Static and Fatigue Performance of Oriented Strandboard As Upholstered Furniture Frame Stock

Mississippi State University Scholars Junction

Theses and Dissertations Theses and Dissertations

1-1-2012

Static and Fatigue Performance of Oriented Strandboard as Upholstered Furniture Frame Stock

Samet Demirel

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STATIC AND FATIGUE PERFORMANCE OF ORIENTED STRANDBOARD AS

UPHOLSTERED FURNITURE FRAME STOCK

Samet Demirel

A Dissertation Submitted to the Faculty of Mississippi State University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Forest Products in the Department of Forest Products

Mississippi State, Mississippi

May 2012 Template Created By: James Nail 2010

Samet Demirel Template Created By: James Nail 2010

STATIC AND FATIGUE PERFORMANCE OF ORIENTED STRANDBOARD AS

UPHOLSTERED FURNITURE FRAME STOCK

Samet Demirel

Approved:

______Jilei Zhang David Jones Professor of Forest Products Assistant Extension Professor of Forest (Director of Dissertation) Products (Committee Member)

______Shane Kitchens William V. Martin Assistant Professor of Forest Products Director of Franklin Furniture (Committee Member) Institute

______Tor P. Schultz George M. Hopper Professor of Forest Products Dean of College of Forest Resources (Graduate Coordinator)

Template Created By: James Nail 2010

Name: Samet Demirel

Date of Degree: May 11, 2012

Institution: Mississippi State University

Major Field: Forest Products

Major Professor: Jilei Zhang

Title of Study: STATIC AND FATIGUE PERFORMANCE OF ORIENTED STRANDBOARD AS UPHOLSTERED FURNITURE FRAME STOCK

Pages in Study: 175

Candidate for Degree of Doctor of Philosophy

This study investigated the lateral shear resistance of multi-staple joints, static and fatigue bending moment resistances of stapled gusset-plate joints, and fatigue bending performance of full size sofa structural members in three oriented strandboard (OSB) materials.

It is concluded that the lateral shear resistance capacity of multi-staple joints in

OSB can be predicted with power equations including single-staple lateral resistance capacity, number of staples, and material density. The bending moment resistance of stapled gusset plate joints in OSB can be predicted by mechanical models including the lateral resistance property of multi-staple joints. The static moment capacity study of a gusset-plate joint concluded that its maximum moment resistance is 2 times of its corresponding proportional limit moment resistance. Experimental results indicated that there was no significant difference in lateral shear resistance among vertically-aligned multi-staple joints constructed of three OSB materials even though there were significant differences in lateral resistance among single-staple joints in these three materials. Template Created By: James Nail 2010

However, there were significant differences in lateral resistances among horizontally-

aligned multi-staple joints in three OSB materials.

Fatigue test results concluded that the ratio of static to passed fatigue moment

capacity of gusset-plate joints was 2.6. The proposed equations reasonably estimated

fatigue life of less brittle OSB materials subjected to cyclic stepped and constant fatigue loads but underestimated the brittle OSB material. The ratios of material modulus of rupture to passed fatigue stress were 2.17 and 2.25 for cyclic stepped and constant cyclic tests, respectively.

Key words: OSB, static, fatigue, upholstered, furniture frame, gusset plate, staple, GSA, BIFMA, moment, standard.

DEDICATION

I dedicate this dissertation to my family: my parents Ismail Hakki Demirel (RIP) and Fikriye Demirel; sisters Atika Nur Balta and Tugba Koral; brother Hakan Demirel for their irrecoverable efforts and supports on me. I also dedicate this dissertation to my niece Hatice K. Balta; nephews Mustafa F. Balta and Enes Koral; Brothers in law

Mehmet A. Balta and Veysel Koral.

I am honored to dedicate this dissertation to Turkish Government which provided me the opportunity to have a degree and many life experiences from abroad and financially supported my study for all these years. I am also honored to dedicate this dissertation to Turkish People.

ACKNOWLEDGEMENTS

I am and will be always grateful to my major professor, Dr. Jilei Zhang, whose

plenty experiences, logical way of the thinking, encouragement, and guidance during the

my entire doctorate program. His wide knowledge and critical contributions made a good

basis on this dissertation.

I would like to give my sincere thanks to my committee, Dr. David Jones, Dr.

Shane Kitchens, from Mississippi State University, and Mr. William V. Martin, from

Franklin Furniture Institution for their considerable review and perfect recommendations

during the preparation of my proposal and dissertation.

I especially desire to extend my words of thanks to Mr. Franklin Quin Jr. for his

indispensible guide, help, valuable suggestion on every single period of my study. I

would also like to give my appreciations to Mr. Bob Tackett for his valuable help and

necessary advices on my experiments in the laboratories. I would like to express my deep appreciation to my colleague, Mr. Onder Tor, for his significant statistical consulting and the rest of his help on my work.

I wish to express my sincere thanks to the faculty and staff of the Mississippi

State University Forest Products Department. I also wish to give my sincere appreciation to Forest Products Department Head, Dr. Rubin Shmulsky, for his permanent warm smiling face and essential helps during my entire education program.

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TABLE OF CONTENTS

Page

DEDICATION ...... ii

ACKNOWLEDGEMENTS ...... iii

LIST OF TABLES ...... ix

LIST OF FIGURES ...... xvii

CHAPTER

I. INTRODUCTION ...... 1

1.1 Problem Statement ...... 1 1.2 Literature Review...... 3 1.2.1 Sofa Frame Structural Systems ...... 3 1.2.2 Frame Performance Tests ...... 4 1.2.3 Joint Static and Fatigue Resistances ...... 8 1.2.3.1 Static Resistance ...... 8 1.2.3.2 Staple-Connected Gusset-Plate Joints ...... 8 1.2.3.3 Face Lateral Shear Resistance of Staple-Connected Joints ...... 12 1.2.3.4 Lateral Shear Resistance of Glued Face-to-Face Joints ...... 14 1.2.3.5 Neutral Axis ...... 14 1.2.3.6 Fatigue Resistance ...... 17 1.2.4 Fatigue Resistance Properties of Wood-based Composites as Furniture Frame Members ...... 20 1.2.4.1 Fatigue Test ...... 20 1.3 Objectives ...... 21

II. STATIC LATERAL SHEAR RESISTANCE OF STAPLED AND GLUED FACE-TO-FACE JOINTS ...... 24

2.1 Materials and Methods ...... 24 2.1.1 Approach ...... 24 2.1.2 Specimen Configurations ...... 24 2.1.3 Materials ...... 25 iv

2.2 Experimental Design ...... 29 2.2.1 One-Row Vertically-Aligned Multi-Staple Joints ...... 29 2.2.2 Two-Row Vertically-Aligned Multi-Staple Joints ...... 30 2.2.3 Two-Row Horizontally-Aligned Multi-Staple Joints ...... 31 2.2.4 Glued Joints ...... 32 2.3 Specimen Preparations ...... 33 2.3.1 Vertically-Aligned Joints ...... 33 2.3.2 Horizontally-Aligned Joints ...... 33 2.4 Lateral Shear Test ...... 34 2.4.1 Vertically-Aligned Joints ...... 34 2.4.2 Horizontally-Aligned Joints ...... 35 2.5 Results and Discussion ...... 36 2.5.1 One-Row Vertically-Aligned Multi-Staple Joints ...... 36 2.5.1.1 Load-Displacement Curves ...... 36 2.5.1.2 Mean Ultimate Lateral Shear Loads and Comparisons ...... 37 2.5.1.3 Material Type Effects ...... 39 2.5.1.4 Staple Number Effects ...... 40 2.5.1.5 Estimation Equations ...... 40 2.5.1.5.1 Prediction Equation Comparisons ...... 45 2.5.2 Two-Row Vertically-Aligned Multi-Staple Joints ...... 46 2.5.2.1 Load-Displacement Curves ...... 46 2.5.2.2 Mean Ultimate Lateral Loads and Comparison ...... 48 2.5.2.2.1 Material Type by Number of Staples Interaction ...... 49 2.5.2.2.2 Connection Type by Number of Staples Interaction ...... 51 2.5.2.2.3 Connection Type Effects ...... 52 2.5.2.2.4 Number of Staple Effects ...... 53 2.5.2.2.5 Material Type Effects ...... 53 2.5.2.3 Displacements Loads at Proportional Limit ...... 53 2.5.2.4 Estimation Equations ...... 54 2.5.3 Two-Row Horizontally-Aligned Multi-Staple Joints ...... 56 2.5.3.1 Load-Displacement Curves ...... 56 2.5.3.2 Mean Ultimate Lateral Loads and Comparisons ...... 57 2.5.3.2.1 Material Type Effect ...... 59 2.5.3.2.2 Number of Staples Effect ...... 59 2.5.3.3 Mean Comparison Between Vertically and Horizontally-Aligned Multi-Staple Joints...... 60 2.5.3.3.1 Staple Alignment by Number of Staples ...... 62 2.5.3.3.2 Staple Alignment by Material Type ...... 63 2.5.3.3.3 Number of Staples by Material Type ...... 64 2.5.3.3.4 Staple Alignment Effects ...... 65 2.5.3.3.5 Material Type Effects ...... 65 2.5.3.3.6 Number of Staples Effects ...... 66 2.5.3.4 Estimation Equations ...... 66

2.5.4 Glued Joints ...... 71 2.5.4.1 Load-Displacement Curve ...... 71 2.5.4.2 Mean Ultimate Lateral Loads and Comparisons ...... 71 2.5.4.3 Mean Comparison among Only Glue Joints, Two- Row Vertically-Aligned Multi Stapled and Glued Joints ...... 72 2.6 Conclusion ...... 74

III. STATIC BENDING MOMENT CAPACITY OF GUSSET-PLATE JOINTS ...... 78

3.1 Material and Methods ...... 78 3.1.1 Approach ...... 78 3.1.2 Specimen Configurations and Materials ...... 78 3.2 Experimental Design ...... 79 3.2.1 L-type Joints...... 79 3.2.2 T-type Joints...... 80 3.3 Model Development ...... 80 3.3.1 L-type Joint ...... 80 3.3.1.1 e-value ...... 83 3.3.2 T-type Joint ...... 84 3.3.2.1 e-value ...... 86 3.4 Specimen Preparation ...... 88 3.4.1 L-type Joints...... 88 3.4.2 T-type Joints...... 90 3.5 Testing...... 92 3.6 Results and Discussion ...... 94 3.6.1 L-type Joints...... 94 3.6.1.1 Load-Displacement Curve ...... 94 3.6.1.2 Failure Modes ...... 95 3.6.1.3 Mean Comparisons ...... 97 3.6.1.3.1 Material Type by Rail Width Interaction ...... 99 3.6.1.3.2 Number of Staples by Rail Width Interaction ...... 100 3.6.1.3.3 Rail Width Effects ...... 101 3.6.1.3.4 Material Type Effects ...... 102 3.6.1.3.5 Number of Staples Effects ...... 103 3.6.2 T-type Joint ...... 104 3.6.2.1 Load-Displacement Curve ...... 104 3.6.2.2 Failure Modes ...... 105 3.6.2.3 Mean Comparisons ...... 107 3.6.2.3.1 Number of Staples by Stump Width Interaction ...... 109 3.6.2.3.2 Material Type by Stump Width Interaction ...... 109 3.6.2.3.3 Stump Width Effects ...... 110 3.6.2.3.4 Number of Staples Effects ...... 111 3.6.2.3.5 Material Type Effects ...... 112 3.6.3 Ratio of Proportional Limit to Ultimate Moment Load ...... 113 vi

3.6.4 Model Verification ...... 114 3.6.4.1 L-type Joints...... 114 3.6.4.2 T-type Joints...... 120 3.6.5 Conclusions ...... 125

IV. LATERAL SHEAR RESISTANCE OF L-TYPE, GUSSET-PLATE JOINTS CONSTRUCTED OF OSB ...... 128

4.1 Material and Method ...... 128 4.1.1 Joint Configurations and Materials ...... 128 4.2 Experimental Design ...... 128 4.3 Specimen Preparation ...... 128 4.3.1 Testing...... 129 4.4 Results and Discussion ...... 131 4.4.1 Mean Ultimate Lateral Load Comparisons ...... 131 4.4.1.1 Load-Displacement Curve ...... 131 4.4.1.2 Failure Modes ...... 131 4.4.1.3 Mean Comparisons ...... 132 4.4.1.4 Material Type Effect ...... 135 4.4.1.5 Number of Staples Effect ...... 135 4.4.1.6 Rail Width Effect ...... 135 4.5 Estimation Equations ...... 136 4.6 Conclusions ...... 138

