,dydx,dysav,ysav,yscal real*4 strength integer ic EXTERNAL derivs A P P E N D I X III C calculate initial value of damage parameter C if there are other damages from prior loading condition, C it can be incorporated here using the variable STARTDAMAGE in C 'INITCOND.INC i.e. ysav = 1.0-startdamage-strength/A(5) ysav= 1.0-(strength/A(5))**A(6) !A(5) ideal strength, initial value x=0.0 call derivs(x,ysav,dysav,II,strength) yscal=1.0 y=ysav dydx=dysav htry=0.6 ic=l eps=exp(-float(acc)) ! accuracy x=0.0 C Write(6;(/lx,t7,a,tl7,a,t28,a,t38,a,t45,a,t56,a,t64,a,t70)') C * 'hdid'.'hnext'.'dydx'.'time'.'damage'/strength', C * 'temp'/stress' Do While (y .LT. 0.999) call derivs(x,y,dydx,II,strength) yscal=abs (y) + abs(htry*dydx)+TINY call rkqs(y,dydx,II,x,htry,eps,yscal,hdid,hnext, derivs,strength) if (hnext.gt. 100.)hnext= 100 htry=hnext ic=ic+l if (ic .gt. 9999) then write (*,'(lx,i4,8el0.2)') 1 ii,strength,a( 1) ,a(2) ,a(3),a(4),a(5) ,x,y pause end if C write(6,'(2x,f8.3,f8.3,lx,el2.5,lx,f8.2,lx,el2.5,3f9.2)') C * hdid,hnext,dydx,x,y,strength,T,S 13 End do 15 TTF=X END SUBROUTINE derivs(x,y,dydx,II,strength) INTEGER II REAL* 8 x,y,dydx,time real*4 SS.SO.strength COMMON A( 10) COMMON /SAMPLE SIZE AND VARIABLES/ N , NPAR, NVAR, 1 NTILE, SCALLING, THRESHOLD, TO $include:'OTTFPARAINC' C C TTFPAR(NT*NS,1) = TEMPERATURE OF EXPOSURE . A P P E N D I X III C TTFPAR(NT*NS,2) = STARTING TIME OF TEMPERATURE EXPOSURE C TTFPAR(NT*NS,3) = MODE OF LOADING C TTFPAR(NT*NS,4) = STARTING TIME OF LOADING C TTFPAR(NT*NS,5) = STRESS VALUE (DEPENDS ON MODE OF LOADING) $INCLUDE:'INITCOND.INC C C TPAROX = PO C TPAR(2)' = PI C TPAR(3) = K IF (y .GE. 1.0) THEN dydx = l.e+5 return END IF SO = THRESHOLD * strength TEXP=TTFPAR(II,1)-T0 (calculate net exposure temperature IF (x .LE. TTFPAR(II,2) .OR. TEXP .EQ. 0.) THEN !if time < time heating begins OR !net exposure = zero T = TO ELSE time = x - TTFPAR(II,2) T = T0+(TPAR(l)*TEXP+TPAR(2)*time)* 1 (l-exp(-TPAR(3)*time/TPAR(l))) END IF if (x .LE. TTFPAR(II,4)) then S = 0.0 SS = 0.0 else if (TTFPAR(II,3) .EQ. 1.0) then S = TTFPAR(II,5) - SO SS = S*A(4)/(1.0-y) if(SS .GT. 300) SS=300 !limit the exponent to 300 else S =TTFPAR(II,5)* (x-TTFPAR(IL4))-S0 if (S .LE. 0.0) S=0.0 SS=S*A(4)/(1.0-y) if(SS .GT. 300) SS=300 end if dydx=exp (-A( 1 )/T) * (A(2) + (1 -y) * A(3) *exp (S S)) if (dydx .gt. l.e+5) dydx= l.e+5 !limit the rate return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. $debug C C SUBROUTINE dfunc.FOR C C This function calculate the partial derivatives of the APPENDIX III C minimization function with respect to each parameter. C C UsesFUNC C SUBROUTINE dfunc(x,dfi) COMMON /SAMPLE SIZE AND VARIABLES/ N , NPAR, NVAR real x(10), dfi(10), xu(10), xl(10) C x() original parameter vector C xu() modified parameter vector for derivative calculation C xl() modified parameter vector for derivative calculation $INCLUDE:'LOGNORPA.INC C ST(I) = SAMPLE OF SHORT-TERM STRENGTH C P( 10) = ARRAY STORING THE INITIAL LOGNORMAL PARAMETER VALUES C C P( 1) = LOCATION PARAMETER M U of the first parameter - b = A( 1) C P(2) = SCALE PARAMETER SIGMA of the first parameter] - b C P(3) = LOCATION PARAMETER M U of the second parameter - c = A(2) C P(4) = SCALE PARAMETER SIGMA of the second parameter] - c C P(5) = LOCATION PARAMETER M U of the third parameter - h = A(3) C P(6) = SCALE PARAMETER SIGMA of the third parameter] - h C etc. C C initialize xi do 10 I = 1, NPAR xu(I) = x(I) xl(I) = x(I) 10 continue do 15 I = l .NPAR h = 0.01*x(I) xu(I) = x(I) + h ! modified parameter value xl(I) = x(I)-h Imodified parameter value dfi(I) = (func(xu) - func(xl))/(0.02*x(I)) xu(I) = x(I) !retum parameter to original value xl(I) = x(I) !return parameter to original value 15 continue return SUBROUTINE linmin(p,xi,n,fret) INTEGER n,NMAX REAL fret,p(n),xi(n),TOL PARAMETER (NMAX=50,TOL= 1 .e-4) CU USES brent,fldim,mnbrak INTEGER j,ncom REAL ax,bx,fa,fb,fx,xmin,xx,pcom(NMAX),xicom(NMAX),dbrent COMMON /f lcom/ pcom,xicom,ncom EXTERNAL fldim, dfldim 190 APPENDIX III ncom=n do 11 j=l,n pcom(j)=p(j) xicom(j)=xi(j) 11 continue ax=0. xx=l. call mnbrak(ax,xx,bx,fa,fx,fb,f ldim) fret=dbrent(ax,xx,bx,dfldim,fldim,TOL,xmiri) do 12 j=l,n xi(j)=xmin*xi(j) P(j)=P(J)+xi(j) 12 continue return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. END SUBROUTINE mnbrak(ax,bx,cx,fa,fb,fc,func) REAL ax,bx,cx,fa,fb,fc,func,GOLD,GLIMIT,TINY EXTERNAL func PARAMETER (GOLD = 1.618034, GLIMIT=100., TINY=l.e-20) REAL dum,fu,q,r,u,ulim fa=func(ax) fb=func(bx) if(fb.gt.fa)then dum=ax ax=bx bx=dum dum=fb fb=fa fa=dum endif cx=bx+GOLD*(bx-ax) fc=func(cx) 1 if(fb.ge.fc)then r=(bx-ax)*(fb-fc) q=(bx-cx)*(fb-fa) u=bx-( (bx-cx) *q-(bx-ax) *r)/(2. *sign(max(abs (q-r) ,TINY) ,q-r)) ulim=bx+GLIMIT* (cx-bx) if((bx-u)*(u-cx).gt.O.)then fu=func(u) if(fu.lt.fc)then ax=bx fa=fb bx=u fb=fu return else if(fu.gt.fb)then cx=u fc=fu . return 191 APPENDIX III endif u=cx+GOLD * (cx-bx) fu=func(u) else if((cx-u)*(u-ulim).gt.O.)then fu=func(u) if(fu.lt.fc)then bx=cx cx=u u=cx+ GOLD* (cx-bx) fb=fc fc=fu fu=func(u) endif else if((u-ulim) * (ulim-cx) .ge.0.)then u=ulim fu=func(u) else u=cx+ GOLD* (cx-bx) fu=func(u) endif ax=bx bx=cx cx=u fa=fb fb=fc fc=fu goto 1 endif return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. FUNCTION dbrent(ax,bx,cx,df,f,tol,xmin) INTEGER ITMAX REAL dbrent,ax,bx,cx,tol,xmin,df,f,ZEPS EXTERNAL df,f PARAMETER (ITMAX=100,ZEPS = 1.0e-10) INTEGER iter REALa,b,d,dl,d2,du,dv4w,dx,e,fu,fv,fw,fx,olde,toll,tol2,u,ul,u2, *v,w,x,xm LOGICAL okl ,ok2 a=min(ax,cx) b=max(ax,cx) v=bx w=v x=v e=0. fx=f(x) fv=fx fw=fx dx=df(x) dv=dx APPENDIX III dw=dx do 11 iter =1,UMAX xm=0.5*(a+b) toll=tol*abs(x)+ZEPS tol2=2.*toll if(abs(x-xm).le.(tol2-.5*(b-a))) goto 3 if(abs(e).gt.toll) then dl=2.*(b-a) d2=dl if(dw.ne.dx) d l =(w-x)*dx/(dx-dw) if(dv.ne.dx) d2 = (v-x) *dx/(dx-dv) ul=x+dl u2=x+d2 okl = ((a-ul)*(ul-b).gt.O.).and.(dx*dl.le.O.) ok2 = ((a-u2) * (u2-b) .gt.O.) .and. (dx*d2.1e.O.) olde=e e=d if(.not.(okl.or.ok2))then goto 1 else if (okl.and.ok2)then if(abs(dl).lt.abs(d2))then d=dl else d=d2 endif else if (okl)then d=dl else d=d2 endif if(abs(d).gt.abs(0.5*olde))goto 1 u=x+d if(u-a.lt.tol2 .or. b-u.lt.tol2) d=sign(toll,xm-x) goto 2 endif if(dx.ge.O.) then e=a-x else e=b-x endif d=0.5*e if(abs(d).ge.toll) then u=x+d fu=f(u) else u=x+sign(toll,d) fu=f(u) if(fu.gt.fx)goto 3 endif du=df(u) if(fu.le.fx) then if(u.ge.x) then 193 A P P E N D I X III else b=x endif v=w fv=fw dv=dw w=x fw=fx dw=dx x=u fx=fu dx=du else if(u.lt.x) then a=u else b=u endif if(fu.le.fw .or. w.eq.x) then v=w fv=fw dv=dw w=u fw=fu dw=du else if(fu.le.fv .or. v.eq.x .or. v.eq.w) then ^ v=u fv=fu dv=du endif endif 11 continue pause 'dbrent exceeded maximum iterations' 3 xmin=x dbrent=fx return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. FUNCTION dfldim(x) INTEGER NMAX REAL df ldim,x PARAMETER (NMAX=50) C USES dfunc INTEGER j , ncom REAL df (NMAX) ,pcom(NMAX) .xicom(NMAX) ,xt(NMAX) COMMON /f lcom/ pcom,xicom,ncom do 11 j = 1 ,ncom xt(j)=pcom(j)+x*xicom(j) 11 continue call dfunc(xt,df) dfldim=0. 194 APPENDIX III do 12 j= l,ncom dfldim=dfldim-t-df(j)*xicom(j) 12 continue return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. $DEBUG SUBROUTINE rkqs(y,dydx,ii,x,htry,eps,yscal,hdid,hnext, * derivs, strength) C IMPLICIT REAL*8(A-H,0-Z) INTEGER ii REAL*8 eps,hdid,hnext,htry,x,dydx,y,yscal real*4 strength COMMON A(10) EXTERNAL derivs CU USES derivs.rkck REAL*8 errmax,h,htemp)xnew)yerr,ytemp,SAFETY,PGROW, *PSHRNICERRCON PARAMETER (SAFETY=0.5,PGROW=-.2JPSHRNK=-.25,ERRCON= 1.89e-4) h=htry 1 call rkck(y,dydx,ii,x,h,ytemp,yerr,derivs,strength) errmax=abs (yerr/yscal)/eps if(errmax .gt. l.)then htemp=S AFETY*h* (errmax* *PSHRNK) h=sign(max(abs(htemp),0.1*abs(h)),h) xnew=x+h if(xnew.le.(x+0.01))then ! x increases less than 10 miniseconds y=0.999 return endif goto 1 else if(errmax.gt.ERRCON)then hnext=SAFETY*h*(errmax**PGROW) else hnext=5.