ABSTRACT
In this study, 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 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 .
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 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 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 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
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
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
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
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
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
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
INTRODUCTION
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.
REFERENCES
Afolayan, J. O. and Abubakar, I. (2003). Reliability-based design program for reinforced concrete one-way slabs in accordance with BS 8110 (1985). Nig. Journ. of Engg. Ahmadu Bello University, Zaria. 11(2) pp. 1-5.
Afolayan, J. O. (2004). Cost effective vibration criteria for wooden floors. Asian Journal of Civil Engineering (Building and Housing) 5(1-2) pp 57-67.
Afolayan, J. O. (2005) Probability-based design of glued thin-webbed timber beams. Asian Journal of Civil Engineering (Building and Housing). 4(1-2) pp 75- 84.
Afolayan, J. O. and Abdulkareen, Y. O. (2005). Effective material utilization in timber industry: Problem of glued thin-webbed beams. Asian Journal of Civil Engineering (Building and Housing) 6(1-2) pp 55-65.
Afolayan, J. O. and Opeyemi, D. A. (2008). Reliability Analysis of static pile capacity for Concrete in cohesive and cohessionless soils. Research Journal on applied sciences 3(5) pp 407-411.
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