V. FATIGUE BENDING MOMENT RESISTANCES OF L-TYPE AND T-TYPE GUSSET-PLATE JOINTS IN OSB ...... 140

5.1 Materials and Methods ...... 140 5.1.1 Approach ...... 140 5.2 Experimental Design ...... 140 5.3 Testing...... 142 5.4 Results and Discussion ...... 145 5.4.1 Failure Modes ...... 145 5.4.2 Mean Comparison ...... 149 5.4.2.1 L-type Joints...... 149 5.4.2.1.1 Material Type Effect ...... 152 5.4.2.1.2 Static Moment Levels ...... 152 5.4.2.2 T-type Joints...... 152 5.4.2.2.1 Material Type Effect ...... 155 5.4.2.2.2 Static Moment Effect ...... 155 5.4.3 Static to Fatigue Moment Resistance Capacity Ratio ...... 156 5.4.3.1 L-type Gusset-Plate Joints ...... 156 5.4.3.2 T-type Gusset-Plate Joints ...... 157 5.5 Conclusions ...... 158

vii

VI. FATIGUE PERFORMANCE OF OSB AS UPHOLSTERED FURNITURE FRAME STRUCTURAL MEMBERS...... 160

6.1 Material and Methods ...... 160 6.1.1 Materials ...... 160 6.1.2 Experimental Design ...... 160 6.1.2.1 Cyclic Stepped Load Tests...... 160 6.1.2.2 Constant Cyclic Load Test ...... 164 6.1.3 Specimen Preparation ...... 164 6.1.4 Testing...... 165 6.1.5 Results and Discussion ...... 167 6.1.5.1 Failure Modes ...... 167 6.1.5.2 Cyclic Stepped Load Test ...... 168 6.1.5.3 Constant Cyclic Load Test ...... 170 6.2 Conclusion ...... 172

REFERENCES ...... 173

viii

LIST OF TABLES

TABLE Page

1.1 GSA upholstery furniture frame cyclic loading schedules and performance-acceptance levels...... 6

1.2 BIFMA lounge seating test loading schedules and performance- acceptance levels...... 8

2.1 Mean comparisons of lateral loads of face-to-face, single-staple connected joints in three OSB materials for each OSB face strand grain orientation...... 26

2.2 Mean comparisons of lateral loads of face-to-face, single-staple joints in OSB materials for material surface strand grain orientation for each OSB material...... 26

2.3 Mean value of physical properties of tested materials...... 27

2.4 Mean ultimate lateral shear load values of face-to-face, one-row vertically-aligned multi-staple joints and their COVs...... 37

2.5 General linear model procedure output for main effects and interactions of 3 by 3 face-to-face one-row vertically-aligned multi-staple joints with 10 replication of each combination...... 38

2.6 Mean comparisons of ultimate lateral shear loads of one-row vertically- aligned multi-staple joints for material type for each number of staples...... 39

2.7 Mean comparisons of ultimate lateral shear loads of one-row vertically- aligned multi-staple joints for number of staples for each material type...... 39

2.8 Each of 60 lateral shear test data points was arranged in the following format for each OSB material, for instance, OSB-I...... 41

2.9 Conversion of number of staples and ultimate lateral load to their Log 10 value for OSB-I...... 41

2.10 Results of linear regression analysis of OSB-I data...... 42

2.11 Regression constants and associated r2 and p-values for derived equations for estimating mean ultimate lateral resistance loads of face- to-face one-row vertically-aligned multi-staple connected joints in three OSB materials...... 42

2.12 Log conversion of single-staple ultimate lateral shear load, number of staples, and multi-staple ultimate lateral load of all three OSB materials...... 44

2.13 Log conversion of OSB density, number of staples, and multi-staple ultimate lateral load of all three OSB materials...... 45

2.14 Comparison of estimated ultimate lateral shear resistance loads of one- row vertically-aligned multi-staple joints in OSB using Equations (2.1), (2.5), (2.6) with observed values...... 46

2.15 Mean ultimate lateral resistance loads of face-to-face two-row vertically-aligned multi-staple joints and their COVs...... 48

2.16 General linear model procedure output for main effects and interactions of 3 by4 by 2 face-to-face two-row vertically-aligned multi-staple joints with 10 replication of each combination...... 49

2.17 Mean comparisons of ultimate lateral load resistances of face-to-face two-row vertically-aligned multi-staple joints for number of staples for each of three materials...... 50

2.18 Mean comparisons of the ultimate lateral resistance loads of face-to-face two-row vertically-aligned multi-staple joints for material type for each of number of staples...... 50

2.19 Mean comparisons of ultimate lateral load resistances of face-to-face two-row vertically-aligned multi-staple joints for number of staples for each of glue existence...... 51

2.20 Mean comparisons of the ultimate lateral load resistances of face-to-face two-row vertically-aligned multi-staple joints for connection type for each of number of staples...... 52

2.21 Displacements of the two-row vertically aligned multi-staple joint at proportional limit and their corresponding lateral shear load value...... 54

2.22 Mean ultimate lateral shear load ratios of two-row vertically-aligned multi-staple OSB gusset-plate joints to one-row vertically-aligned multi- staple OSB gusset-plate joints...... 55

2.23 Comparison of estimated ultimate lateral shear resistance loads of two- row vertically-aligned multi-staple joints in OSB using Equations (2.7) through substituting Equations (2.1), (2.5), (2.6) with observed values...... 56

2.24 Mean ultimate face to face lateral load values of two-row horizontally- aligned multi-staple joints and their COVs...... 57

2.25 General linear model procedure output for main effects and interactions of 3 by 3 face-to-face two-row horizontally-aligned multi-staple joints with 10 replication of each combination...... 58

2.26 Mean comparisons of ultimate lateral loads of two-row horizontally- aligned multi-staple OSB gusset-plate joints for material type...... 58

2.27 Mean comparisons of ultimate lateral loads of two-row horizontally- aligned multi-staple OSB gusset-plate joints for number of staples...... 59

2.28 General linear model procedure output for main effects and interactions of 3 by 2 by 2 face-to-face two-row vertically-aligned and two-row horizontally-aligned multi-staple joints with 10 replication of each combination...... 61

2.29 The mean comparisons of face to face ultimate lateral resistance of two- row vertically and two-row horizontally aligned multi-staple joints for number of staples with respect to staple alignment...... 62

2.30 The mean comparisons of face to face ultimate lateral resistance of two- row vertically and two-row horizontally aligned multi-staple joints for staple alignment with respect to number of staples with respect to number of staples...... 63

2.31 The mean comparisons of face to face ultimate lateral resistance of two- row-vertically and two-row horizontally-aligned multi-staple joints for staple alignment with respect to material type...... 63

2.32 The mean comparisons of face to face ultimate lateral resistance of two- row-vertically and two-row horizontally-aligned multi-staple joints for material type with respect to staple alignment...... 64

2.33 The mean comparisons of face to face ultimate lateral resistance of two- row-vertically and two-row horizontally-aligned multi-staple joints for material type with respect to number of staples...... 64

2.34 The mean comparisons of face to face ultimate lateral resistance of two- row-vertically and two-row horizontally-aligned multi-staple joints for number of staples with respect to material type...... 65

2.35 Each of 30 lateral shear test data points was arranged in the following format for each OSB material, for instance, OSB-I...... 67

2.36 Conversion of number of staples and ultimate lateral load to their Log 10 value for OSB-I...... 68

2.37 Results of linear regression analysis of OSB-I data...... 68

2.38 Regression constants and associated r2 for derived equations for estimating mean ultimate lateral resistance loads of face-to-face two- row horizontally-aligned multi-staple connected joints in three OSB materials...... 69

2.39 Results of linear regression analysis of all OSB data...... 70

2.40 Comparison of estimated ultimate lateral shear resistance loads of two- row horizontally-aligned multi-staple joints in OSB using Equations (2.1) and (2.6) with observed values...... 70

2.41 Mean ultimate face lateral load values of only glued joints and their COVs...... 72

2.42 Mean comparisons of ultimate lateral load values of face-to-face only glue connected joints...... 72

2.43 The relationship among only-glue and glue-staple joints...... 73

2.44 The relationship among OSB-I, II, and III...... 73

3.1 Mean ultimate static bending moment resistance loads and their coefficients of variation of L-type, end-to-side, staple-connected gusset- plate joints in OSB for ten observations of each combination of material type, number of staples, and rail width...... 98

3.2 General linear model procedure output for main effects and interactions of 2 by 3 by 3 L-type gusset-plate joint factorial experiment with 10 replication of each combination...... 98

3.3 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, stapled, one-side, two gusset-plate joints for rail width for each material type...... 99

3.4 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, stapled, one-side, two gusset-plate joints for material type for each rail width...... 100

xii

3.5 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, stapled, one-side, two gusset-plate joints for each rail width for each number of staples...... 100

3.6 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, stapled, one-side, two gusset-plate joints for number of staples for each rail width...... 101

3.7 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, stapled, one-side, two gusset-plate joints for rail width for each number of staples and material types...... 102

3.8 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, one sided, two gusset-plate joints for material type for each number of staples and rail widths...... 103

3.9 Mean comparisons of ultimate moment resistance loads of L-type, end- to-side, one sided, two gusset-plate joints for number of staples for each material types and rail widths...... 104

3.10 Mean ultimate moment resistance loads and their coefficients of variation of T-type, end-to-side, staple-connected, one-side, two gusset- plate joints in OSB for ten observations of each combination of material type, number of staples, and stump width...... 108

3.11 General linear model procedure output for main effects and interactions of 2 by 3 by 3 T-type gusset-plate joint factorial experiment with 10 replication of each combination...... 108

3.12 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for stump width for each number of staples...... 109

3.13 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for number of staples for each stump width...... 109

3.14 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for stump width for each material type...... 110

3.15 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for material type for each stump width...... 110

xiii

3.16 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for stump width for each combination of number of staples and material types...... 111

3.17 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for number of staples for each combination of material types and stump widths...... 112

3.18 Mean comparisons of ultimate moment resistance loads of T-type, end- to-side, one-side, two gusset-plate joints for material type for each number of staples and stump widths...... 113

3.19 Mean ratios of proportional limit moment resistance load to its corresponding maximum moment resistance load of L-type and T-type joints...... 114

3.20 Average value two-row vertically-aligned multi staple displacement at proportional limit (displacement 1) and of load head displacement at proportional limit (displacement 2)...... 115

3.21 Two-row-vertically-aligned 4 and 6 staple joint displacement values at proportional limit and load head displacement values of the L-type gusset-plate joints at proportional limit...... 117

3.22 The ratio of predicted P value of the L type end-to-side, one sided, two gusset-plate joints at proportional limit point to observed P load value of the L-type end-to-side, one sided, two gusset-plate joints...... 120

3.23 Two-row-vertically-aligned 4 and 6 staple joint displacement values at proportional limit and load head displacement values of the T-type gusset-plate joints at proportional limit...... 122

3.24 The ratio of predicted P value of the L type end-to-side, one sided, two gusset-plate joints at proportional limit to observed P load value of the T-type end-to-side, one sided, two gusset-plate joints...... 124

4.1 Mean ultimate lateral resistance load values and their coefficients of variation of L-type, staple-connected gusset-plate joints in OSB...... 132

4.2 General linear model procedure output for main effects and interactions of 2 by 3 by 3 L-type gusset-plate joint factorial experiment with 10 replication of each combination...... 133

4.3 Mean comparisons of ultimate lateral shear loads of L-type joints for material type...... 134

xiv

4.4 Mean comparisons of ultimate lateral shear loads of L-type joints for number of staples...... 134

4.5 Mean comparisons of ultimate lateral shear loads of L-type joints for rail width...... 135

4.6 Mean lateral shear resistance ratios of L-type OSB stapled gusset-plate joints to two-row horizontally-aligned multi-staple gusset plate joints...... 137

4.7 Comparison of estimated ultimate lateral shear resistance loads of L- type OSB gusset-plate joints using Equations (2.1) and (2.6) with observed values...... 138

5.1 GSA cyclic stepped loading schedule for arm test...... 141

5.2 Static bending moment resisting load capacities of L-type gusset-plate joints subjected to a testing load 12 inches in front of the rail...... 142

5.3 Static bending moment resisting load capacities of T-type gusset-plate joints subjected to a testing load 12 inches in front of the rail...... 142

5.4 Failure mode summary of five tested L-type gusset-plate joints for each combination of material type and number of staples, and rail widths...... 148

5.5 Failure mode summary of five tested T-type gusset-plate joints for each combination of material type and number of staples, and stump widths...... 149

5.6 Mean passed fatigue moment resistance load values and their coefficients of variation of L-type, staple-connected gusset-plate joints in OSB...... 150

5.7 General linear model procedure output for main effects and interactions of 3 by 3 L-type gusset-plate joint factorial experiment with 5 replication of each combination...... 150

5.8 Mean comparisons of passed fatigue moment resistance loads of L-type, one-side, stapled, two gusset-plate joints for material type for each static moment resistance...... 151

5.9 Mean comparisons of passed fatigue moment resistance loads of L-type, one-side, stapled, two gusset-plate joints for static moment resistance for each material type...... 151

5.10 Mean passed fatigue moment resistance and their coefficients of variation of T-type, staple-connected gusset-plate joints in OSB...... 153

5.11 General linear model procedure output for main effects and interactions of 3 by 3 T-type gusset-plate joint factorial experiment with 5 replication of each combination...... 154

5.12 Mean comparisons of passed fatigue moment resistance loads of T-type, one-side, stapled, two gusset-plate joints for material type for each static moment resistance...... 154

5.13 Mean comparisons of passed fatigue moment resistance loads of T-type, one-side, stapled, two gusset-plate joints for static moment resistance for each material type...... 155

5.14 Summary of dimension and static moment resistance load values of L- type gusset-plate joints and their corresponding fatigue performance results...... 156

