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ABSTRACT

In this study, laboratory tests were conducted on some commonly used timber species (Alstonia boonei, Triplochiton Scleroxylon, Terminalia Ivorensis, Terminalia superba and Lophira Alata) in Nigeria. The tests were in accordance with, EN 408, EN 13153-1 and ASTM D-143). The test results were analysed in accordance with Eurocode 5. Eurocode 0, JCSS and EN 384, with the aid of Easyfit statistical package. The statistics of the reference properties (density, modulus of elasticity and bending strength) of each specie were generated, and EN 338 strength class assigned to each species after adjustment to 18% Nigerian reference moisture content. The mean values of the densities are: 360.76kg/m3, 380.25kg/m3, 472.10kg/m3, 533.89kg/m3, 955.93kg/m3, for the Alstonia boonei, Triplochiton Scleroxylon, Terminalia Ivorensis, Terminalia superba and Lophira Alata respectively. The corresponding coefficients of variation are 4%, 16%, 18%, 19% and 4%. Likewise, the mean values of moduli of elasticity are 8192.0N/mm2, 6137.80N/mm2, 12161.0N/mm2, 11614.0N/mm2 and 22750.0N/mm2, for Alstonia boonei, Triplochiton Scleroxylon, Terminalia Ivorensis, Terminalia superba and Lophira Alata, with the corresponding coefficients of variation of 6%, 27%, 22%, 21% and 12% respectively. Also, the mean values of bending strengths are 43.09N/mm2, 54.07N/mm2, 70.49N/mm2, 83.63N/mm2 and 97.79N/mm2, for the Alstonia boonei, Triplochiton Scleroxylon, Terminalia Ivorensis, Terminalia superba and Lophira Alata, with the corresponding coefficients of variation of 12% 16%, 19%, 19%, and 16% respectively. Three theoretical distribution models (normal, lognormal and gumbel) were fitted to the reference material properties, using Kolmogorov Simonov test. Normal distribution was found to be the most fit for the timber density, and the best fit theoretical distribution
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model for modulus of elasticity and bending strength is lognormal distribution. Based on the class limits of EN 338, strength class D18 was assigned to Alstonia boonei, Triplochiton Scleroxylon and Terminalia Ivorensis. Terminalia superba,, was assigned to strength class D24 and Lophira Alata was assigned to strength class D60. The derived material properties (tension and compression strengths parallel and perpendicular to grain, shear strength and shear modulus) were generated from the reference properties based on EN 384. The generated statistical data on the material properties and load statistics reported in various international references were used for the reliability-based analyses and calibration of the Eurocode 5 design criteria for a three-hinged solid timber portal frame. Thirty two failure modes were identified for the frame and limit state function developed for each failure mode. Component and system reliability analyses were implemented using first order reliability method and genetic algorithms. The rafter-column joint failure mode was found to be predominant. The implied safety for the predominant mode was found to correspond well with the frame implied system reliability. This is an indication that, the system reliability of timber structures is the reliability of its critical mode of failure. Uncertainty sensitive mathematical models for the prediction of material safety factors were developed. The models were recommended for use in a proposed Nigerian national annex to the Eurocode 5.

 

 

TABLE OF CONTENTS

 