*h endif hdid=h x=x+h y=ytemp return endif END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. $DEBUG SUBROUTINE rkck(y,dydx,ii,x,h,yout,yerr,derivs,strength) C IMPLICIT REAL*8(A-H,0-Z) A P P E N D I X III INTEGER ii REAL* 8 h,x,dydx,y,yerr,yout real*4 strength COMMON A( 10) EXTERNAL derivs CU USES derivs REAL*8 ak2,ak3,ak4,ak5,ak6, *ytemp ,A2 A3 A4 A5 A6,B21 ,B31 ,B32 ,B41 ,B42 ,B43 ,B51 ,B5 2 ,B53, *B54,B61,B62,B63,B64,B65,C1,C3,C4,C6>DC1(DC3,DC4>DC5>DC6. PARAMETER (A2 = .2,A3=.3A4=.6A5 = l.,A6=.875,B21=.2,B31=3./40., *B32=9./40.,B41=.3,B42=-.9,B43=1.2,B51=-11./54.,B52=2.5, *B53=-70./27.,B54=35./27.,B61 = 1631./55296.,B62=175./512., *B63=575./13824.,B64=44275./110592.,B65=253./4096.,Cl=37./378., *C3=250./621.,C4 = 125./594.,C6=512./1771.,DCl=Cl-2825./27648., *DC3=C3-18575./48384.,DC4=C4-13525./55296.,DC5=-277./14336., *DC6=C6-.25) ytemp =y+B21 *h*dydx call derivs(x+A2*h,ytemp,ak2,ii,strength) ytemp =y+h* (B31 *dydx+B32 * al<2) call derivs(x+A3*h,ytemp,ak3,ii,strength) ytemp =y+h* (B41 *dydx+ B42 * ak2+B43 * ak3) call derivs(x+A4*h,ytemp,ak4,ii,strength) ytemp=y+h*(B5 I*dydx+B52*ak2+B53*ak3+B54*ak4) call derivs(x+A5*h,ytemp,ak5,ii,strength) ytemp=y+h*(B61*dydx+B62*ak2+B63*ak3+B64*ak4+B65*ak5)' call derivs(x+A6*h,ytemp,ak6,ii,strength) yout=y+h*(Cl*dydx+C3*ak3+C4*ak4+C6*ak6) yerr=h*(DCl*dydx+DC3*ak3+DC4*ak4+DC5*ak5+DC6*ak6) return END C (C) Copr. 1986-92 Numerical Recipes Software 0NLY5. 196 APPENDIX IV Sample Number = 001, 002, 003; Temperature = 20°C; Rate of Loading = 1.85 kN/s ordered value T T F c.c. (sec) ln(x) rate of loading = 1.85 kN/sec (n-i)/ %tile ordered value loads (kN) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 16. 20. 24. 2 4 , 24. 25. 26. : 26 26. 26; 27 27 27. 27. 28. 28. 29. 29. 31. 31 31. 31 32. 32 32. 33. 35. 35. 36 37 37. 38 38. 38 38. 38. 38. 40 40 41. 41 42. 42. 4 2 , 42. 42. 43. 43. 43. 44. 44. 45. 45. 46. 47. 47. 47. 49. 49, 50 50 50 51 51 51. 51. 52. 52. 52. 52. 63 44 09 44 68 97 32 32 75 91 62 65 81 85 32 98 02 61 02 02 25 37 08 43 78 14 60 95 18 36 71 06 30 42 65 77 81 18 30 70 82 17 17 41 41 41 19 58 94 29 99 11 35 40 11 .34 34 22 22 04 .98 98 22 .69 81 81 04 :.28 L39 39 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 1 1 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 1 0 1 0 1 2.811 3.017 3.182 3.196 3.206 3.257 3.270 3.270 3.287 3.292 3.318 3.320 3.325 3.327 3.344 3.367 3.368 3.388 3.435 3.435 3.442 3.446 3.468 3.479 3.490 3.501 3.572 3.582 3.589 3.621 3.630 3.639 3.645 3.648 3.655 3.658 3.659 3.693 3.696 3.731 3.733 3.742 3.742 3.747 3.747 3.747 3.766 3.775 3.783 3.791 3.807 3.809 3.814 3.837 3.852 3.857 3.857 3.896 3.896 3.913 3.932 3.932 3.936 3.945 3.947 3.947 3.952 3.957 3.959 3.959 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 1.000 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 1.000 0.994 1.000 1.000 0.994 0.994 0.994 0.994 0.994 0.993 1.000 1.000 1.000 0.993 0.993 1.000 0.993 0.993 0.993 0.993 1.000 1.000 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.992 0.992 1.000 0.992 0.992 0.992 0.992 0.992 0.992 1.000 0.992 0.992 0.992 1.000 0.992 0.992 0.991 1.000 1.000 0.991 1.000 0.991 1.000 1 0.99 0.99 0.98 0.98 0.97 0.97 0.96 0.96 0.96 0.95 0.94 0.94 0.93 0.93 0.92 0.92 0.91 0.91 0.91 0.90 0.90 0.90 0.89 0.89 0.88 0.88 0.87 0.87 0.87 0.87 0.87 0.86 0.85 0.85 0.85 0.84 0.84 0.83 0.83 0.83 0.82 0.82 0.81 0.81 0.80 0.79 0.79 0.78 0.78 0.78 0.77 0.77 0.76 0.75 0.75 0.74 0.74 0.74 0.73 0.72 0.72 0.72 0.71 0.70 0.70 0.70 0.70 0.70 0.69 0.69 0.006 0.011 0.017 0.022 0.028 0.033 0.039 0.044 0.044 0.050 0.056 0.061 0.067 0.072 0.078 0.084 0.089 0.095 0.095 0.100 0.100 0.100 0.106 0.112 0.117 0.123 0.129 0.135 0.135 0.135 0.135 0.140 0.146 0.146 0.152 0.158 0.164 0.170 0.170 0.170 0.175 0.181 0.187 0.193 0.199 0.205 0.211 0.217 0.223 0.223 0.229 0.235 0.241 0.247 0.253 0.259 0.259 0.265 0.271 0.277 0.277 0.283 0.289 0.295 0.295 0.295 0.301 0.301 0.308 0.308 -2.54 -2.29 -2.13 -2.01 -1.91 -1.83 -1.76 -1.70 -1.70 -1.64 -1.59 -1.54 -1.50 -1.46 -1.42 -1.38 -1.35 -1.31 -1.31 -1.28 -1.28 -1.28 -1.25 -1.22 -1.19 -1.16 -1.13 -1.11 -1.11 -1.11 -1.11 -1.08 -1.05 -1.05 -1.03 -1.00 -0.98 -0.96 -0.96 -0.96 -0.93 -0.91 -0.89 -0.87 -0.84 -0.82 -0.80 -0.78 -0.76 -0.76 -0.74 -0.72 -0.70 -0.68 -0.67 -0.65 -0.65 -0.63 -0.61 -0.59 -0.59 -0.57 -0.56 -0.54 -0.54 -0.54 -0.52 -0.52 -0.50 -0.50 0.006 0.055 0.086 0.109 0.127 0.143 0.157 0.169 0.169 0.180 0.190 0.199 0.208 0.216 0.224 0.231 0.238 0.245 0.245 0.251 0.251 0.251 0.257 0.263 0.269 0.274 0.280 0.285 0.285 0.285 0.285 0.290 0.295 0.295 0.300 0.305 0.309 0.314 0.314 0.314 0.318 0.323 0.327 0.331 0.336 0.340 0.344 0.348 0.352 0.352 0.356 0.359 0.363 0.367 0.370 0.374 0.374 0.378 0.381 0.385 0.385 0.388 0.392 0.395 0.395 0.395 0.399 0.399 0.402 0.402 sample statistics number of specimens in sample = mean of column B : B = standard deviatin of column B : B = 180 60.156 22.654 threshold parameter by trial and error = 0 slope of regression line = 0.3830 intercept of regression line = -1.0984 location parameter (y=0.5) by quantile estimate = 4.1679 scale parameter by quantile estimate = 0.4990 2-P LOG-NORMAL PROBABILITY PLOT O DATA — L i n e a r (DATA) T h e above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. T h e T T F data were censored for c.c. = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters m u and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H . L Harterand A. H . Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter L o g Normal Populations from Complete and Censored Samples , J . Amer. Stat. Assoc. , Vol. 61, 1966. T h e method of Quantile Estimator is used to find mu (the location parameter) and s igma (the scale parameter) since it can deal with censored data. T h e quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from zero up to the minimum value, were tried. T h e fit was judged to be the best when the value was zero. Therefore the 2-P lognormal model was used. Zn.25 Zo.75 Ko,25 LnX,,.: Kn.75 LnXo., -0.67449 0.67449 0.369191 3.831388 0.627009 4.504463 30.77 37.81 44.57 45.22 45.65 48.04 48.70 48.70 49.49 49.78 51.09 51.16 51.45 51.52 52.39 53.62 53.69 54.78 57.39 57.39 57.82 58.04 59.34 59.99 60.64 61.30 65.86 66.51 66.94 69.12 69.77 70.42 70.85 71.07 71.51 71.72 71.80 74.33 74.55 77.15 77.37 78.02 78.02 78.46 78.46 78.46 79.91 80.63 81.28 81.93 83.24 83.45 83.89 85.84 87.15 87.58 87.58 91.06 91.06 92.58 94.32 94.32 94.75 95.62 95.84 95.84 96.27 96.71 96.92 96.92 197 APPENDIX IV Sample Number = 001, 002, 003; Temperature = 20°C; Rate of Loading = 1.85 kN/s ' ordered value rate of loading = 1.85 kN/sec ordered value T T F (sec) c.c. ln(x) (n-i)/ (n-i+1) R %tile Z K loads (kN) 71 52.86 0 3.968 0.991 0.69 0.314 -0.49 0.406 97.79 72 53.45 0 3.979 0.991 0.68 0.320 -0.47 0.409 98.88 73 53.45 0 3.979 0.991 0.67 0.326 -0.45 0.412 98.88 74 53.49 0 3.979 0.991 0.67 0.333 -0.43 0.416 98.95 75 54.27 0 3.994 0.991 0.66 0.339 -0.42 0.419 100.40 76 54.39 0 3.996 0.990 0.65 0.345 -0.40 0.423 100.62 77 54.50 1 3.998 1.000 0.65 0.345 -0.40 0.423 100.83 78 54.86 0 4.005 0.990 0.65 0.352 -0.38 0.426 101.49 79 55.56 1 4.018 1.000 0.65 0.352 -0.38 0.426 102.79 80 55.56 1 4.018 1.000 0.65 0.352 -0.38 0.426 102.79 81 55.79 0 4.022 0.990 0.64 0.358 -0.36 0.429 103.22 82 55.79 0 4.022 0.990 0.64 0.365 -0.35 0.433 103.22 83 56.26 1 4.030 1.000 0.64 0.365 -0.35 0.433 104.09 84 56.62 0 4.036 0.990 0.63 0.371 -0.33 0.436 104.74 85 56.85 0 4.040 0.990 0.62 0.378 -0.31 0.439 105.18 86 56.85 1 4.040 1.000 0.62 0.378 -0.31 0.439 105.18 87 56.97 1 4.043 1.000 0.62 0.378 -0.31 0.439 105.40 88 . 57.24 1 4.047 1.000 0.62 0.378 -0.31 0.439 105.90 89 57.44 1 4.051 1.000 0.62 0.378 -0.31 0.439 106.27 90 57.79 1 4.057 1.000 0.62 0.378 -0.31 0.439 106.92 91 58.38 0 4.067 0.989 0.62 0.385 -0.29 0.443 108.00 92 58.85 0 4.075 0.989 0.61 0.392 -0.28 0.446 108.87 93 59.20 0 4.081 0.989 0.60 0.398 -0.26 0.450 109.52 94 59.56 1 4.087 1.000 0.60 0.398 -0.26 0.450 110.18 95 59.67 0 4.089 0.988 0.59 0.405 -0.24 0.453 110.39 96 59.71 1 4.090 1.000 0.59 0.405 -0.24 0.453 110.47 97 60.26 0 4.099 0.988 0.59 0.413 -0.22 0.457 111.48 98 60.96 0 4.110 0.988 0.58 0.420 -0.20 0.461 112.78 99 60.96 0 4.110 0.988 0.57 0.427 -0.18 0.464 112.78 100 61.31 0 4.116 0.988 0.57 0.434 -0.17 0.468 113.43 101 62.02 T 4.127 1.000 0.57 0.434 -0.17 0.468 114.74 102 62.49 0 4.135 0.987 0.56 0.441 -0.15 0.471 115.61 103 62.96 1 4.143 1.000 0.56 0.441 -0.15 0.471 116.48 104 63.43 0 4.150 0.987 0.55 0.448 -0.13 0.475 117.34 105 63.78 0 4.155 0.987 0.54 0.455 -0.11 0.478 118.00 106 63.78 0 4.155 0.987 0.54 0.463 -0.09 0.482 118.00 107 64.14 1 4.161 1.000 0.54 0.463 -0.09 0.482 118.65 108 64.45 1 4.166 1.000 0.54 0.463 -0.09 0.482 119.23 109 64.49 1 4.166 1.000 0.54 0.463 -0.09 0.482 119.30 110 64.49 0 4.166 0.986 0.53 0.470 -0.07 0.485 119.30 111 65.08 1 4.176 1.000 0.53 0.470 -0.07 0.485 120.39 112 65.54 0 4.183 0.986 0.52 0.478 -0.06 0.489 121.25 113 66.25 0 4.193 0.985 0.51 0.486 -0.04 0.493 122.56 114 66.83 1 4.202 1.000 0.51 0.486 -0.04 0.493 123.64 115 67.42 1 v 4.211 1.000 0.51 0.486 -0.04 0.493 124.73 116 67.66 0 4.214 0.985 0.51 0.494 -0.02 0.497 125.17 117 67.77 1 4.216 1.000 0.51 0.494 -0.02 0.497 125.38 118 67.89 1 4.218 1.000 0.51 0.494 -0.02 0.497 125.60 119 68.59 0 4.228 0.984 0.50 0.502 0.00 0.501 126.90 120 68.83 1 4.232 1.000 0.50 0.502 0.00 0.501 127.34 121 69.42 0 4.240 0.983 0.49 0.510 0.03 0.505 128.42 122 69.42 0 4.240 0.983 0.48 0.518 0.05 0.509 128.42 123 69.77 0 4.245 0.983 0.47 0.527 0.07 0.513 129.08 124 69.89 0 4.247 0.982 0.47 0.535 0.09 0.517 129.29 125 70.36 0 4.254 0.982 0.46 0.543 0.11 0.521 130.16 126 70.59 1 4.257 1.000 0.46 0.543 0.11 0.521 . 