5.15 Summary of dimension and static moment resistance load values of T- type gusset-plate joints and their corresponding fatigue performance results...... 158

6.1 Cyclic stepped loading schedule for 72-inch-long back top rail fatigue tests and calculated maximum moments in back top rail for each fatigue load level...... 161

6.2 Depths of 72-inch-long back top rail specimens for each OSB material passing three stepped cyclic load acceptance levels...... 163

6.3 BIFMA horizontal backrest loading schedule...... 164

6.4 Depths (in.) of back top rails subjected to BIFMA constant cyclic load test for each OSB material...... 164

6.5 The ratio of Estimated to observed mean fatigue life of full-size back top rail specimens for each combination of material type and service acceptance level...... 169

6.6 Summary of the stress ratios ranges for service acceptance level for each OSB group in this study...... 170

6.7 The ratios of OSB MOR to bending fatigue stress of OSB member that were subjected to constant cyclic fatigue load...... 171

xvi

LIST OF FIGURES

FIGURE Page

1.1 Typical structural members in a simplified three-seat sofa frame (Tu 2010)...... 3

1.2 Illustration of the six structural performance test loads of three-seat upholstery sofa frames...... 5

1.3 Position of the neutral axis in an isotropic and homogenous beam ...... 15

2.1 The general configuration of a face-to-face joint...... 25

2.2 Lateral resistance load versus material density for of single-staple joints in three OSB materials...... 28

2.3 Density profile of OSB-I, OSB-II, and OSB-III...... 29

2.4 Diagram showing the placement of staples in the three joint specimens connected with one-row vertically-aligned multi-staples of: a) two, b) three, and c) four...... 30

2.5 Diagram showing the placement of staples in the four joint specimens connected with two-row vertically-aligned multi-staples of: a) two, b) four, c) six, and d) eight...... 31

2.6 Diagram showing the placement of joints connected with two-row- horizontal multi-staples: a) 4; b) 6; and c) 8 staples...... 32

2.7 Test set-up for evaluating lateral shear resistance of face-to-face, stapled or glued joints: a) front view; and b) back view...... 34

2.8 Test set-up for evaluating the lateral shear resistance of face-to-face two-row horizontally-aligned multi-staple joint...... 35

2.9 Load-displacement curves of face-to-face joints connected with one-row vertically-aligned multi-staple...... 37

2.10 A typical load-displacement curve of face-to-face joints connected with two-row vertically-aligned multi-staple...... 47 xvii

2.11 A typical load-displacement curve of two-row vertically-aligned multi- staple and glued joints...... 47

2.12 A typical load-displacement curve of two-row horizontally-aligned multi-staple joints...... 57

2.13 Diagram showing the placement of joints connected with two-row- vertically and two-row horizontally-aligned multi-staples of: a) vertical 6, b) vertical 8, c) horizontal 6, and d) horizontal 8...... 61

2.14 A typical load-displacement curve for glued joint in OSB...... 71

2.15 Typical load-displacement curve two-row vertically-aligned multi-staple and glued OSB gusset-plate joints and only glued joint...... 74

3.1 Configuration of joint specimens for evaluating moment capacity of gusset-plate joints in OSB, a) L-type, end-to-side joints, b) T-type, end- to-side joints...... 79

3.2 Mechanical analysis model for deriving ultimate moment resistance loads of L-type, end-to-side joints...... 81

3.3 a) two-row vertically-aligned 4 staples gusset-plate joint; b) Load- displacement curve of the joint...... 83

3.4 Diagram showing the position of e, load-head displacement, and multi- staple joint displacements...... 83

3.5 Mechanical analysis model for deriving ultimate moment resistance loads of T-type, end-to-side joints...... 85

3.6 Diagram showing the θ displacement angle of T-type end-to-side joints...... 87

3.7 L-type joints with: a) 6 in. wide rail with 8-staple joint, b) 7 in. wide rail with 8-staple joint, c) 8 in. wide rail with 8-staple joint, d) 6 in. wide rail with 12-staple joint, e) 7 in. wide rail with 12-staple joint, and e) 8 in. wide rail with 12-staple joint...... 89

3.8 T-type joints with: a) 4.5 inch wide stump with 8-staple joint, b) 6 inch wide stump with 8-staple joint, c) 7 inch wide stump with 8-staple joint, d) 4.5 inch wide stump with 12-staple joint, e) 6 inch wide stump with 12-staple joint, and e) 7 inch wide stump with 12-staple joint...... 91

3.9 Test set-up for evaluation of bending moment resistances of a) L-type; b) T-type gusset-plate joints...... 93

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3.10 A typical load-displacement curve of L-type, end-to-side, staple- connected gusset-plate joints in OSB...... 94

3.11 The failure modes : a) the staples legs lateral shear withdrawal from rail (wr); b) the staples legs lateral shear withdrawal from stump (ws); c) the staples legs lateral shear withdrawal the same amount from rail and stump (both); d)gusset plate rupture (g.p.r.); e)stump rupture...... 95

3.12 A typical load-displacement curve of T-type, end-to-side, staple- connected, one-side, two gusset-plate joints in OSB...... 105

3.13 Typical failure modes of T-type joints: a) Bottom failure, b) little bottom failure, and c) no bottom failure...... 106

3.14 Diagram showing the load arm of L-type end-to-side gusset-plate joint...... 118

4.1 Lateral shear resistance test a) specimen attachment and loading; b) metal piece between specimen and cylindrical load head...... 130

4.2 A typical load-displacement curve of L-type staple-connected gusset- plate joints subjected to lateral shear loads...... 131

4.3 Typical failure mode of lateral shear resistance of L-type, end-to-side, one-side, two gusset-plate joint...... 132

5.1 A specially designed air cylinder and pipe rack system for evaluating fatigue bending moment resistance capacity of gusset-plate joints in OSB materials...... 143

5.2 Setup details: a) electrical re-settable counter, b) a Programmable Logic Controller, and c) limit switch...... 144

5.3 Failure modes of L-type and T-type gusset-plate joints in OSB materials: a) staple legs lateral shear withdrawal from rail; b) staple legs lateral shear withdrawal from stump; c) staple legs lateral shear withdrawal from rail and staple break-off d) staple legs lateral shear withdrawal from stump and staple break-off...... 146

6.1 An air cylinder-pipe rack system for cyclic fatigue load tests...... 166

6.2 Diagram showing the locations of three cyclic loads applied to a tested specimen...... 166

6.3 A wooden fixture and transfer roller system used to prevent tested members from turning...... 167

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6.4 Failure modes of OSB members subjected to cyclic fatigue bending loads: a) splintering tension mode; b) brush tension mode...... 168

CHAPTER I

INTRODUCTION

1.1 Problem Statement The increase use of wood-based panel composites such as oriented strandboard

(OSB) as upholstery furniture frame stock is due to several of its inherent advantages compared to solid lumber. Specifically, it eliminates several steps necessary for processing lumber as frame stock, such as drying, end-cutting, and planning (Eckelman

2000). Therefore, capital investment, raw material costs, handling and processing costs are reduced. In addition, use of panel materials with computer numerical control (CNC) router technology facilitates optimization of cutting schedules with accompanying high yields and accelerated production. Also, CNC router technology allows the design and construction of forms, shapes, and processes which are not feasible with solid wood construction. Compared to plywood, in general, OSB panels are less expensive; therefore, the use of OSB in construction of upholstery furniture frames can reduce production cost and produce more profits. OSB is a structural engineered wood panel which is manufactured by using rectangular-shaped wood strands and waterproof, heat-cured adhesives. OSB panels are usually made of southern yellow pine, aspen-poplar strands or mixed hardwood species such as birch and sweetgum. Wood strands are placed in cross- oriented layers as in plywood. Therefore, OSB illustrates similarity with most of the strength and performance characteristics of plywood.

The rational design of upholstery furniture frames constructed of OSB should meet specified in service strength and durability criteria such as furniture performance test standard FNAE-80-214A (GSA 1998). The rational design requires that fundamental information be available concerning the holding resistance capacity of various fasteners such as staples in OSB materials. It also requires static and fatigue moment resistance capacities of various joints constructed with those fasteners such as staple connected gusset-plate joints. It is crucial for furniture manufacturers to know such basic strength properties of the materials they are using and understand what each property means to their frame performance, especially for panel products like OSB newly introduced to the upholstery furniture industry.

This study was undertaken, accordingly, to obtain information on OSB materials as furniture frame stock, and it also compares the mechanical properties among three

OSB materials because there is limited information available, especially the comparison data among different OSB products on the market. This study examined two major parts: static and fatigue performance evaluation of staple-connected gusset-plate joints in OSB and fatigue performance evaluation of OSB as frame structural members such as back top rails. Staple-connected, gusset-plate joints were considered because of their wide use in upholstery frame construction. The gusset-plate joints, connected with power-driven staples that are quick and easy to use, are commonly used at highly stressed critical joints such as front-rail-to-stump joints and back-post-to-bottom side rails. OSB, constructed of gusset plate joint with power-driven staple, was tested to have information for those critical points in upholstered furniture frame.

1.2 Literature Review

1.2.1 Sofa Frame Structural Systems A three-seat sofa frame consists of three basic structural subsystems: a) seat

foundation system, b) back foundation system, and c) side frame system as shown in

Figure 1.1 (Tu 2010). The principal structural members in a seat foundation system are

front and back rails, front and back spring rails, and stretchers. The structural members in

a side frame system are front stumps, top arm rails, and bottom side rails. The critical structural members in a back foundation system are back top rail, back posts, and back uprights.

Figure 1.1 Typical structural members in a simplified three-seat sofa frame (Tu 2010).

1.2.2 Frame Performance Tests Usage of performance tests is growing because they are necessary to determine the ability of products to implement their targeted function (Dai 2007). Performance tests provide the maximum amount of engineering design information about the furniture being tested and also supply manufacturer information to market their products.

Performance tests also provide customer information buy furniture. These tests are supposed to be universal in their geographical range of application and should provide a means to determine the key strength parameter of furniture (Tu 2010).

Most failures of furniture occur because of fatigue as a result of repeated use.

Therefore, Eckelman (1988b) developed a cyclic stepped load method which includes the critical parameters of the process, such as the cyclic load rate, the initial starting load, the load increments, and the number of cycles to be completed at each load level. A cyclic stepped load model was incorporated into the performance test method developed by the

General Services Administration (GSA) of the federal government for the evaluation of upholstered furniture.

Eckelman and Zhang (1995) defined six performance tests for upholstered furniture sofa frames. They are seat load foundation test, backrest foundation test, backrest frame test, horizontal side thrust arm load test, front to back load test for legs, and horizontal side thrust test on legs. These six tests evaluate the most important strength properties of the upholstered furniture frames, and they are equal-rated effective for determining weakness and hidden defects in design. Figure 1.2 illustrates the six test configurations to evaluate structural durable properties of upholstered sofa frames (Dai and Zhang 2007).

Figure 1.2 Illustration of the six structural performance test loads of three-seat upholstery sofa frames.

Table 1.1 GSA upholstery furniture frame cyclic loading schedules and performance- acceptance levels.

Number Initial Load Acceptance levels Test of Load increment Type Light Medium Heavy Loads (lb.) (lb.) (lb.) (lb.) (lb.) Seat loud foundation 3 100/50 25/12.5 200/100 250/125 275/137.5 Test Backrest foundation 3 50 12.5 112.5 125 150 Test Backrest frame 3 75 25 75 100 150 Test Front to back on 1 150 50 150 200 300 legs Test Side trust on arm 1 50 25 75 150 200 outward Side trust test on 1 200 50 200 250 350 legs Test

Table 1.1 gives detailed cyclic load schedules of the six tests. The seat load

foundation test evaluates the strength of highly stressed joints, such as side rail to back spring rail joints, the side rail to front rail joints, and the back rail to stretcher joints. The backrest foundation test is related with spring systems in back of the frame. The backrest frame test evaluates critical joints such as the top rail to back post joints and top arm rail to back post joints. In addition to these, the backrest frame test also evaluates the strength of critical structural members such as the top rail. The two legs tests are related with the strength of the legs to the seat foundation frame. The side trust on arm-outward test considers

the stump to front rail joints and stump to side rail joints.

Besides GSA performance testing standard, The Business and Institutional

Furniture Manufacturer’s Association (BIFMA) has also a testing standard ANSI/BIFMA 6

X5.4-2005 (BIFMA 2005) for strength evaluation of lounge seating which includes upholstered furniture. This standard describes specific tests, laboratory equipment, the conditions of tests, and recommended minimum levels to be used in the test and evaluation of the durability, performance, and structural adequacy of lounge seating units.