Title Page i
Declaration ii
Certification iii
Dedication iv
Acknowledgement v
Abstract vi
Table of Contents viii
List of Figures xv
List of Tables xxi
List of Plates xxvi
List of Appendices xxvii
Notations xxviii
CHAPTER ONE: INTRODUCTION 1
1.1 Preamble 1
1.2 Problem Statement and Justification of Research 3
1.3 Aim and Objectives 4
1.4 Research Hypotheses 4
1.5 scope and limitation 4
CHAPTER TWO: LITERATURE REVIEW 7
2.1 Preamble 7
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2.2 Basic Material Properties of Timber 10
2.2.1 Background 10
2.2.2 Variability of stiffness and strength in structural timber 13
2.2.3 Background of the Tested Timber Species 15
2.3 Strength Classes of Timber 19
2.3.1 The Timber Strength Classification System 19
2.3.2 Timber Grading System in the Nigerian Code of Practice (NCP 2) 22
2.4 Effect Load Duration on Timber Structures 23
2.4.1 The Eurocode 5 Load Duration Factor Kmod 24
2.5 Timber Exposure to Fire 25
2.5.1 BS 5268: Part 4-1978 Fire Design Requirements 31
2.5.2 Fire Resistance Assessment According to Eurocode 5 31
2.6 Genetic Algorithms 33
2.6.1 Selection Operator 34
2.6.2 Selection mechanisms 34
2.6.3 Roulette Wheel Selection 35
2.6.4 Linear Ranking selection 35
2.6.5 Tournament selection 35
2.6.6 Elitism 36
2.6.7 Encoding 36
2.6.8 Crossover and Mutation 36
2.7 Structural Safety Concepts 36
2.7.1 Theoretical Framework on Structural Reliability. 39
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2.7.2 Monte Carlo Simulation Method 42
2.7.3 First and Second Order Reliability Method 43
2.7.4 Probabilistic Transformation Method (PTM) 45
2.7.5 Structural Reliability Using Genetic Algorithms 47
2.7.6 Reliability Analysis Using Artificial Neural Networks (ANN) 50
2.7.7 Properties Affecting Reliability Analysis and Design of Timber Structures 51
2.8 Probabilistic Calibration of Material Safety Factors 51
CHAPTER THREE: MATERIALS AND METHODS 53
3.1 Preamble 53
3.2 Materials 54
3.3 Methods of Laboratory Experiments and Data Analysis 56
3.3.1 Determination of Density and Moisture Content 56
3.3.2 Three-point Bending Test Method 62
3.3.3 The Four Point Bending Test Method 63
3.3.4 Adjustment Factors for Bending Strength 63
3.3.5 Derived Material Properties 73
3.3.6 Moisture Adjustment Factors 75
3.3.7 Distributions Fitting and Tests of Goodness of Fit 76
3.3.8 Probability Density Function 78
3.3.9 Characteristic Values of Material Properties 80
3.3.10 Percentile Values of Material Properties 80
3.3.11 Analysis of Variance of the Reference Material Properties 81
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3.3.12 The Two-way Analysis of Variance (Two-way ANOVA) 81
3.3.13 Allocation of Strength Classes 82
3.4 Methodology for the Reliability Analysis and Calibration 83
3.4.1 Failure Modes 85
3.4.2 Ultimate Limit State Modes of Failure 85
3.4.3 Service Limit State Mode of Failure 87
3.4.4 Frame Geometry 88
3.4.5 Effect of Actions and Load Combination 88
3.4.6 Structural Analysis 89
3.4.7 The Eurocode 5 Design Values 90
3.4.8 Limit State Functions for the Various Failure Modes 91
3.4.9 Evaluation of the Limit State Functions 105
3.4.10 Setup of Reliability Analysis by Genetic Algorithm 107
3.4.11 System Reliability Analysis 112
3.4.12 Statistical Models of Material Properties of Timber 113
3.4.13 Statistics of Loading Parameters 115