130.60 127 71.06 0 4.264 0.981 0.45 0.552 0.13 0.525 131.47 128 71.18 0 4.265 0.981 0.44 0.560 0.15 0.529 131.68 129 71.53 1 4.270 1.000 0.44 0.560 0.15 0.529 132.33 130 72.12 0 4.278 0.980 0.43 0.569 0.17 0.534 133.42 131 72.47 0 4.283 0.980 0.42 0.577 0.20 0.538 134.07 132 72.59 0 4.285 0.980 0.41 0.586 0.22 0.542 134.29 133 72.71 0 4.286 0.979 0.41 0.595 0.24 0.547 134.51 134 72.94 1 4.290 1.000 0.41 0.595 0.24 0.547 134.94 135 73.25 0 4.294 0.978 0.40 0.603 0.26 0.551 135.52 136 73.64 1 4.299 1.000 0.40 0.603 0.26 0.551 136.24 137 73.88 0 4.302 .0.977 0.39 0.612 0.29 0.556 136.68 138 74.23 0 4.307 0.977 0.38 0.621 0.31 0.560 137.33 139 75.52 1 4.324 1.000 0.38 0.621 0.31 0.560 139.72 140 75.76 0 4.328 0.976 0.37 0.631 0.33 0.565 140.15 141 76.23 1 4.334 1.000 0.37 0.631 0.33 0.565 141.02 APPENDIX IV Sample Number = 001, 002, 003; Temperature = 20°C; Rate of Loading = 1.85 kN/s 198 ordered value T T F c c . (sec) ln(x) (n-i)/ (n-i+1) R %tile Z K rate of loading = 1.85 kN/sec ordered value loads (KN) 142 76.70 1 4.340 1.000 0.37 0.631 0.33 0.565 141.89 143 76.70 1 4.340 1.000 0.37 0.631 0.33 0.565 141.89 144 76.82 1 4.341 1.000 0.37 0.631 0.33 0.565 142.11 145 77.99 1 4.357 1.000 0.37 0.631 0.33 0.565 144.28 146 78.34 0 4.361 0.971 0.36 0.641 0.36 0.570 144.93 147 78.70 1 4.366 1.000 0.36 0.641 0.36 0.570 145.59 148 79.59 1 4.377 1.000 0.36 0.641 0.36 0.570 147.25 149 80.69 0 4.391 0.969 0.35 0.652 0.39 0.576 149.28 150 80.69 0 4.391 0.968 0.34 0.664 0.42 0.582 149.28 151 81.51 1 4.401 1.000 0.34 0.664 0.42 0.582 150.80 152 82.45 1 4.412 1.000 0.34 0.664 0.42 0.582 152.54 153 83.28 0 4.422 0.964 0.32 0.676 0.46 0.589 154.06 154 84.80 1 4.440 1.000 0.32 0.676 0.46 0.589 156.88 155 84.92 0 4.442 0.962 0.31 0.688 0.49 0.595 157.10 156 85.51 1 4.449 1.000 0.31 0.688 0.49 0.595 158.19 157 87.38 0 4.470 0.958 0.30 0.701 0.53 0.603 161.66 158 87.50 0 4.472 0.957 0.29 0.714 0.57 0.610 161.88 159 87.62 0 4.473 0.955 0.27 0.727 0.60 0.618 162.10 160 88.13 0 4.479 0.952 0.26 0.740 0.64 0.625 163.04 161 89.03 0 4.489 0.950 0.25 0.753 0.68 0.633 164.70 162 91.73 0 4.519 0.947 0.23 0.766 0.73 0.641 169.70 163 92.08 1 4.523 1.000 0.23 0.766 0.73 0.641 170.35 164 92.55 0 4.528 0.941 0.22 0.780 0.77 0.650 171.22 165 93.96 1 4.543 1.000 0.22 0.780 0.77 0.650 173.83 166 93.96 0 4.543 0.933 0.21 0.795 0.82 0.660 173.83 167 96.19 0 4.566 0.929 0.19 0.809 0.88 0.670 177.95 168 98.30 1 4.588 1.000 0.19 0.809 0.88 0.670 181.86 169 99.48 1 4.600 1.000 0.19 0.809 0.88 0.670 184.04 170 99.48 0 4.600 0.909 0.17 0.827 0.94 0.683 184.04 171 100.06 0 4.606 0.900 0.16 0.844 1.01 0.697 185.12 172 102.65 0 4.631 0.889 0.14 0.861 1.09 0.711 189.90 173 102.89 0 4.634 0.875 0.12 0.879 1.17 0.727 190.34 174 104.41 0 4.648 0.857 0.10 0.896 1.26 0.745 193.16 175 106.41 0 4.667 0.833 0.09 0.913 1.36 0.765 196.85 176 109.35 1 4.695 1.000 0.09 0.913 1.36 0.765 202.29 177 115.10 0 4.746 0.750 0.07 0.935 1.51 0.795 212.93 178 115.45 1 4.749 1.000 0.07 0.935 1.51 0.795 213.58 179 121.91 1 4.803 1.000 0.07 0.935 1.51 0.795 225.53 180 129.78 0 4.866 0.000 0.00 1.000 240.09 199 APPENDIX IV Sample Number = 004, 005, 006; Temperature = 20°C; Rate of Loading = 0.2 kN/s ordered value T T F c c . (sec) ln(x) (n-i)/ (n-i+D rate of loading = • 0.2 kN/sec %tile ordered value loads (KN) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 213.20 214.65 231.55 245.30 246.75 252.15 255.45 261.95 270.65 270.65 276.05 284.75 286.55 288.75 291.25 305.00 305.40 310.10 310.85 314.10 316.25 318.45 320.60 326.75 327.10 336.90 338.70 340.15 345.95 348.10 370.00 371.65 372.75 376.00 383.25 385.75 398.80 398.80 399.90 401.00 405.35 407.50 407.50 416.20 422.70 423.80 425.95 427.05 429.20 429.20 433.55 435.40 443.35 456.40 .458.20 458.55 464.00 468.35 470.50 477.00 478.10 479.90 482.45 490.40 490.75 493.30 494.40 496.55 499.10 500.90 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 1 0 1 0 0 5.362 5.369 5.445 5.502 5.508 5.530 5.543 5.568 5.601 5.601 5.621 5.652 5.658 5.666 5.674 5.720 5.722 5.737 5.739 5.750 5.757 5.763 5.770 5.789 5.790 5.820 5.825 5.829 5.846 5.852 5.914 5.918 5.921 5.930 5.949 5.955 5.988 5.988 5.991 5.994 6.005 6.010 6.010 6.031 6.047 6.049 6.054 6.057 6.062 6.062 6.072 6.076 6.094 6.123 6.127 6.128 6.140 6.149 6.154 6.168 6.170 6.174 6.179 6.195 6.196 6.201 6.203 6.208 6.213 6.216 0.994 0.994 0.994 0.994 0.994 1.000 0.994 0.994 0.994 0.994 0.994 0.994 0.994 0.994 1.000 1.000 0.994 0.994 1.000 0.994 1.000 0.994 1.000 0.994 0.994 0.994 0.994 1.000 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 0.993 1.000 0.993 1.000 0.993 0.993 0.993 1.000 0.993 0.992 0.992 0.992 0.992 0.992 0.992 0.992 0.992 0.992 0.992 0.992 1.000 0.992 0.992 0.992 1.000 0.991 1.000 1.000 0.991 1.000 0.991 0.991 1 0.99 0.99 0.98 0.98 0.97 0.97 0.97 0.96 0.96 0.95 0.94 0.94 0.93 0.93 0.93 0.93 0.92 0.92 0.92 0.91 0.91 0.90 0.90 0.90 0.89 0.89 0.88 0.88 0.88 0.87 0.86 0.86 0.85 0.85 0.84 0.84 0.83 0.82 0.82 0.82 0.81 0.81 0.81 0.80 0.79 0.79 0.79 0.78 0.78 0.77 0.76 0.76 0.75 0.75 0.74 0.74 0.73 0.72 0.72 0.72 0.71 0.71 . 0.71 0.70 0.70. 0.70 0.69 0.69 0.69 0.68 0.006 0.011 0.017 0.022 0.028 0.028 0.033 0.039 0.045 0.050 0.056 0.061 0.067 0.072 0.072 0.072 0.078 0.084 0.084 0.089 0.089 0.095 0.095 0.101 0.107 0.112 0.118 0.118 0.124 0.130 0.136 0.141 0.147 0.153 0.159 0.165 0.170 0.176 0.182 0.182 0.188 0.188 0.194 0.200 0.206 0.206 0.211 0.217 0.223 0.229 0.235 0.241 0.247 0.253 0.259 0.265 0.271 0.277 0.277 0.283 0.289 0.295 0.295 0.301 0.301 0.301 0.307 0.307 0.313 0.319 -2.54 -2.29 -2.13 -2.01 -1.91 -1.91 -1.83 -1.76 -1.70 -1.64 -1.59 -1.54 -1.50 -1.46 -1.46 -1.46 -1.42 -1.38 -1.38 -1.34 -1.34 -1.31 -1.31 -1.28 -1.24 -1.21 -1.18 -1.18 -1.15 -1.13 -1.10 -1.07 -1.05 -1.02 -1.00 -0.98 -0.95 -0.93 -0.91 -0.91 -0.89 -0.89 -0.86 -0.84 -0.82 -0.82 -0.80 -0.78 -0.76 -0.74 -0.72 -0.70 -0.68 -0.67 -0.65 -0:63 -0.61 -0.59 -0.59 -0.57 -0.56 -0.54 -0.54 -0.52 -0.52 -0.52 -0.50 -0.50 -0.49 -0.47 0.006 0.055 0.086 0.109 0.127 0.127 0.143 0.157 0.169 0.180 0.190 0.200 0.208 0.216 0.216 0.216 0.224 0.231 0.231 0.238 0.238 0.245 0.245 0.252 0.258 0.264 0.270 0.270 0.275 0.281 0.286 0.291 0.296 0.301 0.306 0.310 0.315 0.319 0.323 0.323 0.328 0.328 0.332 0.336 0.340 0.340 0.344 0.348 0.352 0.356 0.360 0.363 0.367 0.371 0.374 0.378 0.381 0.385 0.385 0.388 0.392 0.395 0.395 0.398 0.398 0.398 0.402 0.402 0.405 0.409 sample statistics number of specimens in sample = mean of column B : B = standard deviatin of column B : B = 180 576.745 204.543 threshold parameter by trial and error = 0 slope of regression line = 0.4403 intercept of regression line = -2.3157 location parameter (y=0.5) by quantile estimate = 6.3908 scale parameter by quantile estimate = 0.4341 LOG-NORMAL PROBABILITY PLOT T h e above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. T h e T T F data were censored for c c . = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters m u and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H . L Harterand A. H . Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter Log Normal Populations from Complete and Censored Samples , J . Amer. Stat. Assoc . , Vol. 61, 1966. The method of Quantile Estimator is used to find mu (the location parameter) and s igma (the scale parameter) since it can deal with censored data. T h e quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from zero up to the minimum value, were tried. T h e fit was judged to be the best when the value was zero. Therefore the 2-P lognormal model was used. Zo.25 Zo.75 Ko.25 LnXo.2: Kn.75 L n X „ . 7 -0.67449 0.67449 0.36919 6.098 0.62701 . 