The acceptance levels given in this standard are based on the actual field use and test experience of BIFMA International members. This standard defines the means of evaluating lounge seating, manufacturing processes, mechanical designs or aesthetic designs. Table 1.2 shows the BIFMA test schedules (ANSI/BIFMA 2005). BIFMA has a static and a constant cyclic load model. For instance, the backrest horizontal test has functional and proof level loads as static test and only one level for fatigue test

Accordingly, there are two types of fatigue test methods, cyclic stepped load method (GSA) and constant amplitude cycling load method (BIFMA) (Eckelman 1988a

1988b). In cyclic stepped load method, an early determined initial maximum load is applied to the furniture at a rate of 20 cycles per minute, for 25,000 cycles. The maximum load is increased by a given increment after the prescribed number of cycles has been completed, and the procedure is repeated. This process is continued until a desired load level has been accomplished or specimen is failed (Eckelman 1995). In constant amplitude cycling load method, the specimen is tested under different nominal stress levels such as 80, 70, or 60 percent of modulus of rupture (MOR) values. Zero to maximum cyclic load is applied to the specimens by air cylinders for each load level

(GSA 1998). There is no load increment for BIFMA test standard. Load is applied to a specimen at a rate from 20 to 30 cycles per minute in BIFMA while load is applied to a specimen at a rate of 20 cycles per minute in GSA.

Table 1.2 BIFMA lounge seating test loading schedules and performance-acceptance levels.

Loading types Static Fatigue Impact Test Type Functional Proof Load No. of Functional Proof lb. lb. lb. cycles lb. lb. Backrest horizontal 150 250 75 120,000 n/a n/a Backrest vertical 200 300 200 10,000 n/a n/a Arm strength 150 200 100 50,000 n/a n/a Arm strength vertical 200 300 200 10,000 n/a n/a Seat durability n/a n/a 125 100,000 n/a n/a Seat durability right n/a n/a 165 20,000 n/a n/a Seat durability left n/a n/a 165 20,000 n/a n/a Seat drop test n/a n/a n/a n/a 225 300 Structural durability n/a n/a 100 100,000 n/a n/a Leg strength-front 75 125 n/a n/a n/a n/a

1.2.3 Joint Static and Fatigue Resistances

1.2.3.1 Static Resistance Static tests are conducted to measure static resistances which are moment resistance, bending strength and stiffness, and direct and lateral withdrawal strength of solid or engineered wood materials. A load is applied to the test specimen until failure of member occurs. The load is applied gradually, and it reaches its maximum value and remains constant until failure of the specimen.

1.2.3.2 Staple-Connected Gusset-Plate Joints A gusset-plate joint can be defined as a place in a frame structure where two members meet edge-to-edge and are connected with plates fastened to the member sides with fasteners driven perpendicularly through the plates into the member faces. Gusset 8

plates can be metal or wood and wood-based composites such as plywood. Metal gusset plates may vary as a barbed metal gusset plate, and a toothed gusset plate which is attached to the members with their teeth or nailed metal gusset plate (Wilkinson 1984).

One of the most popular wood gusset plate materials is plywood. Plywood is commonly used as gusset-plate due to its great tensile strength and split-resistance (APA 1997).

Since power-driven staples are fast and easy to assemble gusset-plate joints in upholstered furniture frames, the staple is one of the most commonly used fasteners for joining structural members in upholstery furniture (Zhang et al. 2002). There are two physical appearance variations of gusset-plates commonly seen in upholstery furniture frame construction: one wider gusset plate attached to the same side of two connected members alone, and two narrower gusset plates attached to the upper and lower part of the same side of two connected members. A gusset-plate can be attached to two jointed members using staples alone or staples with glue applied on the surfaces of members and gusset-plates.

Gusset-plates connect highly stressed joints, such as stump-front-rail and bottom- side-rail back-post joints in upholstery furniture frame construction because staple- connected gusset-plate joints yield high bending moment resistance capacity. Staples as mechanical fasteners resist face lateral shear forces rather than direct withdrawal forces when the joint is subjected to an in-plane bending moment (Zhang 2005). Therefore, the bending moment resistance capacity of a staple-connected gusset-plate joint in wood- based composites such as OSB materials might be governed by the resistance capacity of the OSB materials to face lateral shear withdrawal load of staples. Limited studies have been found concerning development of mechanical models in predicting bending moment capacities of staple-connected gusset-plate joints in OSB materials, especially for the

joints connected with two narrower gusset-plates located on the upper and lower part of the same side of two jointed members. Developing such models can yield moment capacity predicting equations as a function of relevant variables, such as face lateral shear resistances of staples in OSB materials and joint member width. Such quantitative information can help furniture manufacturers carry out a rational strength design of furniture frames.

Eckelman (1971) investigated the bending moment resistance capacity of T-type, staple-glued gusset-plates joints in solid wood Douglas fir. The two joint members were connected with two plywood gusset-plates symmetrically located on each side of the joint, respectively. Experimental results indicated that the joint moment resistance capacity was not particularly sensitive to construction variables such as the number of staples used. Rather, the moment capacity was limited by the strength properties of the gusset-plate materials, specifically, by rolling shear strength of the plywood used as gusset-plates. The moment resistance capacity of the evaluated joints improved considerably when width and length of gusset-plates were increased. The average ultimate moment resistance reported was from 294 to 14,724 lb.-in. with the coefficients of variation ranging from 4.2 to 19.0 %.

Zhang et al. (2001) studied the bending moment resistance capacity of T-type, staple-glued gusset-plates joints constructed of wood-based composites. Two joint members were also connected with two plywood gusset-plates symmetrically located on each side of the joint, respectively. Wood-based composites used as joint members were southern yellow pine plywood, aspen Timberstrand® laminated strand lumber (LSL), and aspen engineered strand lumber (ESL). Test results showed that the joint moment

resistance was significantly affected by gusset-plate thickness, width, and length, and

among these parameters plate width affected joint moment resistance the most. Joint member material type and the number of staples used had no effect on the moment resistance capacity, and all joint failures happened at gusset plates. The average ultimate moment resistance capacity ranged from 6,073 to 18,528 lb.-in. with the coefficients of variation ranging from 4.7 to 23.7%.

Erdil et al. (2003) investigated the effects of the number of staples and glue on the bending moment resistance capacity of T-type, stapled glued gusset-plates joints constructed with ¾-inch-thick Douglas-fir plywood. The two joint members were connected with two 3/16-inch-thick 3-ply Douglas-fir plywood gusset-plates symmetrically located on each side of the joint specimen. The numbers of staples evaluated on each plate were 6, 10, and 12, respectively. Test results showed that the larger gusset plate dimension and higher number of staples were the key factors in increasing the overall moment resistance capacity of joints evaluated. The average ultimate moment value of the joints connected with stapled gusset-plates ranged from

1,183 to 2,728 lb.-in with the coefficients of variation ranging from 5 to 10 %. The average ultimate moment value of the joints connected with stapled glued gusset-plates ranged from 3,763 to 4,500 lb.-in with the coefficients of variation ranging from 10 to 20

Wang et al. (2007b) evaluated the static moment capacity of T-type joints connected with two OSB gusset-plates symmetrically attached on both sides of joint members using glue and staples. The mean ultimate moment resistance load values of the joints with staples only were from 670 to 1,032 lb. with coefficients of variation ranging from 4.9 to 9.4 percent, while with staples and glue were from 680 to 1,270 lb with coefficients of variation ranging from 7.0 to 11.8 percent. The moment resistance

capacity of the joint increased in proportion with the length of the gusset-plate until the strength of the plate exceeded that of the joint members. Application of glue to the connection surface increased the moment resistance capacity of the gusset-plate joints.

Typical joint failure modes were staple withdrawal, OSB shear-out, in-plane shear failure of OSB, gusset-plate rupture, and rail rupture. The moment capacity of an unglued stapled gusset-plate joint in OSB can be reasonably estimated using analytical equations if the load capacity of a single staple is known. Mean differences between predicted and observed values differed by less than 16 percent.

1.2.3.3 Face Lateral Shear Resistance of Staple-Connected Joints Staples are commonly used to assemble structural members in upholstered furniture frames constructed of wood-based panel composites. The connectors of upholstered furniture frame such as glue or mechanical fasteners (staple or metal plate) are simply subjected to tensile forces only, or lateral shear forces only, or a combination of tensile and lateral shear forces regardless of how complicated are loads applied to an upholstered furniture frame. In the case of staple connected gusset-plate joints, the staples are subjected to face lateral shear withdrawal forces. Therefore, the essential fastener holding capacity, such as lateral shear resistances, of a material needs to be known.

Yadama et al. (2002) investigated effects of the number of staples and spacing staples on the lateral resistance of stapled joints in selected solid wood and wood-based materials. Wood-based composites were medium density fiberboard with a specific gravity of 0.78 and OSB with a specific gravity of 0.74. Experimental results indicated that number of staples positively affected the joint resistance to lateral loads; however, the relationship was not linear for most materials. The mean ultimate lateral load values

of the joints in OSB were 212, 385, 584, and 1,107 lb. for the number of staples 1, 2, 4, and 8, respectively. The spacing effect on the lateral resistance of joints in OSB was not

statistically significant. In general, joints with higher density members provided the most

resistance to lateral loads. Linear regression equations were derived for the prediction of

the lateral resistance of stapled joints in wood and wood-based materials.

Zhang and Maupin (2004) studied face lateral resistance of face-to-face single-

and multi-staple joints in furniture-grade, ¾-inch-thick 5-ply southern yellow pine

plywood. The specimens were constructed with a fastened member and a fastening

member of the same type material that were combined with staples. Experimental results

indicated that mean ultimate face lateral resistances of single-staple joints in the pine

plywood ranged from 268 to 315 pounds with coefficients of variation ranging from 11

to18 percent. The face lateral shear withdrawal resistance of single-staple joints in the plywood was affected by staple crown orientation, but not plywood grain orientation.

The face lateral withdrawal resistance of one-row vertically-aligned multi-staple joints in

pine plywood increased significantly as the number of staples increased from 2 to 5

staples with an increment of one. Plywood grain orientation when more than 2 staples

were used affected the lateral withdrawal resistances of one-row vertically-aligned mult-

staple joints. Mean ultimate face lateral resistances of one-row vertically-aligned multi-

staple joints in pine plywood ranged from 569 to 1,425 with coefficients of variation

ranging from 7 to 12 percent. The face lateral withdrawal resistance of one-row

vertically-aligned multi-staple joints in pine plywood can be estimated with the empirical

power expression including the single-staple joint resistance value and the number of

staples raised to the 0.88 power.

1.2.3.4 Lateral Shear Resistance of Glued Face-to-Face Joints The combination of glue and staples to connect upholstery furniture frame members is one of the most popular construction methods, especially in gusset-plate joint construction. As a connector such as staples in gusset-plate joints, glue is also mainly subjected to shear forces.

Dai (2008) investigated the lateral shear load resistances of glued face-to-face joints in southern yellow pine plywood and OSB. Experimental results indicated that the mean ultimate lateral shear strength of glued face-to-face joints in OSB ranged from 90 to

295 psi with coefficients of variation ranging from 13 to 26 percent. The wax on OSB surfaces tended to weaken joint load resistances. Plywood joints had significantly higher resistances to shear loads than OSB joints. The mean ultimate lateral shear strength of glued face-to-face joints in the pine plywood ranged from 245 to 510 psi with coefficients of variation ranging from 15 to 24 percent. The face grain orientation of joint members had a significant effect on the shear load resistances of plywood joints, but not on OSB joints.

1.2.3.5 Neutral Axis The neutral axis is the line in a beam where stress and strain are both zero. If the beam is isotropic, homogenous, and is not curved under a bending load, then the neutral axis is in the center of the beam. One side of neutral axis is called tension whereas the other side is called compression as shown in Figure 1.3.

Figure 1.3 Position of the neutral axis in an isotropic and homogenous beam

An isotropic material, such as steel, shows the same properties in all directions.

Therefore, the modulus of elasticity in tension and compression are equal under a

bending load, and the neutral axis is in the middle of the beam. On the other hand, an

anisotropic material, such as wood, shows different properties in its different directions

which are longitudinal, radial, and tangential directions. Since wood is an anisotropic and

non-homogenous material, the neutral axis may move up or down depending on

individual characteristics of the wood beam such as knots and grain angle (Voigt 2011).

Saleh et al. (2006) developed a new stress model to estimate the ultimate bending strength of solid timber beams by using the principle of plasticity. When the applied load was small within the elastic range, it was realized that the first position of the neutral axis was slightly above or below the mid-depth of the beam. The position of the neutral axis was still the same at proportional limit load in the elastic range; however, after proportional limit load, the neutral axis moved towards the tension side of the beam until maximum load. This was explained by the loading the beam beyond the proportional

limit induced the redistribution of compressive stresses across the depth of beam which

caused the shifting of the neutral axis towards the tension side.

Holm (2007) tested 1x1 inches Douglas fir beams. Each beam had different

characteristics: one had no knot, one had a knot in tension, one had a knot in

compression, and one had a knot in the center of the beam. The beams were subjected to

the four-point loading. According to results, in the clear beam, the average neutral axis

was 0.462 inch from the bottom of the beam, which was expected because the modulus of

elasticity in tension is greater than the one in compression. In the center knot beam, the

average neutral axis was 0.564 inch. In the beam with a knot in compression side, the

average neutral axis was 0.222 inch. In the beam with a knot in tension side, the average

neutral axis was 0.715 inch from the bottom of the beam. The neutral axis in the beam

with a knot in tension side moved up in accordance with normal neutral axis level.

Davis (2010) expanded the researched conducted by Holm, ad he tested not only

1x1 inch Douglas fir beams, but also southern yellow pine, hem fir, alder, oak and

unknown species. The result showed that the position of neutral axis varied among the

various species. He investigated that the neutral axis for Douglas fir was higher than ones

for the other species. The tested beam consisted of one clear specimen, one contained a compression knot, one contained a tension knot, and one contained a knot in the center. It was found that, in the clear beam, the neutral axis was located at % 52 of the depth of the beam measured from the tension face.