3.4.14 Statistics of other Parameters 116
3.4.15 Reliability-based Calibration 117
3.4.16 Methods of Code Calibration 118
3.4.17 Method of Standardized FORM Sensitivity Coefficients 119
3.4.18 Code Calibration Using Minimum Error 121
3.5 Setup of the Numerical Experiments 122
3.5.1 Main Directory 124
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3.5.2 Form directory 124
3.5.3 Distribution Model Setup Directory 125
3.5.4 Distribution transformation directory 125
3.5.5 Coefficient of variation directory 125
3.5.6 Probability of failure directory 125
3.5.7 System reliability directory 125
3.5.8 Wind load directory 126
3.5.9 Material properties directory 126
3.5.10 Genetic algorithm operations directory 126
CHAPTER FOUR: RESULTS AND DISCUSSION 127
4.1 Experimental Results and Discussion 127
4.1.1 Moisture Content Test Results and Discussion 127
4.1.2 Density Test Results and Discussion 127
4.1.3 Three-point bending Test Results and Discussion 128
4.1.4 Modulus of Elasticity and Bending Strength from the
Four-point bending Test 130
4.1.5 Mathematical Transfer Models for Bending Strength and
Modulus of Elasticity 131
4.1.6 Moisture Adjusted Density 139
4.1.7 Moisture Adjusted Modulus of Elasticity 139
4.1.8 Moisture Adjusted Bending Strength 140
4.1.9 Distributions Fitting and Tests of Goodness of Fit 141
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4.1.10 Distribution Model for Density 142
4.1.11 Distribution Model for Modulus of Elasticity 143
4.1.12 Distribution Model for Bending Strength 145
4.1.13 Skeweness and Excess Kurtosis of Density 146
4.1.14 Skeweness and Excess Kurtosis of Modulus of Elasticity 150
4.1.15 Skeweness and Excess Kurtosis of Bending Strength 154
4.1.16 Percentile Values 157
4.1.17 Characteristic Values of the Reference Material Properties 160
4.1.18 Characteristic Value of the Derived Material Properties 161
4.1.19 Bartlet’s Test 164
4.1.20 The Two-way Analysis of Variance (Two-way ANOVA) 166
4.1.21 Allocation of Strength Classes 167
4.2 Reliability Analysis results and Discussion 172
4.2.1 Component and System Reliability of Frame 172
4.2.2 Sensitivity Analysis 177
4.2.3 Reliability of the Portal Frame in Fire 182
4.2.4 Reliability Analysis of the Frame Subjected to Wind Action 192
4.2.5. Effect of Frame Rafter Slope on the Frame Reliability 193
4.2.6 Sensitivity Analysis due to Change in Frame Size
(Default size factor = 1.0) 194
4.2.7 Effect of Timber Service Class on the Frame Reliability 195
4.2.8 Effect of Frame Member Slenderness 196
4.2.9 Effect of Drift Limit on Sway Mode Reliability 197
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4.2.10 Effect of Variable to Total Load Ratio of Frame Safety 198
4.2.11 Effect of Load Participation on Frame Safety 199
4.2.12 Effect of Change in Distribution Model of Material Property 200
4.2.13 Effect of Change in Distribution Model of Load Parameters 201
4.2.14 Effect of Change in Coefficientt of Variation of Material
Property and Load 202
4.3 Reliability-Based Calibration 204
4.3.1 Calibration of Material Safety Factors 204
4.3.2 Effect Load Ratio on the Computed Material Safety Factor 209
4.3.3 Effect of Material Coefficient of Variation on the Computed
Material Safety Factor 210
4.3.4 Summary 215
CHAPTER FIVE: CONCLUSION AND RECOMMENDATION 217
5.1 Conclusion 217
5.2 Recommendations 219
REFERENCES 221