6.68356 42.64 42.93 46.31 49.06 49.35 50.43 51.09 52.39 54.13 54.13 55.21 56.95 57.31 57.75 58.25 61.00 61.08 62.02 62.17 62.82 63.25 63.69 64.12 65.35 65.42 67.38 67.74 68.03 69.19 69.62 74.00 74.33 74.55 75.20 76.65 77.15 79.76 79.76 79.98 80.20 81.07 81.50 81.50 83.24 84.54 84.76 85.19 85.41 85.84 85.84 86.71 87.08 88.67 91.28 91.64 91.71 92.80 93.67 94.10 95.40 95.62 95.98 96.49 98.08 98.15 98.66 98.88 - 99.3.1 99.82 100.18 200 APPENDIX IV Sample Number = 004, 005, 006; Temperature = 20°C; Rate of Loading = 0.2 kN/s ordered value rate of loading = 0.2 kN/sec ordered value T T F c.c. ln(x) (n-i)/ R %tile Z K loads (sec) (n-i+1) '(kN) 71 502.35 0 6.219 0.991 0.67 0.325 -0.45 0.412 100.47 72 503.10 0 6.221 0.991 0.67 0.332 -0.44 0.415 100.62 73 503.80 0 6.222 0.991 0.66 0.338 -0.42 0.419 100.76 74 504.55 1 6.224 1.000 0.66 0.338 -0.42 0.419 100.91 75 508.90 0 6.232 0.991 0.66 0.344 -0.40 0.422 101.78 76 512.15 0 6.239 0.990 0.65 0.350 -0.38 0.425 102.43 77 518.30 0 6.251 0.990 0.64 0.356 -0.37 0.428 103.66 78 519.00 0 6.252 0.990 0.64 0.363 -0.35 0.432 103.80 79 522.65 0 6.259 0.990 0.63 0.369 -0.33 0.435 104.53 80 523.70 1 6.261 1.000 0.63 0.369 -0.33 0.435 104.74 81 535.30 0 6.283 0.990 0.62 0.375 -0.32 0.438 107.06 82 535.65 0 6.283 0.990 0.62 0.382 -0.30 0.441 107.13 83 540.00 0 6.292 0.990 0.61 0.388 -0.28 0.445 108.00 84 542.90 0 6.297 0.990 0.61 0.394 -0.27 0.448 108.58 85 545.45 0 6.302 0.990 0.60 0.401 -0.25 0.451 109.09 86 546.55 1 6.304 1.000 0.60 0.401 -0.25 0.451 109.31 87 548.70 0 6.308 0.989 0.59 0.407 -0.24 0.454 109.74 88 549.80 1 6.310 1.000 0.59 0.407 -0.24 0.454 109.96 89 551.95 0 6.313 0.989 0.59 0.413 -0.22 0.457 110.39 90 563.90 1 6.335 1.000 0.59 0.413 -0.22 0.457 112.78 91 570.45 0 6.346 0.989 0.58 0.420 -0.20 0.461 114.09 92 570.45 1 6.346 1.000 0.58 0.420 -0.20 0.461 114.09 93 571.15 1 6.348 1.000 0.58 0.420 -0.20 0.461 114.23 94 578.05 0 6.360 0.989 0.57 0.427 -0.19 0.464 115.61 95 582.40 0 6.367 0.988 0.57 0.433 -0.17 0.467 116.48 96 582.40 0 6.367 0.988 0.56 0.440 -0.15 0.471 116.48 97 585.65 0 6.373 0.988 0.55 0.447 -0.13 0.474 117.13 98 587.80 0 6.376 0.988 0.55 0.453 -0.12 0.477 117.56 99 599.75 0 6.397 0.988 0.54 0.460 -0.10 0.480 119.95 100 606.25 1 6.407 1.000 0.54 0.460 -0.10 0.480 121.25 101 607.35 0 6.409 0.988 0.53 0.467 -0.08 0.484 121.47 102 610.60 1 6.414 1.000 0.53 0.467 -0.08 0.484 122.12 103 611.35 0 6.416 0.987 0.53 0.473 -0.07 0.487 122.27 104 614.95 0 6.422 0.987 0.52 0.480 -0.05 0.490 122.99 105 614.95 0 6.422 0.987 0.51 0.487 -0.03 0.494 122.99 106 620.40 0 6.430 0.987 0.51 0.494 -0.02 0.497 124.08 107 ' 621.10 1 6.431 1.000 0.51 0.494 -0.02 0.497 124.22 108 629.10 1 6.444 1.000 0.51 0.494 -0.02 0.497 125.82 109 631.25 1 6.448 1.000 0.51 0.494 -0.02 0.497 • 126.25 110 631.25 0 6.448 0.986 0.50 0.501 0.00' 0.501 126.25 111 633.45 1 6.451 1.000 0.50 0.501 0.00 0.501 126.69 112 633.45 0 6.451 0.986 0.49 0.508 0.02 0.504 126.69 113 638.15 0 6.459 0.985 0.48 0.516 0.04 0.508 127.63 114 642.10 0 6.465 0.985 0.48 0.523 0.06 0.511 128.42 115 644.30 0 6.468 0.985 0.47 0.530 0.08 0.515 128.86 116 651.55 0 6.479 0.985 0.46 0.537 0.09 0.518 130.31 117 653.35 0 6.482 0.984 0.46 0.545 0.11 0.522 130.67 118 655.15 1 6.485 1.000 0.46 0.545 0.11 0.522 131.03 119 655.15 1 6.485 1.000 0.46 0.545 0.11 0.522 131.03 120 658.40 0 6.490 0.984 0.45 0.552 0.13 0.525 . 131.68 121 660.60 1 6.493 1.000 0.45 0.552 0.13 0.525 132.12 122 663.85 0 6.498 0.983 0.44 0.560 0.15 0.529 132.77 123 666.40 0 6.502 0.983 0.43 0.567 0.17 0.533 133.28 124 670.70 0 6.508 0.982 0.43 0.575 0.19 0.537 134.14 125 671.45 1 6.509 1.000 0.43 0.575 0.19 0.537 134.29 126 671.45 1 6.509 1.000 0.43 0.575 0.19 0.537 134.29 127 672.55 0 6.511 0.981 0.42 0.583 0.21 0.541 134.51 128 686.65 0 6.532 0.981 0.41 0.590 0.23 0.545 137.33 129 691.00 1 6.538 1.000 0.41 0.590 0.23 0.545 138.20 130 702.60 0 6.555 0.980 0.40 0.599 0.25 0.549 140.52 131 702.95 1 6.555 1.000 0.40 0.599 0.25 0.549 140.59 132 707.30 1 6.561 .1.000 0.40 0.599 0.25 0.549 141.46 133 707.65 0 6.562 0.979 0.39 0.607 0.27 0.553 141.53 134 716.00 0 6.574 0.979 0.38 0.615 0.29 0.557 143.20 135 721.40 1 6.581 1.000 0.38 0.615 0.29 0.557 144.28 • 136 725.75 0 6.587 0.978 0.38 0.624 0.32 0.561 145.15 137 725.75 0 6.587 0.977 0.37 0.632 0.34 0.566 145.15 138 730.10 1 6.593 1.000 0.37 0.632 0.34 0.566 146.02 139 733.35 1 6.598 1.000 0.37 0.632 0.34 0.566 -. ' • 146.67 140 734.45 0 6.599 0.976 0.36 0.641 0.36 0.570 146.89 , 141 738.05 0 6.604 0.975 0.35 0.650 0.39 0.575 147.61 APPENDIX IV Sample Number = 004, 005, 006; Temperature = 20°C; Rate of Loading = 0.2 kN/s 201 ordered value rate of loading = 0.2 kN/sec ordered value TTF c c . ln(x) (n-i)/ R %tile •z -K loads (sec) (n-i+1) (kN) 142 739.90 0 6.607 0.974 0.34 0.659 0.41 0.580 147.98 143 740.95 0 6.608 0.974 0.33 0.668 0.44 0.585 148.19 144 746.40 0 6.615 0.973 0.32 0.677 0.46 0.589 149.28 145 755.10 0 6.627 0.972 0.31 0.686 0.48 0.594 151.02 146 764.85 0 6.640 0.971 0.30 0.695 0.51 0.599 152.97 147 774.65 0 6.652 0.971 0.30 0.704 0.54 0.604 154.93 148 774.65 0 6.652 0.970 0.29 0.713 0.56 0.609 154.93 149 778.60 1 6.657 1.000 0.29 0.713 0.56 0.609 155.72 150 784.40 0 6.665 0.968 0.28 0.722 0.59 0.615 156.88 151 787.65 1 6.669 1.000 0.28 0.722 0.59 0.615 157.53 152 787.65 0 6.669 0.966 0.27 0.732 0.62 0.620 157.53 153 794.20 0 6.677 0.964 0.26 0.741- 0.65 0.626 158.84 154 797.45 0 6.681 0.963 0.25 0.751 0.68 0.632 159.49 155 797.45 1 6.681 1.000 0.25 0.751 0.68 0.632 159.49 156 800.70 0 6.685 0.960 0.24 0.761 0.71 0.638 160.14 157 808.65 0 6.695 0.958 0.23 0.771 0.74 0.644 161.73 158 815.90 0 6.704 0.957 0.22 0.781 0.78 0.651 163.18 159 817.00 0 6.706 0.955 0.21 0.791 0.81 0.658 163.40 160 822.45 0 6.712 0.952 0.20 0.801 0.84 0.664 164.49 161 826.40 1 6.717 1.000 0.20 0.801 0.84 0.664 165.28 162 826.75 0 6.718 0.947 0.19 0.811 0.88 0.672 165.35 163 836.55 1 6.729 1.000 0.19 0.811 0.88 0.672 167.31 164 846.30 1 6.741 1.000 0.19 0.811 0.88 0.672 169.26 165 858.65 0 6.755 0.938 0.18 0.823 0.93 0.680 171.73 166 885.45 0 6.786 0.933 0.17 0.835 0.97 0.689 177.09 167 889.75 1 6.791 1.000 0.17 0.835 0.97 0.689 177.95 168 889.75 0 6.791 0.923 0.15 0.848 1.03 0.700 177.95 169 899.90 0 6.802 0.917 0.14 0.860 1.08 0.710 179.98 170 908.95 0 6.812 0.909 0.13 0.873 1.14 0.722 181.79 171 928.90 1 6.834 1.000 0.13 0.873 1.14 0.722 185.78 172 941.90 0 6.848 0.889 0.11 0.887 1.21 0.736 188.38 173 963.65 1 6.871 1.000 0.11 0.887 1.21 0.736 192.73 174 982.10 0 6.890 0.857 0.10 0.903 1.30 0.753 196.42 175 983.20 0 6.891 0.833 0.08 0.919 1.40 0.773 196.64 176 984.25 0 6.892 0.800 0.06 0.935 1.52 0.795 196.85 177 1041.10 0 6.948 0.750 0.05 0.952 1.66 0.823 208.22 178 1064.65 0 6.970 0.667 0.03 0.968 1.85 0.860 212.93 179 1102.65 1 7.005 1.000 0.03 0.968 1.85 0.860 220.53 180 1216.70 0 7.104 0.000 0.00 1.000 243.34 APPENDIX IV Sample Number = 007, 008, 009; Temperature = 20°C; Rate of loading •  0.067kN/s ordered value rate of loading = 0.06667 kN/sec T T F (sec) c c . ln(x) 1 519.76 0 6.253 2 546.61 0 6.304 3 575.86 0 6.356 4 581.56 0 6.366 5 706.51 0 6.560 6 740.26 0 6.607 7 785.86 1 6.667 8 817.36 0 6.706 9 853.21 0 6.749 10 922.66 0 6.827 11 929.26 1 6.834 12 929.26 0 6.834 13 929.26 0 6.834 14 943.36 1 6.849 15 954.16 0 6.861 16 957.46 0 6.864 17 971.56 0 6.879 18 1030.21 1 6.938 19 1038.91 0 6.946 20 1048.66 1 6.955 21 1062.76 0 6.969 22 1071.46 0 6.977 23 1092.16 1 6.996 24 1092.16 1 6.996 25 1093.21 0 6.997 26 1098.61 0 7.002 27 1110.61 0 7.013 28 1137.76 0 7.037 29 1149.76 0 7.047 30 1150.81 1 7.048 31 1157.26 1 7.054 32 1172.56 0 7.067 33 1176.91 0 7.071 34 1187.71 0 7.080 35 1225.81 1 7.111 36 1231.21 1 7.116 37 1240.96 0 7.124 38 1242.01 0 7.124 39 1242.01 0 7.124 40 1248.61 0 7.130 41 1255.06 0 7.135 42 1256.11 0 7.136 43 1276.21 1 7.152 44 1305.31 0 7.174 45 1323.46 0 7.188 46 1333.36 0 7.195 47 1336.51 0 7.198 48 1339.81 0 7.200 49 1349.56 0 7.208 50 1350.16 0 7.208 51 1359.31 0 7.215 52 1360.51 0 7.216 53 1361.56 0 7.216 54 1366.96 0 7.220 55 1376.71 0 7.227 56 1390.81 1 7.238 57 1390.81 1 7.238 58 1395.16 0 7.241 59 1395.16 0 7.241 60 1401.76 0 7.245 61 1405.06 1 7.248 62 1410.46 1 7.252 63 1410.46 0 7.252 64 1425.61 0 7.262 65 1441.96 0 7.274 66 1444.06 0 7.275 67 1451.71 0 7.281 68 1451.71 1 7.281 69 1452.76 1 7.281 70 1455.01 1 7.283 %tile 202 ordered value loads (kN) 0.994 0.994 0.994 0.994 0.994 0.994 1.000 0.994 0.994 0.994 1.000 0.994 0.994 1.000 0.994 0.994 0.994 1.000 0.994 1.000 0.994 0.994 1.000 1.000 0.994 0.994 0.994 