Shim (2009) studied on improvement of prediction accuracy of glulam modulus of elasticity by considering the neutral axis shift in bending. He measured the neutral axis of glulam by using strain gages at the middle of test samples. In the beginning of the test, neutral axis was positioned 6-7 mm down from the center. As the load increased, the

neutral axis shifted up to 15 mm. According to some samples, neutral axis formerly moved up and later moved down. To delay the movement of the neutral axis to the down of the glulam under a bending load, the reinforced compression laminate should be considered to increase bending performance of glulam.

1.2.3.6 Fatigue Resistance Strength and durability design of upholstered furniture frames needs to take consideration of joint resistance to fatigue loads since most failures of the frames in the field appear to be fatigue related (Eckelman and Zhang1995). As more engineered wood- based composites, such as OSB, are constructed into upholstered furniture frames, the information related to fatigue resistance properties of various types of joints of the composites becomes increasingly essential for furniture manufacturers in order to re- engineer their products. Upholstered furniture manufacturers perform furniture performance tests, such as General Service Administration (GSA) performance test regimen FNAE-80-214A (GSA 1998), are based on a stepped fatigue load model

(Eckelman 1988a and 1988b). BIFMA testing standard is based on a constant fatigue load model. Therefore, the information related to resistance capacity to cyclic stepped loads and constant loads of various types of joints in different types of wood-based materials is necessary to have rational design for manufacturing.

Fatigue, in engineering, is described as the progressive damage on a material that is subjected to cyclic loading (USDA 1999). Stress has the same sign which can be expressed either tension or compression. In this case, there is zero-to-maximum complete repeated stress with a zero stress level. Stress, on the other hand, is changing between tension and compression which has a non-zero stress ratio. The ratio of stress, R, is

clarified as the ratio of minimum stress over maximum stress per cycle (Dowling 1999).

The range of stress is the difference between minimum and maximum stress values. The stress amplitude refers to half of the stress range (Zhang et al. 2004).

Fatigue life refers to the number of cycles that are sustained until material failure.

Fatigue strength, on the other hand, is the maximum stress attained in the stress cycle to determine fatigue life. Fatigue stress versus fatigue life is a stress-life curve which is also named as S-N curve. The stress amplitude or nominal stress versus the number of cycles to failure is generally plotted for metal. The stress level, which is the percentage of the static strength versus the number of cycles to failure, is commonly used for wood and wood composites (Kommers 1943).

Three basic approaches are used for analyzing and designing against fatigue failures which are the stress-based approach, the strain-based approach, and the fracture mechanics approach (Dowling 1999). Frequency of cycling, repetition or reversal loading, stress ratio, temperature, moisture content (MC), and sample size affect fatigue strength and life of wood and wood composites (USDA 1999).

Research to determine fatigue performance of gusset-plate joints in wood-based composites has been minimal, especially for one-side two-narrower plate joints in OSB.

But one study was found in related to gusset-plate joints in OSB, and others found were in other types of joints such as dowel type and metal-plate type joints.

The most recent study on fatigue moment capacity of gusset-plate joints in OSB was carried by Wang et al. (2007c). In this study, T-type, end-to-side joints were connected with a pair of OSB gusset-plates symmetrically attached on both sides of the joint with staples with or without glue. All joints were subjected to one-side cyclic

stepped bending loads. Test results showed that the passing static-to-fatigue ratio averaged 2.1 with a COV of 12 percent.

Wang et al. (2007a) studied the fatigue bending resistance of T-type OSB joints connected with one pair or two pairs of metal-plates symmetrically attached on both sides of the joint. Joints were subjected to two cyclic stepped loading schedules. It was concluded that the passing static-to-fatigue ratios averaged 2.5 with a COV of 22 percent.

Zhang et al. (2006) investigated fatigue bending performances of T-type, end-to- side, metal-plate-connected (MPC) joints in furniture grade pine plywood. Each joint was constructed from two members (a post and a rail) assembled with two identical metal plates symmetrically attached to both sides of the members. All joints were subjected to one-side cyclic stepped bending loads. The ratio of static moment to passed moment ranged 2.2 to 3.1 and averaged 2.5 with a coefficient of variation of 11 percent.

Zhang et al (2003) studied the bending fatigue life of two-pin dowel joints in furniture grade pine plywood. All joints were subjected to constant and one-side cyclic stepped bending loads. The Palmgren-Miner rule was verified as an effective method in estimating fatigue life of two-pine joints. A simplified method of deriving the fatigue life estimation equation based on known information such as the joint static bending moment capacity was proposed. A minimal ratio of static moment capacity to passed fatigue moment was found to be 2.6.

Zhang et al. (2001) investigated fatigue moment capacities of T-type, two-pin moment-resisting dowel joints subjected to constant and stepped cyclic bending loads.

Red Oak, Yellow Poplar, plywood, Aspen Engineered Strand Lumber (ESL), and particleboard were tested in the joint construction. Regression of M-N data (moment versus log number of cycles to failure) of each joint group subjected to constant cyclic

bending loads resulted in linear equations for M-N curves of all tested joint groups. The

results indicated that the fatigue life of dowel joints subjected to a given stepped cyclic

bending schedule can be predicted with the Palmgen-Miner rule based on their M-N

curves. Joint stepped load test results indicated that the static to fatigue moment capacity ratios for tested joints were 1.9, 1.8, 1.6, 1.9, and 2.1 for tested joints in red oak, yellow poplar, plywood, ESL, and particleboard, respectively.

1.2.4 Fatigue Resistance Properties of Wood-based Composites as Furniture Frame Members

1.2.4.1 Fatigue Test Zhang et al. (2005) used the stress-based approach to analyze fatigue performance of simply supported wood-based composites, southern yellow pine plywood, OSB, and particleboard, subjected to edgewise zero-to-maximum center cyclic loading. The S-N curves (applied nominal stress versus the number of cycles to failure) were proposed to describe the fatigue properties of wood-based composites subjected to the zero-to- maximum repeated cyclic loading. Regression analyses of S-N data indicated that a linear relationship between applied nominal stress and the log number of cycles to failure. It was observed that the S-N function relationship would be expressed with the form S =

MOR (1 – H

Dai and Zhang (2007) continued the work of Zhang et al. (2005), derived the regression equations of S-N curves through low 5 percent data points for wood-based composites, and proposed design equations for achieving a conservative design of using wood-based composites as furniture frame structural members considering fatigue effects. The equation had the form of S = MOR (0.85 – H ൈ log10 Nf). The constant H values in the equation were 0.06, 0.08, and 0.10, for plywood, OSB, and particleboard, respectively. Cyclic stepped load tests of full-size back top rails indicated that Palmgren-

Miner rule provided a conservative estimation of the fatigue life of wood-based composites subjected to cyclic stepped bending stresses based on their low 5 percent limit

S-N curves. Results of stress ratio analyses suggested that the ratio of material modulus of rupture (MOR) to the fatigue stress level required to be achieved for design of upholstered furniture frame members could be set to 1.85 for plywood, 1.56 for OSB, and

1.46 for particleboard.

1.3 Objectives The main objective of this study evaluated and compared static and fatigue performance of staple-connected gusset-plate joints in three different OSB materials and fatigue performance of these OSB materials as frame structural members such as back top rails. To achieve the objective, this study was divided into five parts: 1) static face lateral resistance of stapled and glued joints in OSBs, 2) static bending moment capacity of gusset-plate joints constructed of OSBs, 3) static lateral shear resistance of L-type, gusset-plate joint constructed of OSBs, 4) fatigue bending moment capacity of gusset- plate joints in OSBs, and 5) fatigue performance of OSBs subjected to edgewise bending stresses.

The first part of this study sought to: 1) evaluate the face lateral resistance of one- row and two-rows vertically aligned multi-staples joints in three OSB materials; 2) evaluate the face lateral resistance of two-rows horizontally aligned multi-staples joints in three OSB materials; 3) investigate the additive effects of multi-staples on the face lateral resistance of the staple joints for each OSB material; 4) quantify the effect of the number of staples and OSB material density on the face lateral resistance of multi-staples joints in OSB; 5) evaluate the face lateral resistance of only glued and glued-stapled joints; 6) compare face lateral resistances among the joints constructed of three different

OSB materials.

The second part of this study were to: 1) evaluate the static bending moment resistance of L-type, stapled, one-side, two gusset-plate joints in three different OSB materials; 2) evaluate the static bending moment resistance of T-type, stapled, one-side, two gusset-plates joint in three different OSB materials; 3) compare the moment resistances of joints constructed of three different OSB materials; 4) develop mechanical analysis models of L-type and T-type, stapled, one-side, two gusset-plate joints in OSB, and derive equations to estimate moment resistances of the two types of joints in OSB.

The third part of this study examined ways to: 1) evaluate the lateral shear resistance of L-type, stapled, one-side, two gusset-plate joints in three different OSB materials; 2) compare the lateral shear resistances of the joints constructed of three OSB materials; 3) derive equations to estimate the lateral shear resistance of the L-type joints in OSB.

The fourth part of this study sought to: 1) evaluate the fatigue bending moment resistances of L-type and T-type, stapled, one-side, two gusset-plate joints constructed of three OSB materials by subjecting these joints to GSA arm test loading schedules; 2)

compare bending fatigue life among the joints constructed of three OSB materials; 3) determine the ratio of the static moment capacities of the gusset-plates joints in these

OSB materials to their fatigue moment capacities.

The specific objectives of the fifth part study were to: 1) evaluate bending fatigue performance of three OSB materials subjected to edgewise cyclic stepped and constant amplitude bending stresses; 2) verify previous proposed stress-based approach in estimating full-size back top rails using Palmgren-Miner rule based on OSB material low

5 percent limit S-N curves; and 3) determine the ratio of OSB MOR to the fatigue stress;

CHAPTER II

STATIC LATERAL SHEAR RESISTANCE OF STAPLED AND GLUED FACE-TO-

FACE JOINTS

2.1 Materials and Methods

2.1.1 Approach This part of study evaluated the lateral resistance of face-to-face one-row

vertically-aligned, two-row vertically-aligned and two-row horizontally-aligned multi-

staple joints constructed of three OSB materials. Mean lateral shear resistances of joints

in three different materials were compared. The estimation equations of the lateral shear resistance of face-to-face one-row vertically-aligned multi-staple joints in OSB materials were derived as a function of the lateral shear resistances of single-staple joints, number of staples, and material density. The lateral resistance prediction equations of one-row vertically-aligned multi-staple joints were used to derive equations predicting two-row vertically-aligned multi-staple joints. For two-row horizontally-aligned multi-staple joints, estimation equations were derived as a function of number of staples and material density.

2.1.2 Specimen Configurations The general configuration of the face-to-face joint specimens in this study is shown in Figure 2.1. The specimen consisted of two principal structural members, a fastened member and a fastening member, joined together by staples or glue, or staples

and glue. The fastening member was OSB and had nominal dimensions of 11.5 inches long by 7 inches wide by 23/32 inch thick. The fastened member was pine plywood and had nominal dimensions of 6 inches long by 2 inches wide by ¾ inch thick.

Figure 2.1 The general configuration of a face-to-face joint.

2.1.3 Materials In this study, three 23/32-inch-thick pine OSB materials named OSB-I, OSB-II,

and OSB-III were used for fastening members to evaluate and compare their resistances

to lateral shear loads. Tables 2.1 and 2.2 summarize the mean values and mean

comparisons of the lateral resistances of face-to-face single-staple connected joints in

these OSBs from the previous study (Zhang et al. 2010). The mean comparison results

were obtained from performing the protected least significant difference (LSD) multiple

comparison procedure at the 5 percent significance level. The single LSD value of 25

pounds was used to determine the differences among these means.

Table 2.1 Mean comparisons of lateral loads of face-to-face, single-staple connected joints in three OSB materials for each OSB face strand grain orientation.

Material Type Ratio Orientation OSB-I OSB-II OSB-III II/I III/I III/II (lb.) 226 A 268 B 303 C 1.19 1.34 1.13 Parallel (23) (22) (13) 244 A 275 B 321 C 1.13 1.32 1.17 Perpendicular (18) (16) (19)

Table 2.2 Mean comparisons of lateral loads of face-to-face, single-staple joints in OSB materials for material surface strand grain orientation for each OSB material.

Orientation Ratio Material Type Parallel Perpendicular Par/Per (lb.) OSB-I 226 A 244 A 1.08 OSB-II 268 A 275 A 1.03 OSB-III 303 A 321 A 1.06

Table 2.1 indicates that in general three OSB materials had significantly different load resistances to single-staple lateral withdrawal. OSB-III had significantly higher load resistance to staple lateral withdrawal than other two materials, followed by OSB-II and

OSB-I. For instance, the resistance to a single staple lateral withdrawal load of OSB-III was 1.34 times of the one of OSB-I (Table 2.1). Table 2.2 shows that OSB surface strand grain orientation had no significant effect on its resistance to single-staple lateral withdrawal load. The ¾-inch-thick 5-ply southern yellow pine plywood was used for fastened members. The 4-foot by 8-foot full-size sheet of plywood was constructed with one center ply and aligned parallel to face plies, and two plies adjacent to face plies aligned perpendicular to the face. The face plies were aligned parallel to the sheet 8-foot direction.

