Euro code 5 – Based Reliability Analysis of Axially Loaded Solid Timber Columns Using Selected Nigerian Timber Species

Euro code 5 – Based Reliability Analysis of Axially Loaded Solid Timber Columns Using Selected Nigerian Timber Species.

ABSTRACT

In this research work, a reliability analysis was carried on three Nigerian timber specie namely: Mitragyna ciliata (Abura), Afromosia elata (Afromosia) and Confusa Grandiflora (Berlinia) after classifying the species to international strength classification system using EN 338 (2003) with the aid of statistical package Easyfit (2010) .

This was done after establishing the physical and mechanical properties in the laboratory using ASTM D193 (2000) and EN408 (2003). Mitragyna ciliata was assigned to strength Class of C18 with minimum characteristic values of density, strength and stiffness properties of 466 kg/m2, 80.2 N/mm2 and 9.21 kn/mm2 respectively as contained in EN 338 (2003).

Afromosia elata and Confusa grandiflora were assigned to strength Class D30 with characteristic properties of density, strength and stiffness of 480 kg/m2, 131.2 N/mm2 and 11.85 kn/mm2 for Afromosia elata and 462 kg/m3, 89.2N/mm2, 12.74 kn/mm2 for Confusa grandiflora.

The reliability analysis carried on the slender timber column was undertaken to check for six failure modes namely: compression, bending, flexural buckling, lateral torsional buckling, and carrying capacity of dowel connection and shear stress capacity of the joint failure modes.

Critical mode of failure from the first four failure modes was found to be lateral torsional buckling mode of failure with the lowest β-value of 2.87 for Mitragyna Ciliata, 3.4 for Afromosia elata and 3.52 for Confusa Grandiflora, at a load ratio of 0.8 for compression and bending failure,0.2 for flexural and lateral-torsional buckling failure modes.

Critical values of safety index obtained are lower than the code value of 3.8 (BS EN 1990:2002). While, the critical mode of failure for dowel connection was found to be in the carrying capacity of Dowel, with safety value of 1.69 at a load ratio of 0.8, also lower than the code value of 3.8 (BS EN 1990:2002).

TABLE OF CONTENTS

Title Page       i

Declaration      ii

Certification              iii

Dedication              iv

Acknowledgement             v

Table of Contents                 vi

List of Tables          xxviii

List of Figures            xiii

List of Plates               xxxxi

List of Symbols and Notations     xix

List of Appendices      xxxii

Abstract           xxxiii

CHAPTER 1: INTRODUCTION

• : Preamble 1
• : Statement of Research Problem 2
• : Aim and Objectives 4
• Scope and Limitations 5

CHAPTER 2: LITERATURE REVIEW

• INTRODUCTION 6
• Material properties of timber 6
  • Physical properties of timber 7
    • Density and specific gravity of timber 7
    • Moisture content of timber 8
  • Mechanical properties of timber 9
    • Compression 9
    • Tension 10
    • Bending strength of timber 11
    • Modulus of elasticity of timber 12
  • Strength Grading of Timber 12
  • Deterministic and Probabilistic Design Approach 12
    • Behaviour of Columns 13
    • Eccentricity of Load 14
    • Stability of Slender Columns 14
  • Design Criteria of Timber Column using Eurocode 15
    • Compression failure 16
    • Bending failure 16
    • Flexural buckling failure 16
    • Lateral torsional buckling 18
    • Carrying capacity of dowel 18
    • Shear capacity failure 18
  • Limit State Design 19
  • Reliability Analysis 20

CHAPTER 3: MATERIALS AND METHODS

• Introduction 25
• Materials 25
  • Preparation of specimen 25
• Methods 26
  • Determination of physical properties of timber 26

3.3.1. (a) Determination of moisture content of test slices   26

3.3.1. (b) Determination of density of test slices      27

3.3.1. (c) Characteristics values of density         28

• Determination of mechanical properties of timber 29
  • Determination of bending strength of test pieces 29
  • Characteristics values of bending strength 34
• Determination of global modulus of elasticity in bending 35
  • Characteristic value of modulus of elasticity 36
• Allocation to a Strength class 37
  • Test for goodness of fit and probability distribution models 37
  • Test for goodness of fit 37
• Reliability Analysis 38
  • Structural design consideration 39
    • Structural configuration 39
  • Eurocode 5 (2004) Provisions for Columns and Limit state Equations 46
    • Compression criterion 46
    • Bending criterion 48
    • Flexural buckling criterion 49
    • Lateral torsional buckling criterion 58
    • Design of moment resisting joint 60
      • Mechanical properties of dowel 62