0.993 0.993 1.000 1.000 0.993 0.993 0.993 1.000 1.000 0.993 0.993 0.993 0.993 0.993 0.993 1.000 0.993 0.993 0.993 0.993 0.992 0.992 0.992 0.992 0.992 0.992 0.992 0.992 1.000 1.000 0.992 0.992 0.992 1.000 1.000 0.992 0.991 0.991 0.991 0.991 1.000 1.000 1.000 1 0.99 0.99 0.98 0.98 0.97 0.97 0.97 0.96 0.96 0.95 0.95 0.94 0.94 0.94 0.93 0.93 0.92 0.92 0.92 0.92 0.91 0.90 0.90 0.90 0.90 0.89 0.89 0.88 0.88 0.88 0.88 0.87 0.86 0.86 0.86 0.86 0.85 0.85 0.84 0.83 0.83 0.82 0.82 0.82 0.81 0.80 0.80 0.79 0.79 0.78 0.77 0.77 0.76 0.76 0.75 0.75 0.75 0.74 0.74 0.73 0.73 0.73 0.73 0.72 0.71 0.71 0.70 0.70 0.70 0.70 0.006 0.011 0.017 0.022 0.028 0.033 0.033 0.039 0.045 0.050 0.050 0.056 0.061 0.061 0.067 0.073 0.078 0.078 0.084 0.084 0.090 0.095 0.095 0.095 0.101 0.107 0.113 0.119 0.124 0.124 0.124 0.130 0.136 0.142 0.142 0.142 0.148 0.154 0.160 0.166 0.172 0.178 0.178 0.184 0.190 0.196 0.202 0.208 0.214 0.220 0.226 0.232 0.238 0.244 0.250 0.250 0.250 0.256 0.262 0.268 0.268 0.268 0.274 0.281 0.287 0.293 0.299 0.299 0.299 0.299 -2.54 -2.29 -2.13 -2.01 -1.91 -1.83 -1.83 -1.76 -1.70 -1.64 -1.64 -1.59 -1.54 -1.54 -1.50 -1.46 -1.42 -1.42 -1.38 -1.38 -1.34 -1.31 -1.31 -1.31 -1.27 -1.24 -1.21 -1.18 -1.15 -1.15 -1.15 -1.12 -1.10 -1.07 -1.07 -1.07 -1.04 -1.02 -0.99 -0.97 -0.95 -0.92 -0.92 -0.90 -0.88 -0.86 -0.84 -0.81 -0.79 -0.77 -0.75 -0.73 -0.71 -0.69 -0.68 -0.68 -0.68 -0.66 -0.64 -0.62 -0.62 -0.62 -0.60 -0.58 -0.56 -0.54 -0.53 -0.53 -0.53 -0.53 0.006 0.055 0.086 0.109 0.127 0.143 0.143 0.157 0.169 0.180 0.180 0.190 0.200 0.200 0.208 0.217 0.224 0.224 0.232 0.232 0.239 0.245 0.245 0.245 0.252 0.258 0.264 0.270 0.276 0.276 0.276 0.281 0.286 0.292 0.292 0.292 0.297 0.302 0.306 0.311 0.316 0.320 0.320 0.325 0.329 0.333 0.337 0.342 0.346 0.350 0.354 0.357 0.361 0.365 0.369 0.369 0.369 0.372 0.376 0.380 0.380 0.380 0.383 0.387 0.390 0.394 0.397 0.397 0.397 0.397 sample statistics number of specimens in sample = mean of column B : B = standard deviatin of column B : B = 180 1738.732 610.766 threshold parameter by trial and error = 0 slope of regression line = 0.4459 intercept of regression line = -2.8512 location parameter (y=0.5) by quantile estimate = 7.5110 scale parameter by quantile estimate = 0.4286 LOG-NORMAL PROBABILITY PLOT O DATA —-Linear (DATA) 7.00 7.50 8.00 Ln(X) T h e above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. T h e T T F data were censored for c c = 1 in the probability plot. However/ in the estimation of the maximum likelihood values for the lognormal parameters mu and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of . H . L . Harter and A. H. Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter L o g Normal Populations from Complete and Censored Samples , J . Amer. Stat. A s s o c , Vol. 61, 1966. T h e method of Quantile Estimator is used to find mu (the location parameter) and s igma (the scale parameter) since it can deal with censored data. T h e quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from zero up to the minimum value, were tried. T h e fit was judged to be the best when the value was zero. Therefore the 2 -P lognormal model was used. Zo.23 Zn.75 Ko.25 LnXo.2! Ko.75 L n X , . 7 -0.67449 0.67449 0.36919 7.22189 0.62701 7.80006 34.65 36.44 38.39 38.77 47.10 49.35 52.39 . 54.49 56.88 61.51 61.95 61.95 61.95 62.89 63.61 63.83 64.77 68.68 69.26 69.91 70.85 71.43 72.81 72.81 72.88 73.24 74.04 75.85 76.65 76.72 77.15 78.17 78.46 79.18 81.72 82.08 82.73 82.80 82.80 83.24 83.67 83.74 85.08 87.02 88.23 88.89 89.10 89.32 89.97 90.01 90.62 90.70 90.77 91.13 91.78 92.72 92.72 93.01 93.01 93.45 93.67 94.03 94.03 95.04 96.13 96.27 96.78 96.78 96.85 97.00 203 APPENDIX IV Sample Number = 007, 008, 009; Temperature = 20°C; Rate of loading = 0.067kN/s ordered value T T F c.c. (sec) ln(x) (n-i)/ (n-i+1) R %tile Z K rate of loading = 0.06667 kN/sec ordered value loads (kN) 71 1460.41 0 7.286 0.991 0.69 0.306 -0.51 0.401 97.36 72 1471.21 0 7.294 0.991 0.69 0.312 -0.49 0.405 98.08 73 1472.26 0 7.295 0.991 0.68 0.318 -0.47 0.408 98.15 74 1499.56 0 7.313 0.991 0.68 0.325 -0.45 0.411 99.97 . 75 1519.07 0 7.326 0.991 0.67 0.331 -0.44 0.415 101.27 76 1526.72 0 7.331 0.990 0.66 0.337 -0.42 0.418 101.78 77 1529.87 0 7.333 0.990 0.66 0.344 -0.40 0.422 101.99 78 1542.92 0 7.341 0.990 0.65 0.350 -0.39 0.425 102.86 79 1548.32 1 7.345 1.000 0.65 0.350 -0.39 0.425 103.22 80 1592.87 0 7.373 0.990 0.64 0.357 -0.37 0.428 106.19 81 . 1609.22 1 7.384 1.000 0.64 0.357 -0.37 0.428 107.28 82 1610.27 1 7.384 1.000 0.64 0.357 -0.37 0.428 107.35 83 1632.02 0 7.398 0.990 0.64 0.363 -0.35 0.432 108.80 84 1633.07 0 7.398 0.990 0.63 0.370 -0.33 0.435 108.87 85 1638.47 0 7.402 0.990 .0 .62 0.376 -0.32 0.439 109.23 86 1639.67 0 7.402 0.989 0.62 0.383 -0.30 0.442 109.31 87 1652.72 1 7.410 1.000 0.62 0.383 -0.30 0.442 110.18 88 1659.17 0 7.414 0.989 0.61 0.389 -0.28 0.445 110.61 89 1664.57 1 7.417 1.000 0.61 0.389 -0.28 0.445 110.97 • 90 1675.52 0 7.424 0.989 0.60 0.396 -0.26 0.449 111.70 91 1675.52 1 7.424 1.000 0.60 0.396 -0.26 0.449 111.70 92 1686.32 0 7.430 0.989 0.60 0.403 -0.25 0.452 112.42 93 1695.02 1 7.435 1.000 0.60 0.403 -0.25 0.452 113.00 94 1711.37 0 7.445 0.989 0.59 0.410 -0.23 0.456 114.09 95 1717.82 1 7.449 1.000 0.59 0.410 -0.23 0.456 114.52 96 1736.27 1 7.459 1.000 0.59 0.410 -0.23 0.456 .115.75 97 1743.92 0 7.464 0.988 0.58 0.417 -0.21 0.459 116.26 98 1746.02 0 7.465 0.988 0.58 0.424 -0.19 0.463 116.40 . 99 1764.47 0 7.476 0.988 0.57 0.431 -0.17 0.466 117.63 100 1768.82 0 7.478 0.988 0.56 0.438 -0.16 0.470 117.92 101 1770.02 1 7.479 1.000 0.56 0.438 -0.16 0.470 118.00 102 1778.72 0 7.484 0.987 0.55 0.445 -0.14 0.473 118.58 103 1789.52 0 7.490 0.987 0.55 0.452 -0.12 0.477 119.30 104 1797.17 1 7.494 1.000 0.55 0.452 -0.12 0.477 119.81 105 1802.57 0 7.497 0.987 0.54 0.459 -0.10 0.480 120.17 106 1805.87 0 7.499 0.987 0.53 0.467 -0.08 0.484 120.39 107 1813.37 0 7.503 0.986 0.53 0.474 -0.07 0.487 120.89 108 1815.62 0 7.504 0.986 0.52 0.481 -0.05 0.491 121.04 109 1822.07 0 7.508 0.986 0.51 0.488 -0.03 0.494 121.47 110 1823.12 0 7.508 0.986 0.50 0.495 -0.01 0.498 121.54 111 1827.47 0 7.511 0.986 0.50 0.503 0.01 0.501 121.83 112 1841.72 0 7.518 0.986 0.49 0.510 0.02 0.505 122.78 113 1856.87 0 7.527 0.985 0.48 0.517 0.04 0.508 123.79 114 1863.32 1 7.530 1.000 0.48 0.517 0.04 0.508 124.22 115 ' 1875.32 0 7.537 0.985 0.48 0.524 0.06 0.512 125.02 116 1884.02 1 7.541 1.000 0.48 0.524 0.06 0.512 125.60 117 1906.82 1 7.553 1.000 0.48 0.524 0.06 0.512 127.12 118 1907.87 0 7.554 0.984 0.47 0.532 0.08 0.516 127.19 119 1923.17 0 7.562 0.984 0.46 0.539 0.10 0.519 128.21 120 1926.32 0 7.563 0.984 0.45 0.547 0.12 0.523 128.42 121 1927.52 1 7.564 1.000 0.45 0.547 0.12 0.523 128.50 122 1939.37 0 7.570 0.983 0.45 0.555 0.14 0.527 129.29 123 1940.57 0 7.571 0.983 0.44 0.562 0.16 0.531 129.37 124 1942.67 0 7.572 0.982 0.43 0.570 0.18 0.534 129.51 125 1952.42 1 7.577 1.000 0.43 0.570 0.18 0.534 130.16 126 1957.82 1 7:580 1.000 0.43 0.570 0.18 0.534 130.52 127 1959.02 1 7.580 1.000 0.43 0.570 0.18 0.534 130.60 128 1965.47 . 0 7.583 0.981 0.42 0.578 0.20 0.538 131.03 129 1999.22 1 7.601 1.000 0.42 0.578 0.20 0.538 133.28 130 2001.32 0 7.602 0.980 0.41 0.586 0.22 0.542 133.42 131 2024.12 0 7.613 0.980 0.41 0.595 0.24 0.547 134.94 132 2030.72 0 7.616 0.980 0.40 0.603 0.26 0.551 135.38 133 2033.87 0 . 7.618 0.979 0.39 0.611 0.28 0.555 ' 135.59 134 2034.92 1 7.618 1.000 0.39 0.611 0.28 0.555 135.66 135 2049.17 0 7.625 0.978 0.38 0.620 0.30 0.559 136.61 136 2065.37 0 7.633 0.978 0.37 0.628 0.33 0.564 137.69 137 2100.17 1' 7.650 1.000 0.37 0.628 0.33 0.564 ' . 140.01 138 2129.42 0 7.664 0.977 0.36 0.637 0.35 0.568 141.96 139 2164.22 1 7.680 1.000 0.36 0.637 0.35 0.568 . 144.28 140 2217.02 1 7.704 1.000 0.36 0.637 0.35 0.568 . 