The staples used were SENCO 16-gage galvanized chisel-end-point types with a

crown with of 7/16 inch and leg length of 1.5 inches. The leg width of staples was 0.062

inch, and thickness was 0.055 inch. The staples were coated with Sencote coating, a

nitro-cellulose based plastic. Glue used to connect joint members was polyvinyl acetate

(PVA) wood with solids contents of 40 % percent.

Table 2.3 summarizes the mean values of physical properties of tested OSB material in this study. Mean comparisons among three materials indicated that OSB-III had the highest density value among all OSB materials, followed by OSB-II, and OSB-I.

Table 2.3 Mean value of physical properties of tested materials.

Material Type Property OSB-I OSB-II OSB-III LSD II/I III/I III/II 40.6 (7) 43.4 (6) 46.4(6) 1.38 1.07 1.15 1.07 Density (pcf) (A) (B) (C) MC (%) 5.0 (6) 5.8 (6) 4.7 (3)

Figure 2.2 shows the lateral resistance load values of single-staple joints in OSB-

I, OSB-II, and OSB-III versus their corresponding densities. In general, the ultimate

lateral resistance load of face-to-face, single-staple-connected joints increased

significantly as the density of OSB increased.

Figure 2.2 Lateral resistance load versus material density for of single-staple joints in three OSB materials.

Figure 2.3 shows density profile of OSB-I, OSB-II, and OSB-III. In general,

OSB-III had higher density in surface layers than other two OSB materials, but had not much difference in core density compared to other two OSB materials. OSB-II had flat density profile that indicated a uniform density across the thickness. All three OSB materials had similar core density.

Figure 2.3 Density profile of OSB-I, OSB-II, and OSB-III.

2.2 Experimental Design

2.2.1 One-Row Vertically-Aligned Multi-Staple Joints A complete 3×3 factorial experiment with 10 replicates per combination was

conducted to evaluate the additive effects of staples on the lateral shear resistance of face- to-face one-row vertically-aligned multi-staple joints. The two factors were fastening member material type (OSB-I, OSB-II, and OSB-III) and the number of staples (2, 3, and

4). Therefore, a total of 90 joints were tested. The multi-staple placement patterns for each staple number level are given in Figure 2.4.

Figure 2.4 Diagram showing the placement of staples in the three joint specimens connected with one-row vertically-aligned multi-staples of: a) two, b) three, and c) four.

2.2.2 Two-Row Vertically-Aligned Multi-Staple Joints A complete 3×4×2 factorial experiment with 10 replicates per combination was conducted to evaluate the additive effects of staples on the lateral shear resistance of face- to-face two-row vertically-aligned multi-staple joints. The three factors were fastening member material type (MT) (OSB-I, OSB-II, and OSB-III), the number of staples (NOS)

(2, 4, 6, and 8), and connection type (CT) (staple only and staple and glue together).

Therefore, a total of 240 joint specimens were tested. The multi-staple placement patterns for each staple number level are given in Figure 2.5.

Figure 2.5 Diagram showing the placement of staples in the four joint specimens connected with two-row vertically-aligned multi-staples of: a) two, b) four, c) six, and d) eight.

2.2.3 Two-Row Horizontally-Aligned Multi-Staple Joints A complete 3×3 factorial experiment with 10 replicates per combination was conducted to evaluate the additive effects of staples on the lateral resistance of two-row horizontally-aligned multi-staple joints. The factors are the fastening member material type (OSB-I, OSB-II, and OSB-III) and number of staples (4, 6, and 8). Therefore, a total of 90 joints were tested. The multi-staple placement pattern is given in Figure 2.6.

Figure 2.6 Diagram showing the placement of joints connected with two-row- horizontal multi-staples: a) 4; b) 6; and c) 8 staples.

2.2.4 Glued Joints A one-way factorial experiment with 10 replicates per cell was conducted to evaluate the lateral shear resistance of face-to-face glued joints. The factor was fastening member material type (OSB-I, OSB-II, and OSB-III). Therefore, a total of 30 joints were tested.

2.3 Specimen Preparations

2.3.1 Vertically-Aligned Joints Seven by 11.5 inches size 360 members were cut from the OSB panels of each material using a rip saw and the radial arm saw. These members were conditioned at 65 ±

4º F and controlled at a relative humidity of 41 ± 1 % for two weeks. Beside these members, 2×6 inches size 360 plywood gusset plates were prepared from one type plywood panels. After conditioning the rails for one-row vertically-aligned multi-staple joints, 90 gusset plates were attached to the OSB rails with different number of staples (2,

3, and 4). 120 gusset plates were attached to 120 OSB rails using 2, 4, 6, and 8 staples, and also 120 gusset plates were glued and stapled to 120 OSB rails for two-row vertically-aligned multi-staple joints. For glued joints, 30 gusset plates were glued to 30

OSB rails without staples. Eventually, 360 specimens were prepared.

Prior to the joint construction, all cut OSB and plywood blanks were conditioned in an 8 percent equilibrium moisture content chamber. For staple connected joints, Senco

16 gauge staple gun was used to drive staples into OSB materials with pressure of 70 psi.

For glued joint assembly, the glue was applied to both fastened member and fastening member. The amount of glue applied was approximately 646 g/m2 per joint. Two joint members were clamped for 48 hours before testing.

2.3.2 Horizontally-Aligned Joints 7 by 11.5 inches size 60 members were cut from the OSB panels of each material by using a rip saw and a radial arm saw. These members were rested in the conditioning room until % 8 humidity. Beside these members, 3×6 inches 60 plywood gusset plates were prepared from one type plywood panels. After conditioning the rails, 30 gusset

plates were attached to the 30 OSB rails (10 OSB rails from each OSB group) for two- row horizontally aligned 6-staple joints and 30 gusset plates were attached to 30 OSB rails two-row horizontally-aligned 8-staple joints. Eventually, 60 specimens were prepared. For staple connected joints, Senco 16 gauge staple gun was used to drive staples into OSB materials with pressure of 70 psi.

2.4 Lateral Shear Test

2.4.1 Vertically-Aligned Joints Figure 2.7 shows the apparatus for evaluating the lateral shear resistance of face- to-face stapled or glued joints. All joints were tested on a Universal Tinius-Olsen testing machine at a loading rate of 0.10 in/min in reference with ASTM D 1761 (ASTM 2010).

(a) (b)

Figure 2.7 Test set-up for evaluating lateral shear resistance of face-to-face, stapled or glued joints: a) front view; and b) back view.

In preparation, the specimen was first placed to the loading fixture that was bolted to the testing machine table. Secondly, a stopper which has a transfer roller on its edge was used to fixed specimen to the loading fixture. The last step of the setup was putting a

U shaped load head on the specimens to apply a vertical load. Ultimate lateral shear load, load-displacement curves, and specimen failure modes were recorded.

2.4.2 Horizontally-Aligned Joints Figure 2.8 shows the test set-up for evaluating the lateral resistance two-row horizontally-aligned multi-staple joints. All joints were tested on a hydraulic universal

SATEC machine at a loading rate of 0.10 in/min in keeping with ASTM D 1761 (ASTM

2010).

Figure 2.8 Test set-up for evaluating the lateral shear resistance of face-to-face two- row horizontally-aligned multi-staple joint.

In preparation, the specimen was first bolted to the loading fixture that was also bolted to the testing machine table. Secondly, a squared shaped metal pieced was put between loading head and specimen to prevent material crush on the top of specimen and to allow loading accurately. After setting up the test, the vertical load calibrated for initiation of the test, and then the lateral resistance of face-to-face joint test was conducted for two-row horizontally-aligned multi-staple joints. Ultimate lateral shear load, load-displacement curves, and specimen failure modes were recorded.

2.5 Results and Discussion

2.5.1 One-Row Vertically-Aligned Multi-Staple Joints

2.5.1.1 Load-Displacement Curves Typical lateral shear load-displacement curve of OSB joints connected with one- row vertically-aligned multi-staples is illustrated in Figure 2.9. In general the curve has two linear regions: first one is from 0 to proportional limit; second one is from proportional limit to ultimate point.

Figure 2.9 Load-displacement curves of face-to-face joints connected with one-row vertically-aligned multi-staple.

2.5.1.2 Mean Ultimate Lateral Shear Loads and Comparisons Mean ultimate lateral shear loads of face-to-face one-row vertically-aligned multi-

staple connected joints and their coefficients of variation are summarized in Table 2.4.

Each value represents a mean of 10 specimens tested. The lateral resistance test

specimens failed with the mode of staple legs lateral shear withdrawal from fastening

members.

Table 2.4 Mean ultimate lateral shear load values of face-to-face, one-row vertically- aligned multi-staple joints and their COVs.

Number of Material Type Staples OSB-I OSB-II OSB-III 2 476 (13) 550 (15) 547 (11) 3 611 (8) 771 (9) 745 (10) 4 858 (11) 931 (13) 985 (15)

A two-factor analysis of variance (ANOVA) general linear model procedure was performed for individual joint data to analyze main effects and the interaction on the mean ultimate lateral shear loads of face-to-face, one-row, vertically-aligned multi-staple joints in OSB materials. Table 2.5 summarizes the ANOVA result.

Table 2.5 General linear model procedure output for main effects and interactions of 3 by 3 face-to-face one-row vertically-aligned multi-staple joints with 10 replication of each combination.

Source DF F Value Pr > F MT 2 14.32 <.0001 S NOS 2 152.20 <.0001 S MT*NOS 4 1.14 0.3422 NS aS = significant; NS = Not significant; MT = material type; NOS = number of staples.

The ANOVA results indicated that the two-factor interaction, material type by

number of staples, was marginally not statistically significant at the 5 percent significance level. The test for the two-factor interaction was considered.

Tables 2.6 and 2.7 show mean comparisons of ultimate lateral shear loads of one- row, vertically-aligned multi-staple joints for material type and number of staples effects, respectively. The results were based on a one way classification with 9 treatments. The protected least significant difference (LSD) multiple comparisons procedure at the 5 percent significance level was performed to determine the mean difference of those treatments using the single LSD value of 79 pounds.

Table 2.6 Mean comparisons of ultimate lateral shear loads of one-row vertically- aligned multi-staple joints for material type for each number of staples.

Number Material Type Ratio of II/I III/I III/II Staples OSB-I OSB-II OSB-III 2 476 (A) 550 (A) 547 (A) 1.16 1.15 0.99 3 611 (A) 771 (B) 745 (B) 1.26 1.22 0.97 4 858 (A) 931 (AB) 985 (B) 1.09 1.15 1.06

Table 2.7 Mean comparisons of ultimate lateral shear loads of one-row vertically- aligned multi-staple joints for number of staples for each material type.

Material Number of Staples Ratio Type 2 3 4 3/2 4/2 4/3 OSB-I 476 (A) 611 (B) 858 (C) 1.28 1.80 1.40 OSB-II 550 (A) 771 (B) 931 (C) 1.40 1.69 1.21 OSB-III 547 (A) 745 (B) 985 (C) 1.36 1.80 1.32

2.5.1.3 Material Type Effects Table 2.6 indicates that the ultimate lateral shear load of one-row vertically- aligned 2-staple joints is not significantly different among three OSB materials. The ultimate lateral shear load of one-row vertically-aligned 3-staple joints in OSB-I is significantly lower than the ones of OSB-II and OSB-III. In the case of joints connected with 4 staples, OSB-III joints had a significantly higher ultimate lateral shear load than

OSB-I, but had no significant difference to OSB-II joints. OSB-II joints had a higher ultimate lateral shear load that OSB-I joints, but this was not significant. These differences might be explained by the fact that the density of OSB-III was significantly higher than the ones of OSB-I and OSB-II. The mean comparison results of multi-staple joint is different from the result of single-staple connected joints (Table 2.1), which indicated there is a significant difference in load resistance between OSB-II and OSB-III.

2.5.1.4 Staple Number Effects According to Table 2.7, one-row vertically-aligned joints with 4 staples had mean ultimate lateral shear load than the joint with 2 and 3 staples, followed by 3 and 2 in all

OSB materials. In general, the mean ultimate lateral load resistance of one-row vertically- aligned multi-staple joints increases significantly as the number of staples increases.

2.5.1.5 Estimation Equations To quantify the effect of the number of staples on the lateral shear resistance of one-row vertically-aligned multi-staple joints in a given OSB material, the following equation was fitted to the individual testing data points from this study and also data points from previous single staple joint study (Zhang and Quin 2010) using the least squares method:

P = K × N a OR (2.1)

where POR = estimated mean ultimate lateral shear load of one-row vertically-aligned

multi-staple joints (lb.); N = the number of staples; K and a = regression constants.

To derive the regression constants the both sides of Equation (2.1) were taken

log10 which yielded the following equation:

log P = log K + a log N (2.2) 10 OR 10 10

By setting y = log10 POR; b = log10 K; x = log10 N, the power equation was

converted to a linear equation:

y = b + a x (2.3) To run linear regression analysis using the individual data point, each of 60 lateral shear

test data points was arranged in the format shown in Table 2.8, i.e., three columns

representing each specimen number, number of staples used in the numbered specimen,

and its ultimate lateral shear load. Then, the values in the second and third columns were

converted to their logarithmic 10 (log10) values as shown in Table 2.9.