3.6.5.1(a) Carrying capacity of dowel in column axis     62

3.6.5.1(b) Carrying capacity of dowel in rafter axis       67

3.6.5.2(a) Shear stress capacity in column axis    67

3.6.5.2(b) Shear stress capacity in rafter axis         68

• Limit state equation for the six failure modes 68
  • Compression criterion 68
  • Bending criterion 69
  • Flexural buckling criterion 70
  • Lateral torsional buckling criterion 71
• Limit State equations for Connections 71
  • carrying capacity of dowels 71
  • Shear stress failure 73
• Program Flowchart 74

CHAPTER 4: RESULTS AND DISCUSSION

• Results of Moisture Content 76
  • Analysis of variance for MC of the selected species 81
• Results of Wet Density 84
  • Analysis if variance for density of timber for the selected species (within group) 85
• Results of Bending Strength of Test Species 86
  • Analysis of variance for bending strength of the timber species (within group) 90
• Results and Discussion of Global Modulus of Elasticity in Bending 92
  • Analysis of variance for MOE of timber species (within group) 95
• Allocation to a Strength Class 97
  • Results for other material properties 98
• Results of test of Goodness of Fit 100
  • Probability distribution models for grade determining properties 116
• Stochastic parameters of the basic variables for reliability analysis 122
  • Stochastic models of the basic variables 123
• Results of reliability analysis 130
  • Compression failure criterion 130
  • Bending failure criterion 133
  • Flexural buckling failure criterion 134
  • Lateral torsional buckling failure criterion 136
• Safety Indices obtained for the Deterministic Design using the Timber Specie 145

CHAPTER 5: CONCLUSION AND RECOMMENDATIONS

• Conclusion 147
• Recommendations 149

REFERENCES           150

APPENDICES            158

INTRODUCTION

Timber is an efficient building material, not only in regards to its mechanical properties but also because it is a highly sustainable material considering all phases of the life cycle of timber structures; production, use and decommissioning.

Due to the low energy use and the low level of pollution associated with the manufacturing of timber structures, the environmental impact of timber structures is much smaller than for structures built using other building materials. Timber is a light material and compared to its weight, the strength is high; the strength to weight ratio is even higher than for steel.

It is a unique structural material, fully renewable, lightweight, and potentially very efficient with many environmentally positive attributes (Steiger, et al 2010; Afolayan, 2005). However, timber is still not utilised to its full potential in the building and construction sector considering its beneficial properties.

Many building owners, but also architects and structural engineers, do not consider timber as a competitive building material compared to concrete, steel or masonry. Attributes such as high performance in regard to reliability, serviceability and durability are generally not associated with timber as a building material.

One of the main reasons for this is that timber is a highly complex material; it actually requires a significant amount of expertise to fully appreciate the potential of timber as a structural building material. Structurally it displays significant variability in properties, both within and between members (Tord, 2001).

REFERENCES

Abubakar, I. And Mohammed, U. A., (2007), “Reliability Investigation of Steel Cased Columns Australian Journal of Basic and Applied Sciences, 1(4): pp 561-570.

Abubakar I., Mohammed J.K and Ejeh S.P.(2011), “Probabilistic Models of Grade Determining Properties of some Common Nigerian Timber Species”. Nigerian Journal of Engineering Faculty of Engineering, Ahmadu Bello University Zaria, Kaduna Nigeria.

Afolayan J. O. (1992).”Reliability-Based Analysis and Design”, Departmental Seminar, Afolayan, J. O. (2004) “Cost Effective Vibration Criteria for Wooden Floors”. Asian Journal of Civil Engineering (Building and Housing) Vol. 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) Vol. 6, Nos. 1-2 (2005) pp. 75-84

Alpo. R. (2004) Theoretical and Practical Aspects of the Reliability Analysis of Timber

StudentsandScholarship Team.