147.80 141 2241.32 1 7.715 1.000 0.36 0.637 0.35 0.568 149.42 204 APPENDIX IV Sample Number = 007, 008, 009; Temperature = 20°C; Rate of loading = 0.067kN/s ordered value rate of loading = 0.06667 kN/sec ordered value T T F c.c. In(x) (n-i)/ R %tile Z K loads (secj (n-i+1) (kN) 142 2254.37 1 7.721 1.000 0.36 0.637 0.35 0.568 150.29 143 2262.02 0 7.724 0.974 0.35 0.646 0.38 0.573 150.80 144 2268.47 1 7.727 1.000 0.35 0.646 0.38 0.573 151.23 145 2330.42 0 7.754 0.972 0.34 0.656 0.40 0.578 155.36 146 2345.72 0 7.760 0.971 0.33 0.666 0.43 0.583 156.38 147 2348.87 1 7.762 1.000 0.33 0.666 0.43 0.583 156.59 148 2349.92 0 7.762 0.970 0.32 0.676 0.46 0.589 156.66 149 2354.27 0 7.764 0.969 0.31 0.686 0.49 0.594 156.95 150 2388.02 0 7.778 0.968 0.30 0.696 0.51 0.600 159.20 151 2396.72 0 7.782 0.967 0.29 0.706 0.54 0.606 159.78 152 2406.47 0 7.786 0.966 0.28 0.717 0.57 0.611 160.43 153 2410.82 0 7.788 0.964 0.27 0.727 0.60 0.617 160.72 154 2448.77 0 7.803 0.963 0.26 0.737 0.63 0.623 163.25 155 2461.82 1 7.809 1.000 0.26 0.737 0.63 0.623 164.12 156 2503.23 0 7.825 0.960 0.25 0.747 0.67 0.630 166.88 157 2526.03 0 7.834 0.958 0.24 0.758 0.70 0.636 168.40 158 2543.28 0 7.841 0.957 0.23 0.768 0.73 0.643 169.55 159 2572.68 1 7.853 1.000 0.23 0.768 0.73 0.643 171.51 160 2582.43 1 7.856 1.000 0.23 0.768 0.73 0.643 172.16 161 2589.03 0 7.859 0.950 0.22 0.780 0.77 0.650 172.60 162 2613.93 0 7.869 0.947 0.21 0.792 0.81 0.658 174.26 163 2633.43 1 7.876 1.000 0.21 0.792 0.81 0.658 175.56 164 2643.33 0 7.880 0.941 0.20 0.804 0.86 0.666 176.22 165 2654.13 0 7.884 0.938 0.18 0.816 0.90 0.675 176.94 166 2694.33 1 7.899 1.000 0.18 0.816 0.90 0.675 179.62 167 2696.43 0 7.900 0.929 0.17 0.829 0.95 0.685 179.76 168 2740.98 0 7.916 0.923 0.16 0.842 1.00 0.695 182.73 169 2762.73 0 7.924 0.917 0.14 0.855 1.06 0.706 184.18 170 2821.38 0 7.945 0.909 0.13 0.869 1.12 0.718 188.09 171 2832.33 0 7.949 0.900 0.12 0.882 1.18 0.730 188.82 172 2882.28 0 7.966 0.889 0.11 0.895 1.25 0.744 192.15 173 2887.68 1 7.968 1.000 0.11 0.895 1.25 0.744 192.51 174 2897.43 0 7.972 0.857 0.09 0.910 1.34 0.761 193.16 175 2906.13 1 7.975 1.000 0.09 0.910 1.34 0.761 193.74 176 2952.78 0 7.991 0.800 0.07 0.928 1.46 0.784 196.85 177 3167.88 0 8.061 0.750 0.05 0.946 1.61 0.813 211.19 178 3223.38 0 8.078 0.667 0.04 0.964 1.80 0.850 214.89 179 3495.93 0 8.159 0.500 0.02 0.982 2.10 0.908 233.06 180 3552.49 0 8.175 0.000 0.00 1.000 236.83 APPENDIX IV Sample Number = 010; Temperature = 150°C; Rate of Loading = 1.85 kN/s 205 ordered value TTF c. rate of loading = 1.85 kN/sec ln(x) (sec) 1 1528.16 0 3.338 2 1533.49 1 3.511 3 1535.58 0 3.572 4 1535.72 0 3.576 5 1536.29 0 3.592 6 1537.82 0 3.633 7 1539.01 0 3.664 8 1540.60 0 3.704 9 1542.67 0 3.753 10 1543.52 0 3.773 11 1544.38 0 3.793 12 1544.80 0 3.802 13 1544.82 0 3.803 14 1545.80 0 3.824 15 1546.17 0 3.832 16 1546.68 0 3.843 17 1546.71 0 3.844 18 1546.74 0 3.845 19 1547.08 0 3.852 20 1547.45 0 3.860 21 1547.83 0 3.868 22 1548.32 0 3.878 23 1548.35 0 3.878 24 1551.78 0 3.947 25 1551.81 0 3.948 26 1552.05 0 3.952 27 1553.59 0 3.981 28 1553.63 0 3.982 29 1554.07 0 3.990 30 1554.62 0 4.000 31 1558.25 0 4.065 32 1558.69 0 4.072 33 1559.09 0 4.079 34 1560.03 0 4.095 35 1560.48 0 4.102 36 1562.31 0 4.132 37 1562.82 0 4.140 38 1563.28 0 4.148 39 1563.52 1 4.151 40 1565.12 0 4.176 41 1565.95 0 4.189 42 1566.39 0 4.196 43 1566.45 0 4.196 44 1567.48 0 4.212 45 1568.00 0 4.220 46 1569.93 0 4.247 47 1570.49 0 4.255 48 1571.32 0 4.267 49 1571.46 0 4.269 50 1573.43 0 4.296 51 1574.53 0 4.311 52 1574.61 0 4.312 53 1575.03 0 4.318 54 1577.68 1 4.353 55 1579.01 0 4.370 56 1579.15 0 4.371 57 1582.24 0 4.410 58 1586.02 0 4.455 59 1594.00 0 4.543 60 1594.27 0 4.546 (n-i)/ %tile 0.983 1.000 0.983 0.982 0.982 0.982 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.979 0.978 0.978 0.977 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.971 0.971 0.970 0.969 0.968 0.967 0.966 0.964 0.963 0.962 0.960 0.958 0.957 1.000 0.952 0.950 0.947 0.944 0.941 0.938 0.933 0.929 0.923 0.917 0.909 0.900 0.889 0.875 1.000 0.833 0.800 0.750 0.667 0.500 0.000 1 0.98 0.98 0.97 0.95 0.93 0.92 0.90 0.88 0.86 0.85 0.83 0.81 0.80 0.78 0.76 0.75 0.73 0.71 0.70 0.68 0.66 0.64 0.63 0.61 0.59 0.58 0.56 0.54 0.53 0.51 0.49 0.47 0.46 0.44 0.42 0.41 0.39 0.37 0.37 0.36 0.34 0.32 0.30 0.28 0.27 0.25 0.23 0.21 0.20 0.18 0.16 0.14 0.12 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0.017 0.017 0.034 0.051 0.068 0.084 0.101 0.118 0.135 0.152 0.169 0.186 0.203 0.220 0.237 0.254 0.271 0.288 0.305 0.322 0.339 0.356 0.373 0.390 0.407 0.424 0.441 0.457 0.474 0.491 0.508 0.525 0.542 0.559 0.576 0.593 0.610 0.627 0.627 0.645 (,0.663 0.680 0.698; 0.716 0.734 0.751 0.769 0.787 0.805 0.822 0.840 0.858 0.876 0.876. 0.896 0.917 0.938 0.959 0.979 1.000 -2.13 -2.13 -1.83 -1.64 -1.49 -1.38 -1.27 -1.18 -1.10 -1.03 -0.96 -0.89 -0.83 -0.77 -0.72 -0.66 -0.61 -0.56 -0.51 -0.46 -0.42 -0.37 -0.32 -0.28 -0.24 -0.19 -0.15 -0.11 -0.06 -0.02 0.02 0.06 0.11 0.15 0.19 0.24 0.28 0.32 0.32 0.37 0.42 0.47 0.52 0.57 0.62 0.68 0.74 0.80 0.86 0.92 1.00 1.07 1.15 1.15 1.26 1.39 1.54 1.73 2.04 0.018 0.018 0.085 0.129 0.161 0.188 0.212 0.232 0.250 0.267 0.283 0.298 0.312 0.325 0.338 0.350 0.362 0.373 0.384 0.395 0.406 0.416 0.426 0.437 0.446 0.456 0.466 0.476 0.485 0.495 0.505 0.514 0.524 0.534 0.544 0.553 0.563 0.573 0.573 0.584 0.595 0.606 0.618 0.629 0.641 0.654 0.667 0.680 0.694 0.709 0.725 0.743 0.761 0.761 0.786 0.814 0.848 0.893 0.962 sample statistics number of specimens in sample = mean of column B:B = standard deviatin of column B:B = 60 1557.843 15.366 threshold parameter by trial and error = slope of regression line = intercept of regression line = location parameter by quantile estimate = scale parameter by quantile estimate = 1500 0.8115 -2.7697 4.0268 0.2355 1.000 T 0.800 0.600 0.400 -• 0.200 0.000 •CMC?* LOG-NORMAL PROBABILITY PLOT y = 0.8115x - 2.7697 R2 = 0.9846 )0 O DATA •Linear (DATA) 5.00 The above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. The TTF data were censored for cc. = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters mu and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H.L. Harter and A. H. Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter Log Normal Populations from Complete and Censored Samples, J. Amer. Stat. Assoc., Vol. 61, 1966. The method of Quantile Estimator is used to find mu (the location parameter) and sigma (the scale parameter) since it can deal with censored data. The quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from 1500 seconds up to the minimum value, were tried. The fit was judged to be the best when the value was 1500 seconds. Z0.25 ZO.75 Ko.25 LnXo.25 Ko.75 LnXrjj5 -0.67449 . 0.67449 0.369191 3.867904 0.627009 4.185604 Sample Number APPENDIX IV 011; Temperature = 200°C; Rate of Loading = 1.85 kN/s 206 ordered value TTF c. In(x) (sec) 1 1525.28 0 3.230 2 1529.13 0 3.372 3 1529.40 0 3.381 4 1531.39 0 3.446 5 1531.48 0 3.449 6 1532.65 0 3.486 7 1533.45 0 3.510 8 1533.93 0 3.524 9 1534.12 0 3.530 10 1535.29 0 3.564 11 1535.50 0 3.570 12 1536.10 0 3.586 13 1537.16 0 3.615 14 1537.66 0 3.629 15 1537.90 1 3.635 16 1538.76 0 3.657 17 1539.09 0 3.666 18 1539.26 0 3.670 19 1540.44 0 3.700 20 1540.57 0 3.703 21 1541.12 0 3.716 22 1541.30 0 3.721 23 1541.78 0 3.732 24 1541.99 0 3.737 25 1542.85 0 3.758 26 1543.06 0 3.763 27 1543.94 0 3.783 28 1544.35 0 3.792 29 1544.41 0 3.793 30 1544.94 0 3.805 31 1545.14 0 3.810 32 1545.92 0 3.827 33 1546.50 0 3.839 34 1546.53 1 3.840 35 1546.59 0 3.841 36 1547.82 0 3.867 37 1549.48 0 3.902 38 1549.68 0 3.906 39 1550.63 0 3.925 40 1550.94 0 3.931 41 1551.07 0 3.933 42 1551.92 0 3.950 43 1552.25 0 3.956 44 1553.43 0 3.978 45 1553.75 0 3.984 46 1554.12 0 3.991 47 1554.68 1 4.001 48 1556.99 0 4.043 49 1557.56 0 4.053 50 1557.61 0 4.054 51 1558.32 0 4.066 52 1559.71 0 4.089 53 1560.43 0 4.101 54 1562.78 0 4.140 55 1563.29 0 4.148 56 1564.93 0 4.173 57 1566.08 b 4.191 58 1570.60 0 4.257 59 1571.58 0 4.271 60 1575.80 0 4.328 (n-i)/ (n-i+1) %tile rate of loading = 1.85 kN/sec 0.983 0.983 0.983 0.982 0.982 0.982 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.979 1.000 0.978 0.977 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.971 0.971 0.970 0.969 0.968 0.967 0.966 0.964 1.000 0.962 0.960 0.958 0.957 0.955 0.952 0.950 0.947 0.944 0.941 0.938 0.933 1.000 0.923 0.917 0.909 0.900 0.889 0.875 0.857 0.833 0.800 0.750 0.667 0.500 0.000 1 0.98 0.97 0.95 0.93 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80 0.78 0.77 0.77 0.75 0.73 0.72 0.70 0.68 0.66 0.65 0.63 0.61 0.60 0.58 0.56 0.55 0.53 0.51 0.49 0.48 0.46 0.46 0.44 0.42 0.41 0.39 0.37 0.35 0.34 0.32 0.30 0.28 0.27 0.25 0.25 0.23 0.21 0.19 0.17 0.15 0.13 0.11 0.10 0.08 0.06 0.04 0.02 0.00 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.167 0.183 0.200 0.217 0.233 0.233 0.250 0.267 0.284 0.301 0.319 0.336 0.353 0.370 0.387 0.404 0.421 0.438 0.455 0.472 0.489 0.506 0.523 0.540 0.540 0.558 0.575 0.593 0.611 0.628 0.646 0.664 0.682 0.699 0.717 0.735 0.752 0.752 0.771 0.790 0.809 0.829 0.848 0.867 0.886 