Table 2.8 Each of 60 lateral shear test data points was arranged in the following format for each OSB material, for instance, OSB-I.

Number of Number of Ultimate Specimens Staples (N) Load (P) (lb.) 1 1 209 2 1 291 3 1 267 ...... 60 4 950

Table 2.9 Conversion of number of staples and ultimate lateral load to their Log 10 value for OSB-I.

Number of Log10 N Log10 P Specimens (x) (y) 1 0 2.32015 2 0 2.46389 3 0 2.42651 ...... 60 0.602059991 2.97772

After the log conversion, linear regression analysis was run for each OSB group.

Table 2.10 gives the results from linear regression analysis of OSB-I data.

Table 2.10 Results of linear regression analysis of OSB-I data.

Variable DF Parameter Pr > |t| Estimate Intercept 1 2.35 < .0001 a 1 0.97 < .0001

Since b = 2.35, then log10 K = 2.35

Therefore, K = 102.35 = 223

The power equation for estimating the lateral shear resistance load of one-row

vertically-aligned multi-staple joints in OSB-I can be expressed in the following

equation:

P=223× N0.9 (2.4) Regression constants K and “a” for OSB-II and OSB-III can be derived with the

same procedure described above for OSB-I. Table 2.11 summarizes the regression fitting

constant values K and a, and coefficient of determination values of derived equations for

each of three OSB materials. The K values were compared with the mean ultimate lateral

resistance of single-staple joints, FO, in column 6. The rates of K values to the mean

ultimate lateral resistance loads (FO) of single-staple joints are 0.99 for all three OSB materials.

Table 2.11 Regression constants and associated r2 and p-values for derived equations for estimating mean ultimate lateral resistance loads of face-to-face one-row vertically-aligned multi-staple connected joints in three OSB materials.

2 Material Type K a r p-value FO K/ FO OSB I 223 0.97 0.90 <0.0001 226 0.99 OSB II 266 0.94 0.90 <0.0001 268 0.99 OSB III 301 0.84 0.94 <0.0001 303 0.99

Therefore, the regression constant, K, in the Equation (2.1) was replaced by the

single-staple lateral resistance load for each OSB material. This substitution yielded the

following equation:

P = F × N a (2.5) OR O

where FO = mean ultimate lateral shear load of single-staple joints in a OSB material

(lb.); N = the number of staples.

Further regression analysis based on log conversions in Table 2.12, which combined all three OSB data together, yielded a single value of 0.92 for the constant, a, with an r2 value of 0.88. Therefore, the lateral shear resistance of face-to-face one-row vertically-aligned multi-staple joints in OSB materials can be estimated using a single form Equation (2.5) with the constant, a, set to be a value of 0.92. This equation requires knowing the lateral shear resistance load of single-staple joints in an OSB material to predict the lateral shear resistance of one-row multi-staple joints.

Table 2.12 Log conversion of single-staple ultimate lateral shear load, number of staples, and multi-staple ultimate lateral load of all three OSB materials.

Number Log10 FO Log10 N Log10 P of Specimens (Log10 226) (Log10 1) 1 2.354108 0 2.320146 2 2.354108 0 2.463893 3 2.354108 0 2.426511 . . . . 60 . . .

(Log10 268) (Log10 1) (Log10 P) 61 2.428135 0 2.534026 ......

(Log10 303) (Log10 1) (Log10 P) 120 2.481443 0 2.487138 . . . . 180 2.481443 0.60206 3.022841

To quantify the effects of the number of staples and material density on the

lateral load resistance of face-to-face one-row vertically-aligned multi-staple joints in

OSB materials, the power Equation (2.6) was fitted to individual testing data points with

the least squares method:

P = K × D a × N b OR (2.6)

where POR = estimated mean ultimate lateral load of face-to-face one-row vertically-

aligned multi-staples joints (lb.); N = number of staples; D = material density (pcf); and a

and b = regression constants.

Regression analysis based on log conversion in Table 2.13, which combined all

three OSB data together considering material density, yielded the values of 0.372, 1.74,

and 0.92 for the regression constants, K, a, b, respectively with an r2 value of 0.91.

Therefore, the lateral shear resistance of face-to-face one-row vertically-aligned multi- staple joints in an OSB material can also be estimated using Equation (2.6) if its density is known.

Table 2.13 Log conversion of OSB density, number of staples, and multi-staple ultimate lateral load of all three OSB materials.

Number Log10 D Log10 N Log10 P of Specimens (Log10 40.6) (Log10 1) 1 1.60853 0 2.320146 2 1.60853 0 2.463893 3 1.60853 0 2.426511 . . . . 60 . . .

(Log10 43.4) (Log10 1) (Log10 P) 61 1.63749 0 2.534026 ......

(Log10 46.4) (Log10 1) (Log10 P) 120 1.66652 0 2.487138 . 1.66652 . . 180 1.66652 0.60206 3.022841

2.5.1.5.1 Prediction Equation Comparisons Table 2.14 shows the lateral shear resistance load values of one-row vertically- aligned multi-staple joints estimated from Equations (2.1), (2.5), and (2.6) in columns 5,

6, and 7, respectively, and also their ratios to corresponding observed values in columns

6, 7, and 8, respectively. The range of predicted to observed value ratios was 0.92 to 1.06,

0.90 to 1.12, and 0.90 to 1.09, for Equations (2.1), (2.5), and (2.6), respectively. This indicates that all three equations can provide reasonable estimation of lateral shear resistance loads of one-row vertically-aligned multi-staple joints in OSB materials.

Table 2.14 Comparison of estimated ultimate lateral shear resistance loads of one-row vertically-aligned multi-staple joints in OSB using Equations (2.1), (2.5), (2.6) with observed values.

Predicted Load Ratio Material Eq.(2.1)/ Eq.(2.5)/ Eq.(2.6)/ D N Obs. Eq.(2.1) Eq.(2.5) Eq.(2.6) Type Obs. Obs. Obs. 40.6 1 226 223 226 233 0.99 1.00 1.03 40.6 2 476 437 428 442 0.92 0.90 0.93 OSB-I 40.6 3 611 647 621 641 1.06 1.02 1.05 40.6 4 858 856 809 836 1.00 0.94 0.97 43.4 1 268 266 268 262 0.99 1.00 0.98 43.4 2 550 510 507 496 0.93 0.92 0.90 OSB-II 43.4 3 771 747 736 720 0.97 0.96 0.93 43.4 4 931 979 959 939 1.05 1.03 1.01 46.4 1 303 301 303 295 0.99 1.00 0.97 46.4 2 547 539 573 557 0.99 1.05 1.02 OSB-III 46.4 3 745 757 833 809 1.02 1.12 1.09 46.4 4 985 964 1085 1054 0.98 1.10 1.07 aD = density of OSBs; N = number of staples; Obs. = observed load values, Eq.= equation.

2.5.2 Two-Row Vertically-Aligned Multi-Staple Joints

2.5.2.1 Load-Displacement Curves A typical load-displacement curve of OSB joints connected with two-row vertically-aligned multi-staple is illustrated in Figure 2.10. The curve has two regions which is the same with the one-row vertically-aligned multi-staple joints. Figure 2.11 illustrates a typical load-displacement curve of OSB connected with two-row vertically- aligned multi-staple and glue. The curve in Figure 2.11 has two peaks. First peak may belong glue connection while second peak may belong staple connection.

Figure 2.10 A typical load-displacement curve of face-to-face joints connected with two-row vertically-aligned multi-staple.

Figure 2.11 A typical load-displacement curve of two-row vertically-aligned multi- staple and glued joints.

2.5.2.2 Mean Ultimate Lateral Loads and Comparison Mean ultimate lateral resistance load values of face-to-face two-row vertically-

aligned multi-staple with/without glue connected joints and their coefficients of variation

are summarized in Table 2.15. Each value represents a mean of 10 specimens tested.

Table 2.15 Mean ultimate lateral resistance loads of face-to-face two-row vertically- aligned multi-staple joints and their COVs.

Connection Type Material Staple Only Staple with Glue 2 4 6 8 2 4 6 8 Type (lb.) 508 886 1416 1780 1317 1523 1578 1761 OSB-I (5) (8) (9) (17) (11) (8) (10) (14) 493 990 1483 1939 1357 1553 1670 1974 OSB-II (13) (12) (12) (6) (13) (15) (5) (13) 589 1082 1695 2227 1297 1646 1590 2217 OSB-III (11) (9) (7) (10) (13) (8) (5) (7)

A three-factor ANOVA general linear model procedure was performed for

individual joint data to analyze main effects and the interaction on the mean ultimate

lateral shear loads of face-to-face, two-row vertically-aligned multi-staple joints in OSB

materials. Table 2.16 summarizes the ANOVA result.

Table 2.16 General linear model procedure output for main effects and interactions of 3 by4 by 2 face-to-face two-row vertically-aligned multi-staple joints with 10 replication of each combination.

Source DF F Value Pr > F CT 1 324.66 <.0001 S NOS 3 466.14 <.0001 S MT 2 33.04 <.0001 S CT*NOS 3 92.01 <.0001 S CT*MT 2 2.24 0.1085 NS NOS*MT 6 5.85 <.0001 S CT*NOS*MT 6 1.30 0.2581 NS aS = significant; NS = not significant; MT = material type; NOS = number of staples; CT = connection type.

According to the results in the ANOVA Table 2.16, the 3-way interaction, connection type× number of staples × OSB type, is not significant at the 5 percent significance level, and the 2-way interaction connection type by OSB type is not significant at the 5 percent significance level. Two significant 2-way interactions,

connection type by number of staples and number of staples by OSB type, were analyzed.

2.5.2.2.1 Material Type by Number of Staples Interaction Tables 2.17 shows mean comparisons of ultimate lateral resistance loads for

number of staples for each of three materials. Table 2.18 gives mean comparisons of

ultimate lateral resistance loads for material type for each of the numbers of staples. The results were based on a one way classification with 12 treatments. The protected least significant difference (LSD) multiple comparisons procedure at the 5 percent significance level was performed to determine the mean difference of those treatments using the LSD value of 189 pounds.

Table 2.17 Mean comparisons of ultimate lateral load resistances of face-to-face two- row vertically-aligned multi-staple joints for number of staples for each of three materials.

As shown in Table 2.17, the mean ultimate lateral shear load of two-row

vertically-aligned joints with 2 staples, 4 staples, 6 staples, and 8 staples are significantly different from one another in OSB-I. The same relationship is valid for the joints in OSB-

II and OSB-III.

Table 2.18 Mean comparisons of the ultimate lateral resistance loads of face-to-face two-row vertically-aligned multi-staple joints for material type for each of number of staples.

Number Material Type Ratio of Staples OSB-I OSB-II OSB-III II/I III/I III/II 2 914 (A) 925 (A) 973 (A) 1.01 1.06 1.05 4 1205 (A) 1272 (A) 1364 (A) 1.06 1.13 1.07 6 1497 (A) 1577 (A) 1642 (A) 1.05 1.10 1.04 8 1771 (A) 1957 (A) 2222 (B) 1.11 1.25 1.14

According to Table 2.18, the ultimate lateral resistance loads of two-row

vertically-aligned 2-staple joints in OSB-I, OSB-II, and OSB-III are not significantly

different from one another. The same relationship exists among two-row vertically-

aligned 4-staple joints and two-row vertically-aligned 6-staple joints. However, the

ultimate lateral resistance loads of two-row vertically-aligned 8-staple joints in OSB-I

and OSB-II are significantly lower than the one of two-row vertically-aligned 8-staple

joints in OSB-III.

2.5.2.2.2 Connection Type by Number of Staples Interaction Tables 2.19 and 2.20 list mean comparisons of ultimate lateral loads of face-to-

face two-row vertically-aligned multi-staple connected joints for number of staples (2, 4,

6, and 8) with respect to connection type ( glue and no glue) and joints for connection type with respect to number of staples, respectively. The results were based on a one way classification with 8 treatments. The protected least significant difference (LSD) multiple

comparisons procedure at the 5 percent significance level was performed to determine the

mean difference of those treatments using the LSD value of 97 pounds.

Table 2.19 Mean comparisons of ultimate lateral load resistances of face-to-face two- row vertically-aligned multi-staple joints for number of staples for each of glue existence.

Accordingly, the ultimate lateral loads of the glued two-row vertically-aligned

joints with 2 staples are significantly lower than the ones of two-row vertically-aligned

joints with 4, 6, and 8 staples. The ultimate lateral load of the glued two-row vertically-

aligned joints with 4 staples and 6 staples are not significantly different; however the

ultimate lateral load of the glued two-row vertically-aligned joints with 8 staple are

significantly higher from the others. The joints which does not have glue show similar

relationship among different staple numbers except the relationship among 4 staple and 6 staple, which 6 staple joints significantly higher than 4 staple joint.

Table 2.20 Mean comparisons of the ultimate lateral load resistances of face-to-face two-row vertically-aligned multi-staple joints for connection type for each of number of staples.