Project Topics

 

CHAPTER ONE

NTRODUCTION
1.1 Preamble
Many nations have either developed or are in the process of developing their own codes of practice, based on the most recent available database. Every country need to develop its design codes because of diversity in geographical and environmental conditions. In most of the Common Wealth countries, including Nigeria (Auta and Mastenikov, 2006; SNiP, 2004; Onundi, et al, 2009), the design or investigation of physical structures and facilities are in accordance with the requirements of the British Standard code of practice. The former British design code for timber structures, BS 5268, is based on permissible stress method. The code was withdrawn in April, 2010 and replaced with the Eurocode 5. The Eurocode 5 is based on the limit state concept. Consequently, since that date, BS 5268 was not maintained. The withdrawal of BS 5268 and the adoption of the Eurocode 5 has wide ramification to Nigeria, and other commonwealth countries. In Nigeria, the code of practice for the design of timber structures was largely based on the withdrawn permissible stress design code. It implied that the NCP 2 is now left without a basis.
The need for local contents in construction of infrastructure is a serious engineering challenge for developing countries (Aguwa and Sadiku, 2011). This is clear on the need for grading of the local timber from any country aspiring to use the new timber design approach embodied in the Eurocode. The available information from the NCP 2 cannot be used because it is not consistent with the criteria established in the Eurocode annexes. The development in the design standards is clear from the crude permissible sresses to the
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advanced limit state design and partial coefficient methods. This is known as level 1 reliability method and takes into account some aspects on the randomness of actions and material properties. For steel and concrete, even more advanced fully probabilistic level 2 method have been largely brought into practice and are used to:
a) Calibrate level 1 codes to ensure a more uniform and consistent safety level.
b) Design of extraordinary structure.
For timber the development has been less impressive for several reasons.
1) The uncertainties in the material properties is much higher than for other building material. (this poses problems but also means that the advantages of introducing level 2 method is higher)
2) The properties and therefore the probability of failure, depend on the whole load and moisture history of the structure: the mechanical properties in a design situation depend on the load duration and moisture content.
All the timber species that appear in the Nigerian Code of Practice for timber structural design (NCP 2, 1973) are hardwoods. In this study, material safety factors for the limit state design format of the Eurocode 5 were calibrated using level 2 approach.. Material properties of five timber species namely: Alstonia boonei (Ahun), Triplochiton scleroxylonI (Obeche), Terminalia ivorensis (Black Afara), Terminalia superba (White Afara) and Lophira Alata (Ekki), that are coomonly used in Nigeria, were tested, and the results used in the calibration exercise.
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1.2 Problem Statement and Justification of Research
NCP 2 (1973) is the design code for timber structures in Nigeria, that was developed with reference to CP 112 of Great Britain. Both the codes were based on permissible stress design approach. CP 112 was severally revised, with the major revision taking place in 1984, when it was replaced with BS 5268; also a permissible design code. BS 5268 was withdrawn and replaced with the Eurocode 5, on 31st March, 2010. The Eurocode 5, is based on the limit state design philosophy. However, the Nigerian Code of Practice for timber structural design (NCP 2) was never updated. There arouse the need for the revision of NCP 2, to meet with the current global best practices on the design of timber structures.
A country adopting the Eurocodes, is allowed to develop its National Annex, containing tropicalised design parameters, known as Nationally determined parameters. One of the most important Nationally determined parameters is the partial safety factors for material properties. The use of this factor is to accommodate uncertainties in the material properties of and ensure low probability of failure.
Among all the major construction materials (concrete, timber and steel), timber is the only one that is entirely natural. The material properties of timber, such as modulus of elasticity, bending strength, density, tension strength, compression strength, shear strength and shear modulus, are random, with varying degree of coefficients of variation.
According to the Eurocode 0 (204), the current recommended safety factors in the Eurocodes, are deterministic in nature, developed based on the long term experience of
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building tradition. The Eurocode 0 (2004) permit the calibration of the material safety factors using probabilistic method in order to properly and fully accommodate the inherent uncertainties in the material properties of timber. The approach to calibrate material safety factors for the proposed adoption of Eurocode 5, for Nigeria, is to use of probabilistic method. With, that factors is expected to be less deterministic.
1. 3 Aim and Objectives
The aim of this study was to perform reliability-based calibration of partial safety factors for material properties located in Nigeria, considering the Eurocode 5 design criteria of timber portal frame. The specific objectives include:
i. To test some Nigerian timber species in the laboratory according to EN 408 (2004) specifications.
ii. Assign EN 338 (2009) Strength classes to each of the species.
iii. To perform reliability analysis on a three hinged timber portal frame designed with five timber species, in accordance with the Eurocode 5, in order to asses the effect of uncertainties on the Eurocode 5 design criteria of timber structural systems.
iv. Assess the effect of fire and load duration on the Eurocode 5 design criteria of timber structures.
v. Conduct reliability-based calibration of partial safety factors for material properties.
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1.4 Research Hypotheses
The hypotheses put forward in this study are as follows:
1. There is large variability in the material properties both within and between timber species.
2. The reliability-based calibration of timber portal frame structural system can be based on the reliability of its critical mode of failure.
3. The material safety factor in the Eurocode 5 is conservative with respect to Nigeria.
1.5 Scope and Limitation
The resistance models in the Eurocode 5 are used in conjunction with the partial safety factors for the materials properties, derived from the long term experience of building tradition to account for uncertainties. The partial safety factors for loading are giving in a separate codes (Eurocode 0, 2004). The reliability-based calibration was therefore limited to the calibration of the partial safety factors for material properties in the Eurocode 5 (2004). The probabilistic models (expected values, coefficient of variation and distribution models) used in the reliability analysis and calibration are from data generated by subjecting five Nigerian timber species to test in the laboratory in accordance with standard procedures and global best practices (EN 408, 2004; EN 384, 2004; JCSS, 2006). The tested species were graded (EN 338, 2009) as necessary criteria for their utilization in timber structures designed in accordance with the Eurocode 5. The study is limited to only five species of timber that are found in Nigeria. Even though are common timbers in the market, there are several other types.
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Three-hinged solid timber portal frame, with moment resisting connection between columns and sloping rafters was used for the reliability-based analyisi and calibration of the Eurocode 5, design criteria. The frame was subjected to gravity load (self weight and live load) and wind load. Wind load data generated from fourty two meteorogical stations across Nigeria, was considered in the specification of the wind load scenario.
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