0.905 0.924 0.943 0.962 0.981 1.000 -2.13 -1.83 -1.64 -1.50 -1.38 -1.28 -1.19 -1.11 -1.04 -0.97 -0.90 -0.84 -0.78 -0.73 -0.73 -0.67 -0.62 -0.57 -0.52 -0.47 -0.42 -0.38 -0.33 -0.29 -0.24 -0.20 -0.16 -0.11 -0.07 -0.03 0.01 0.06 0.10 0.10 0.15 0.19 0.24 0.28 0.33 0.37 0.42 0.47 0.52 0.57 0.63 0.68 0.68 0.74 0.81 0.88 0.95 1.03 1.11 1.20 1.31 1.43 1.58 1.77 2.07 0.018 0.085 0.127 0.160 0.187 0.210 0.230 0.248 0.265 0.281 0.295 0.309 0.323 0.335 0.335 0.347 0.359 0.371 0.382 0.393 0.404 0.414 0.425 0.435 0.445 0.455 0.465 0.474 0.484 0.494 0.503 0.513 0.523 0.523 0.533 0.543 0.553 0.564 0.574 0.585 0.596 0.607 0.618 0.630 0.642 0.654 0.654 0.668 0.683 0.698 0.715 0.732 0.752 0.773 0.797 0.824 0.858 0.902 0.970 sample statistics number of specimens in sample = mean of column B:B = standard deviatin of column B:B = 60 1546.741 11.435 threshold parameter by trial and error = slope of regression line = intercept of regression line = location parameter by quantile estimate = scale parameter by quantile estimate = 1500 0.8798 -2.8586 3.8152 0.2172 1.000 0.800 --0.600 0.400 --0.200 0.000 LOG-NORMAL PROBABILITY PLOT y = 0.8798X - 2.8586 = 0.9947 .3. )0 O DATA ^-Linear (DATA) The above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. The TTF data were censored for cc. = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters mu and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H.L. Harterand A. H. Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter Log Normal Populations from Complete and Censored Samples, J. Amer. Stat. Assoc, Vol. 61, 1966. The method of Quantile Estimator is used to find mu (the location parameter) and sigma (the scale parameter) since it can deal with censored data. The quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from 1500 seconds up to the minimum value, were tried. The fit was judged to be the best when the value was 1500 seconds. Z0.25 Z0.75 Ko.25 LnXo.25 Ko.75 LnXo.75 -0.67449 0.67449 0.369191 3.668716 0.627009 3.961751 APPENDIX IV Sample Number = 012; Temperature = 250°C; Rate of Loading = 1.85 kN/s 207 ordered value TTF c. In(x) (sec) 1 1525.24 0 3.228 2 1526.15 0 3.264 3 1527.20 0 3.303 4 1527.95 0 3.330 5 1528.24 0 3.341 6 1529.51 0 3.385 7 1529.79 0 3.394 8 1529.91 0 3.398 9 1529.91 0 3.398 10 1531.08 0 3.437 11 1531.12 0 3.438 12 1531.24 0 3.442 13 1532.03 0 3.467 14 1532.14 0 3.470 15 1532.20 0 3.472 16 1532.36 0 3.477 17 1533.07 0 3.499 18 1533.37 0 3.508 19 1533.40 0 3.509 20 1533.48 0 3.511 21 1533.98 0 3.526 22 1534.21 0 3.533 23 1534.93 0 3.553 24 1535.04 0 3.556 25 1535.18 0 3.560 26 1535.32 0 3.564 27 1536.16 0 3.588 28 1536.53 0 3.598 29 1537.04 0 3.612 30 1537.31 0 3.619 31 1539.30 0 3.671 32 1539.67 0 3.681 33 1539.68 0 3.681 34 1539.85 0 3.685 35 1539.91 0 3.687 36 1540.00 0 3.689 37 1542.28 0 3.744 38 1542.31 0 3.745 39 1542.71 0 3.754 40 1542.97 0 3.761 41 1543.04 0 3.762 42 1543.68 0 3.777 43 1543.87 0 3.781 44 1543.87 0 3.781 45 1544.40 0 3.793 46 1545.74 0 3.823 47 1545.91 0 3.827 48 1547.36 0 3.858 49 1547.99 0 3.871 50 1548.21 0 3.876 51 1549.22 0 3.896 52 1549.26 0 3.897 53 1549.35 0 3.899 54 1550.26 0 3.917 55 1550.32 0 3.918 56 1553.48 0 3.979 57 1556.22 0 4.029 58 1558.25 0 4.065 59 1559.98 0 4.094 60 1565.28 0 4.179 (n-i)/ (n-i+P %tile rate of loading = 1.85 kN/sec 0.983 0.983 0.983 0.982 0.982 0.982 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.979 0.978 0.978 0.977 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.971 0.971 0.970 0.969 0.968 0.967 0.966 0.964 0.963 0.962 0.960 0.958 0.957 0.955 0.952 0.950 0.947 0.944 0.941 0.938 0.933 0.929 0.923 0.917 0.909 0.900 0.889 0.875 0.857 0.833 0.800 0.750 0.667 0.500 0.000 1 0.98 0.97 0.95 0.93 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.68 0.67 0.65 0.63 0.62 0.60 0.58 0.57 0.55 0.53 0.52 0.50 0.48 0.47 0.45 0.43 0.42 0.40 0.38 0.37 0.35 0.33 0.32 0.30 0.28 0.27 0.25 0.23 0.22 0.20 0.18 0.17 0.15 0.13 0.12 0.10 0.08 0.07 0.05 0.03 0.02 0.00 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.167 0.183 0.200 0.217 0.233 0.250 0.267 0.283 0.300 0.317 0.333 0.350 0.367 0.383 0.400 0.417 0.433 0.450 0.467 0.483 0.500 0.517 0.533 0.550 0.567 0.583 0.600 0.617 0.633 0.650 0.667 0.683 0.700 0.717 0.733 0.750 0.767 0.783 0.800 0.817 0.833 0.850 0.867 0.883 0.900 0.917 0.933 0.950 0.967 0.983 1.000 -2.13 -1.83 -1.64 -1.50 -1.38 -1.28 -1.19 -1.11 -1.04 -0.97 -0.90 -0.84 -0.78 -0.73 -0.67 -0.62 -0.57 -0.52 -0.48 -0.43 -0.39 -0.34 -0.30 -0.25 -0.21 -0.17 -0.13 -0.08 -0.04 0.00 0.04 0.08 0.13 0.17 0.21 0.25 0.30 0.34 0.39 0.43 0.48 0.52 0.57 0.62 0.67 0.73 0.78 0.84 0.90 0.97 1.04 1.11 1.19 1.28 1.38 1.50 1.64 1.83 2.13 0.018 0.085 0.127 0.160 0.187 0.210 0.230 0.248 0.265 0.281 0.295 0.309 0.323 0.335 0.347 0.359 0.370 0.381 0.392 0.402 0.413 0.423 0.433 0.443 0.452 0.462 0.472 0.481 0.491 0.500 0.509 0.519 0.528 0.538 0.548 0.557 0.567 0.577 0.587 0.598 0.608 0.619 0.630 0.641 0.653 0.665 0.677 0.691 0.705 0.719 0.735 0.752 0.770 0.790 0.813 0.840 0.873 0.915 0.982 sample statistics number of specimens in sample = mean of column B:B = standard deviatin of column B:B = 60 1539.491 8.986 threshold parameter by trial and error = slope of regression line = intercept of regression line = location parameter by quantile estimate = scale parameter by quantile estimate = 1500 1.0087 -3.1745 3.6409 0.1895 LOG-NORMAL PROBABILITY PLOT 4.60 The above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. The TTF data were censored for c.c. = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters mu and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H.L. Harter and A. H. Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter Log Normal Populations from Complete and Censored Samples, J. Amer. Stat. Assoc., Vol. 61, 1966. The method of Quantile Estimator is used to find mu (the location parameter) and sigma (the scale parameter) since it can deal with censored data. The quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from 1500 seconds up to the minimum value, were tried. The fit was judged to be the best when the value was 1500 seconds. Z0.25 Zrj.75 K(U5 LnXo25 Ko.75 LnXo.75 -0.67449 0.67449 0.369191 3.51306 0.627009 3.768647 208 APPENDIX IV Sample Number = 013; Temperature = 150°C; Rate of Loading = 0.2 kN/s ordered value TTF c. In(x) (sec) 1 1692.30 0 5.259 2 1720.68 0 5.397 3 1737.12 0 5.469 4 1745.64 0 5.504 5 1750.03 0 5.522 6 1753.17 0 5.534 7 1761.25 0 5.565 8 1766.33 0 5.585 9 1776.67 0 5.623 10 1780.96 0 5.638 11 1782.21 0 5.643 12 1784.13 0 5.649 13 1796.03 0 5.690 14 1805.33 0 5.721 15 1819.79 0 5.768 16 1820.15 0 5.769 17 1826.95 0 5.790 18 1830.94 0 5.802 19 1832.63 0 5.807 20 1839.28 0 5.827 21 1841.53 0 5.833 22 1843.02 0 5.838 23 1849.87 0 5.858 24 1850.42 0 5.859 25 1855.07 0 5.872 26 1859.67 0 5.885 27 1867.56 0 5.907 28 1867.81 0 5.908 29 1868.94 0 5.911 30 1885.15 0 5.954 31 1885.83 0 5.955 32 1890.15 0 5.967 33 1891.94 0 5.971 34 1911.57 0 6.020 35 1913.04 0 6.024 36 1917.47 0 6.034 37 1921.55 0 6.044 38 1925.44 0 6.053 39 1934.54 0 6.074 40 1947.68 0 6.104 41 1959.14 0 6.129 42 1960.65 0 6.133 43 1971.08 0 6.155 44 1974.05 0 6.161 45 1974.63 0 6.163 46 1983.54 0 6.181 47 1992.60 0 6.200 48 1996.76 0 6.208 49 2011.01 0 6.236 50 2017.26 0 6.249 51 2026.41 0 6.266 52 2026.97 0 6.267 53 2027.33 0 6.268 54 2044.66 0 6.300 55 2064.41 0 6.336 56 2076.13 0 6.356 57 2088.24 0 6.377 58 2108.57 0 6.411 59 2110.01 0 6.413 60 2159.12 0 6.491 (n-i)/ (n-i+P rate of loading : 0.2 kN/sec %tile 0.983 0.983 0.983 0.982 0.982 0.982 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.979 0.978 0.978 0.977 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.971 0.971 0.970 0.969 0.968 0.967 0.966 0.964 0.963 0.962 0.960 0.958 0.957 0.955 0.952 0.950 0.947 0.944 0.941 0.938 0.933 0.929 0.923 0.917 0.909 0.900 0.889 0.875 0.857 0.833 0.800 0.750 0.667 0.500 0.000 1 0.98 0.97 0.95 0.93 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.68 0.67 0.65 0.63 0.62 0.60 0.58 0.57 0.55 0.53 0.52 0.50 0.48 0.47 0.45 0.43 0.42 0.40 0.38 0.37 0.35 0.33 0.32 0.30 0.28 0.27 0.25 0.23 0.22 0.20 0.18 0.17 0.15 0.13 0.12 0.10 0.08 0.07 0.05 0.03 0.02 0.00 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.167 0.183 0.200 0.217 0.233 0.250 0.267 0.283 0.300 0.317 0.333 0.350 0.367 0.383 0.400 0.417 0.433 0.450 0.467 0.483 0.500 0.517 0.533 0.550 0.567 0.583 0.600 0.617 0.633 0.650 0.667 0.683 0.700 0.717 0.733 0.750 0.767 0.783 0.800 0.817 0.833 0.850 0.867 0.883 0.900 0.917 0.933 0.950 0.967 0.983 1.000 -2.13 -1.83 -1.64 -1.50 -1.38 -1.28 -1.19 -1.11 -1.04 -0.97 -0.90 -0.84 -0.78 -0.73 -0.67 -0.62 -0.57 -0.52 -0.48 -0.43 -0.39 -0.34 -0.30 -0.25 -0.21 -0.17 -0.13 -0.08 -0.04 0.00 0.04 0.08 0.13 0.17 0.21 0.25 0.30 0.34 0.39 0.43 0.48 0.52 0.57 0.62 0.67 0.73 0.78 0.84 0.90 0.97 1.04 1.11 1.19 1.28 1.38 1.50 1.64 1.83 2.13 0.018 0.085 0.127 0.160 0.187 0.210 0.230 0.248 0.265 0.281 0.295 0.309 0.323 0.335 0.347 0.359 0.370 0.381 0.392 0.402 0.413 0.423 0.433 0.443 0.452 0.462 0.472 0.481 0.491 0.500 0.509 0.519 0.528 0.538 0.548 0.557 0.567 0.577 0.587 0.598 0.608 0.619 0.630 0.641 0.653 0.665 0.677 0.691 0.705 0.719 0.735 0.752 0.770 0.790 0.813 0.840 0.873 0.915 0.982 sample statistics number of specimens in sample = mean of column B:B = standard deviatin of column B:B = 60 1898.707 111.246 threshold parameter by trial and error = slope of regression line = intercept of regression line = location parameter by quantile estimate : scale parameter by quantile estimate = 1500 0.7635 -4.0347 5.9372 0.2503 LOG-NORMAL PROBABILITY PLOT Ln(X) The above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. The TTF data were censored for cc. = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters mu and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H.L. Harterand A. H. Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter Log Normal Populations from Complete and Censored Samples, J. Amer. Stat. Assoc., Vol. 61, 1966. The method of Quantile Estimator is used to find mu (the location parameter) and sigma (the scale parameter) since it can deal with censored data. The quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from 1500 seconds up to the minimum value, were tried. The fit was judged to be the best when the value was 1500 seconds. Z0.25 Z0.75 Ko.25 LnXo.25 Ko.75 LnXn.75 -0.67449 0.67449 0.369191 5.768346 0.627009 6.10604 209 APPENDIX IV Sample Number = 014; Temperature = 200°C; Rate of Loading = 0.2 kN/s ordered value TTF (sec) c.c. ln(x) 1 1645.33 0 4.979 2 1671.54 0 5.145 3 1674.97 0 5.165 4 1675.73 0 5.169 5 1681.03 0 5.199 6 1694.94 0 5.273 7 1704.25 0 5.319 8 1704.93 0 5.323 9 1705.15 0 5.324 10 1706.27 0 5.329 11 1708.80 0 5.341 12 1710.89 0 5.351 13 1711.67 0 5.355 14 1712.48 0 5.359 15 1713.09 0 5.362 16 1723.57 0 5.410 17 1731.06 0 5.443 18 1744.76 0 5.500 19 1745.03 0 5.501 20 1748.70 0 5.516 21 1749.14 0 5.518 22 1765.26 0 5.581 23 1768.69 0 5.594 24 1770.78 0 5.601 25 1772.13 0 5.606 26 1774.59 0 5.615 27 1781.40 0 5.640 28 1785.54 0 5.654 29 1785.94 0 5.656 30 1788.64 0 5.665 31 1788.95 0 5.666 32 1789.89 0 5.670 33 1797.19 0 5.694 34 1797.55 0 5.696 35 1806.48 0 5.725 36 1807.61 0 5.729 37 1817.28 0 5.760 38 1823.30 0 5.779 39 1824.99 0 5.784 40 1828.24 0 5.794 41 1855.66 0 5.874 42 1856.08 0 5.875 43 1856.32 0 5.876 44 1857.68 0 5.880 45 1860.08 0 5.886 46 1865.55 0 5.901 47 1868.60 0 5.910 48 1874.88 0 5.927 49 1877.71 0 5.934 50 1885.15 0 5.954 51 1896.96 0 5.984 52 1905.41 0 6.005 53 1913.05 0 6.024 54 1915.91 0 6.030 55 1927.97 0 6.059 56 1933.71 0 6.072 57 1957.11 0 6.125 58 2071.82 0 6.349 59 2086.09 0 6.373 60 2116.71 1 6.424 (n-i)/ ("-i+1> rate of loading : 0.2 kN/sec %tile 0.983 0.983 0.983 0.982 0.982 0.982 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.979 0.978 0.978 0.977 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.971 0.971 0.970 0.969 0.968 0.967 0.966 0.964 0.963 0.962 0.960 0.958 0.957 0.955 0.952 0.950 0.947 0.944 0.941 0.938 0.933 0.929 0.923 0.917 0.909 0.900 0.889 0.875 0.857 0.833 0.800 0.750 0.667 0.500 1.000 1 0.98 0.97 0.95 0.93 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.68 0.67 0.65 0.63 0.62 0.60 0.58 0.57 0.55 0.53 0.52 0.50 0.48 0.47 0.45 0.43 0.42 0.40 0.38 0.37 0.35 0.33 0.32 0.30 0.28 0.27 0.25 0.23 0.22 0.20 0.18 0.17 0.15 0.13 0.12 0.10 0.08 0.07 0.05 0.03 0.02 0.02 0.017 0.033 0.050 0.067 0.083 0.100 0.117 0.133 0.150 0.167 0.183 0.200 0.217 0.233 0.250 0.267 0.283 0.300 0.317 0.333 0.350 0.367 0.383 0.400 0.417 0.433 0.450 0.467 0.483 0.500 0.517 0.533 0.550 0.567 0.583 0.600 0.617 0.633 0.650 0.667 0.683 0.700 0.717 0.733 0.750 0.767 0.783 0.800 0.817 0.833 0.850 0.867 0.883 0.900 0.917 0.933 0.950 0.967 0.983 0.983 -2.13 -1.83 -1.64 -1.50 -1.38 -1.28 -1.19 -1.11 -1.04 -0.97 -0.90 -0.84 -0.78 -0.73 -0.67 -0.62 -0.57 -0.52 -0.48 -0.43 -0.39 -0.34 -0.30 -0.25 -0.21 -0.17 -0.13 -0.08 -0.04 0.00 0.04 0.08 0.13 0.17 0.21 0.25 0.30 0.34 0.39 0.43 0.48 0.52 0.57 0.62 0.67 0.73 0.78 0.84 0.90 0.97 1.04 1.11 1.19 1.28 1.38 1.50 1.64 1.83 2.13 0.018 0.085 0.127 0.160 0.187 0.210 0.230 0.248 0.265 0.281 0.295 0.309 0.323 0.335 0.347 0.359 0.370 0.381 0.392 0.402 0.413 0.423 0.433 0.443 0.452 0.462 0.472 0.481 0.491 0.500 0.509 0.519 0.528 0.538 0.548 0.557 0.567 0.577 0.587 0.598 0.608 0.619 0.630 0.641 0.653 0.665 0.677 0.691 0.705 0.719 0.735 0.752 0.770 0.790 0.813 0.840 0.873 0.915 0.982 sample statistics number of specimens in sample = mean of column B:B = standard deviatin of column B:B = 60 1805.337 101.350 threshold parameter by trial and error = slope of regression line = intercept of regression line = location parameter by quantile estimate = scale parameter by quantile estimate = 1500 0.6999 -3.4602 5.6554 0.2731 LOG-NORMAL PROBABILITY PLOT 0.000 O DATA — Linear (DATA) Ln(X) The above log-normal probability plot shows that the time to failure (TTF) data were reasonably lognormally distributed. The TTF data were censored for c.c. = 1 in the probability plot. However, in the estimation of the maximum likelihood values for the lognormal parameters mu and sigma, the censored data present some difficulty and can not be conventionally estimated. A more accurate analysis can be carried out using the method of H.L. Harterand A. H. Moore, Local Maximum Likelihood Estimation of the Parameters of Three-Parameter Log Normal Populations from Complete and Censored Samples, J. Amer. Stat. Assoc., Vol. 61, 1966. The method of Quantile Estimator is used to find mu (the location parameter) and sigma (the scale parameter) since it can deal with censored data. The quantiles q1 = 0.25 and q2 = 0.75 were used. Various values of the threshold parameter, ranging from 1500 seconds up to the minimum value, were tried. The fit was judged to be the best when the value was 1500 seconds. Zo.25 Zo.75 Ko.25 LnXrj.25 Ko.75 LnXrj.75 -0.67449 0.67449 0.369191 5.471179 0.627009 5.839527 APPENDIX IV Sample Number = 015; Temperature = 250°C; Rate of Loading = 0.2 kN/s 210 ordered value TTF c. rate of loading = 0.2 kN/sec ln(x) (sec) 1 ' 1609.63 0 4.697 2 1613.53 0 4.732 3 1619.62 0 4.784 4 1637.90 0 4.927 5 1641.05 0 4.949 6 1643.63 0 4.967 7 1657.94 0 5.062 8 1662.35 0 5.090 9 1664.73 0 5.104 10 1668.47 0 5.127 11 1678.31 0 5.184 12 1686.29 0 5.227 13 1688.12 0 5.237 14 1691.03 0 5.252 15 1695.51 0 5.276 16 1698.07 0 5.289 17 1708.21 0 5.339 18 1716.67 0 5.378 19 1716.90 0 5.379 20 1718.30 0 5.386 21 1719.59 0 5.392 22 1721.19 0 5.399 23 1721.75 0 5.402 24 1728.76 0 5.433 25 1732.11 0 5.447 26 1735.13 0 5.460 27 1735.29 0 5.461 28 1736.52 0 5.466 29 1737.35 0 5.470 30 1741.74 0 5.488 31 1741.85 0 5.488 32 1745.07 0 5.502 33 1747.44 0 5.511 34 1755.24 0 5.542 35 1755.35 1 5.543 36 1758.55 0 5.555 37 1762.67 0 5.571 38 1762.97 0 5.572 39 1766.06 0 5.584 40 1766.72 0 5.586 41 1767.00 0 5.587 42 1768.18 0 5.592 43 1770.63 0 5.601 44 1771.88 0 5.605 45 1774.17 0 5.614 46 1783.21 0 5.646 47 1788.66 0 5.665 48 1791.33 0 5.674 49 1792.25 0 5.678 50 1794.49 0 5.685 51 1796.07 0 5.691 52 1797.70 0 5.696 53 1798.59 0 5.699 54 1811.01 0 5.740 55 1815.36 0 5.754 56 1835.27 0 5.815 57 1836.18 0 5.818 58 1837.78 0 5.822 59 1843.13 0 5.838 60 1890.15 0 5.967 (n-i)/ (n-i+P %tile 0.983 0.983 0.983 0.982 0.982 0.982 0.981 0.981 0.981 0.980 0.980 0.980 0.979 0.979 0.978 0.978 0.977 0.977 0.976 0.976 0.975 0.974 0.974 0.973 0.972 0.971 0.971 0.970 0.969 0.968 0.967 0.966 0.964 0.963 1.000 0.960 0.958 0.957 0.955 0.952 0.950 0.947 0.944 0.941 0.938 0.933 0.929 0.923 0.917 0.909 0.900 0.889 0.875 0.857 0.833 0.800 0.750 0.667 0.500 0.000 1 0.98 0.97 0.95 0.93 0.92 0.90 0.88 0.87 0.85 0.83 0.82 0.80 0.78 0.77 0.75 0.73 0.72 0.70 0.68 0.67 0.65 0.63 0.62 0.60 0.58 0.57 0.55 0.53 0.52 0.50 0.48 0.47 0.45 0.43 0.43 0.42 0.40 0.38 0.36 0.35 0.33 0.31 0.29 0.28 0.26 0.24 0.23 0.21 0.19 0.17 0.16 0.14 0.12 0.10 0.09 0.07 0