Connection Type Number of Staples Only Staple With Glue 2 530 (A) 1344 (B) 4 986 (A) 1575 (B) 6 1531 (A) 1613 (A) 8 1984 (A) 1982 (A)

As shown in Table 2.20, two-row vertically-aligned 2-staple joints with glue are

significantly higher from two-row vertically-aligned 2-staple joints without glue.

Likewise, two-row vertically-aligned 4-staple joint with glue are significantly higher

from two-row-vertical 4-staple joints without glue. On the other hand, two-row

vertically-aligned 6-staple joints with glue are not statistically different from two-row

vertically-aligned 6-staple joints without glue. The same rule is valid for two-row

vertically-aligned 8-staple joints with and without glue.

2.5.2.2.3 Connection Type Effects The ultimate lateral load of face to face two-row vertically-aligned multi-staple

joints is ranking between 530-1984 as shown in Tables 2.20. Use of glue in a joint

increases the ultimate lateral load of two-row vertically-aligned 2 and 4 staples joints.

However, it does not increase the ultimate load of two-row vertically-aligned 6 and 8

staples. This shows that increasing number of staples ruins the strength of the glue.

Therefore, staple strength may exceed the glue strength by increasing staple number.

2.5.2.2.4 Number of Staple Effects As shown in Table 2.19 increasing number of staples from 2 to 8 increases the lateral ultimate load of joints. Therefore, number of staples directly affects the strength of joints.

2.5.2.2.5 Material Type Effects According to Table 2.18, using different OSB materials that their density are different does not affect the lateral ultimate load of joints except the joints made of OSB-

II with 8 staples and OSB-III with 8 which are significantly different from each other.

2.5.2.3 Displacements Loads at Proportional Limit Table 2.21 summarizes the displacements and loads at proportional limit of load- displacement curve of two-row 4 and 6-staple joints. These displacement and load values were used in deriving estimating bending moment resistance equations of L-type and T- type gusset-plate of joints in Chapter III.

Table 2.21 Displacements of the two-row vertically aligned multi-staple joint at proportional limit and their corresponding lateral shear load value.

Number Material Disp. P of Staples Type ppl OSB I 0.074 502 4 OSB II 0.068 502 OSB III 0.073 505 OSB I 0.090 804 6 OSB II 0.081 776 OSB III 0.086 805 Disp.=displacement at proportional limit; Pppl =Lateral shear load of two-row vertically- aligned multi-staple joint at proportional limit.

2.5.2.4 Estimation Equations Table 2.22 indicates that the overall ratio of two-row vertically-aligned multi- staple gusset-plate joints to one-row vertically-aligned multi-staple joints is 2.05 which is approximately 2.

Table 2.22 Mean ultimate lateral shear load ratios of two-row vertically-aligned multi- staple OSB gusset-plate joints to one-row vertically-aligned multi-staple OSB gusset-plate joints.

OSB-I Number Number of Staples Over all of Rows 1 2 3 4 1-row 226 476 611 858 2 4 6 8 2-row 508 886 1416 1780 Rate 2.25 1.86 2.32 2.07 2.13 OSB-II Number of Staples 1 2 3 4 1-row 268 550 771 931 2 4 6 8 2-row 493 990 1483 1939 Rate 1.84 1.80 1.92 2.08 1.91 OSB-III Number of Staples 1 2 3 4 1-row 303 547 745 985 2 4 6 8 2-row 589 1082 1695 2227 Rate 1.94 1.98 2.28 2.26 2.11 Over all 2.05

Therefore Equation (2.7) was proposed to estimate lateral shear resistance of two- row vertically-aligned multi-staple joints (2, 4, 6, and 8 staples) in OSB materials.

F = 2P TR OR (2.7) where FTR = the estimated mean ultimate load of only two-row-multi-staple (lb.) and POR

= the estimated mean ultimate load of one-row vertically-aligned multi-staple joints (lb.).

In Equation (2.7), Equations (2.1), (2.5), and (2.6) were substituted with POR.

Table 2.23 summarizes prediction comparisons between observed and predicted mean 55

lateral withdrawal resistances of two-row vertically-aligned multi-staple OSB joints using observed mean lateral withdrawal resistances of one-row vertically-aligned multi-staple

joints, Equation (2.1), Equation (2.5), and Equation (2.6) estimated results.

Table 2.23 Comparison of estimated ultimate lateral shear resistance loads of two-row vertically-aligned multi-staple joints in OSB using Equations (2.7) through substituting Equations (2.1), (2.5), (2.6) with observed values.

Predicted Load Ratio Material Eq.(2.1)/ Eq.(2.6)/ Eq.(2.7)/ D N Obs. Eq.(2.1) Eq.(2.6) Eq.(2.7) Type Obs. Obs. Obs. 40.6 2 508 446 452 467 0.88 0.89 0.92 40.6 4 886 874 855 883 0.99 0.97 1.00 OSB-I 40.6 6 1416 1295 1242 1283 0.91 0.88 0.91 40.6 8 1780 1711 1618 1672 0.96 0.91 0.94 43.4 2 493 532 536 524 1.08 1.09 1.06 43.4 4 990 1021 1014 992 1.03 1.02 1.00 OSB-II 43.4 6 1483 1494 1473 1441 1.01 0.99 0.97 43.4 8 1939 1958 1919 1877 1.01 0.99 0.97 46.4 2 589 602 606 589 1.02 1.03 1.00 46.4 4 1082 1078 1147 1115 1.00 1.06 1.03 OSB-III 46.4 6 1695 1515 1665 1618 0.89 0.98 0.95 46.4 8 2227 1929 2170 2109 0.87 0.97 0.95 aD = density of OSBs; N = number of staples; Obs = observed load values, Eq.= equation.

Accordingly, estimation Equations (2.1), (2.5), and (2.6) are reasonable to

estimate mean lateral shear resistances of two-row vertically-aligned multi-staple joints.

2.5.3 Two-Row Horizontally-Aligned Multi-Staple Joints

2.5.3.1 Load-Displacement Curves Figure 2.12 shows the typical load-displacement curve of two-row horizontally-

aligned multi-staple joints without glue.

Figure 2.12 A typical load-displacement curve of two-row horizontally-aligned multi- staple joints.

2.5.3.2 Mean Ultimate Lateral Loads and Comparisons Mean ultimate lateral load values of face-to-face two-row horizontally-aligned

multi-staple connected joints and their coefficients of variation are summarized in Table

2.24. Each value represents a mean of 10 specimens tested.

Table 2.24 Mean ultimate face to face lateral load values of two-row horizontally- aligned multi-staple joints and their COVs.

Number of Material Type Staples OSB-I OSB-II OSB-III 4 886 (9) 990 (12) 1082 (9) 6 1405 (8) 1585 (14) 1883 (6) 8 1827 (11) 2310 (10) 2472 (9)

A two-factor ANOVA general linear model procedure was performed for

individual joint data to analyze main effects and the interaction on the mean ultimate 57

lateral shear loads of two-row horizontally-aligned multi-staple joints. Table 2.25 lists the

ANOVA result.

Table 2.25 General linear model procedure output for main effects and interactions of 3 by 3 face-to-face two-row horizontally-aligned multi-staple joints with 10 replication of each combination.

Source DF F Value Pr > F MT 2 51.97 <.0001 S NOS 2 395.87 <.0001 S MT*NOS 4 6.10 0.0002 S aS = significant; MT = material type; NOS = number of staples.

The ANOVA results indicated that the two-factor interaction, material type ×

number of staples, was statically significant at the 5 percent significance level. Therefore,

the tests for main effects were ignored, and the significant two factor interaction was analyzed. The results were based on a two way classification with 9 treatments. The protected least significant difference (LSD) multiple comparisons procedure at the 5 percent significance level was performed to determine the mean difference of those treatments using the single LSD value of 149 pounds. Table 2.26 shows the mean comparisons of ultimate lateral shear loads for material type effect for each of number of staples. Table 2.27 gives the mean comparisons of ultimate lateral shear loads for number of staples for each of material type.

Table 2.26 Mean comparisons of ultimate lateral loads of two-row horizontally-aligned multi-staple OSB gusset-plate joints for material type.

Number of Material Type Staples OSB-I OSB-II OSB-III 4 886 (A) 990 (AB) 1082 (B) 6 1405 (A) 1585 (B) 1883 (C) 8 1827 (A) 2310 (B) 2472 (C)

Table 2.27 Mean comparisons of ultimate lateral loads of two-row horizontally-aligned multi-staple OSB gusset-plate joints for number of staples.

Number of Staples Material Type 4 6 8 OSB-I 886 (A) 1405 (B) 1827 (C) OSB-II 990 (A) 1585 (B) 2310 (C) OSB-III 1082 (A) 1883 (B) 2472 (C)

2.5.3.2.1 Material Type Effect Table 2.26 indicates that the mean ultimate lateral shear loads of two-row horizontally-aligned 4-staple joints in OSB-I is significantly lower than the one of two- row horizontally-aligned 4-staple joints in OSB-III, however; the mean ultimate lateral shear loads of two-row horizontally-aligned 4-staple joints in OSB-II is not significantly different than the ones in OSB-I and OSB-III. On the other hand, the means ultimate lateral shear loads of two-row horizontally-aligned 6 and 8-staple joints in OSB-II are significantly higher than the means ultimate lateral shear loads of two-row-horizontal 6 and 8-staple joints in OSB-I and lower than the ones of two-row horizontally-aligned 6 and 8-staple joints in OSB-III. This indicated that increasing the number of staples in horizontal direction on a gusset-plate makes difference among material type, however; increasing the number of staples in vertical direction on a gusset-plate did not make the difference among material type as it mentioned in two-row vertically-aligned joints part.

2.5.3.2.2 Number of Staples Effect According to Table 2.27, the mean ultimate lateral loads of two-row horizontally- aligned 6-staple joint is significantly higher than the one of two-row horizontally-aligned

4-staple joints and lower than the one of two-row horizontally-aligned 8-staple joints in

all OSB groups. This indicated that mean lateral shear load of two-row multi-staple joint increases as number of staples increases.

2.5.3.3 Mean Comparison Between Vertically and Horizontally-Aligned Multi- Staple Joints A three-factor ANOVA general linear model procedure was performed for individual joint data to analyze main effects and the interaction on the mean ultimate lateral loads of two-row vertically and horizontally-aligned multi-staple joints. Three factors were the fastening member material type (OSB-I, OSB-II, and OSB-III), the staple alignment (Vertical (V) and Horizontal (H)), and the number of staples (6 and 8)

Figure 2.13 shows the configuration of compared joints. Table 2.28 gives the ANOVA results.

Figure 2.13 Diagram showing the placement of joints connected with two-row- vertically and two-row horizontally-aligned multi-staples of: a) vertical 6, b) vertical 8, c) horizontal 6, and d) horizontal 8.

Table 2.28 General linear model procedure output for main effects and interactions of 3 by 2 by 2 face-to-face two-row vertically-aligned and two-row horizontally- aligned multi-staple joints with 10 replication of each combination.

Source DF F Value Pr > F SD 1 19.02 <.0001 S NOS 1 220.30 <.0001 S MT 2 61.04 <.0001 S SD*NOS 1 4.02 0.0474 MS SD*MT 2 3.19 0.0451 MS NOS*MT 2 3.44 0.0356 MS SD*NOS*MT 2 0.94 0.3930 NS aS = significant.; NS = not significant; MS = marginally significant; MT = material type; NOS = number of staples; SD = staple direction.

According to the results in the ANOVA table, the 3-way interaction, staple

alignment × number of staples × material type is not significant at the 5 percent

significance level; however all the 2-way interactions are significant at the 5 percent

significance level. All 2-way significant interactions are staple alignment by number of

staples, staple alignment by material type, and number of staples by material type.

Therefore, these three 2 way interactions were analyzed.

2.5.3.3.1 Staple Alignment by Number of Staples A one way classification was created with four treatment combinations of staple alignment by number of staples. The least significant difference (LSD) multiple comparison procedure at a 5 percent significant level was performed to determine the

mean differences of those treatment combinations. The LSD value was 140. Table 2.29

and 2.30 summarize the mean comparison of face to face ultimate lateral resistance of

two-row vertically and two-row horizontally aligned multi-staple joints for number of

staples for each of two alignments and the mean comparison of face to face ultimate

lateral resistance of two-row vertically and two-row horizontally aligned multi-staple

joints for staple alignment for each of two staple numbers, respectively.

Table 2.29 The mean comparisons of face to face ultimate lateral resistance of two-row vertically and two-row horizontally aligned multi-staple joints for number of staples with respect to staple alignment.

Staple Number of Staples Alignment 6 8 Vertical 1624 (A) 2203 (B) Horizontal 1544 (A) 1984 (B)

Table 2.30 The mean comparisons of face to face ultimate lateral resistance of two-row vertically and two-row horizontally aligned multi-staple joints for staple alignment with respect to number of staples with respect to number of staples.

Number of Staple Alignment Staples Vertical Horizontal 6 1544 (A) 1624 (A) 8 1984 (A) 2203 (B)

2.5.3.3.2 Staple Alignment by Material Type Tables 2.31 and 2.32 show the mean comparison of face to face ultimate lateral

resistance of two-row-vertically and two-row horizontally-aligned multi-staple joints for

staple alignment for each of three material types and the mean comparison of face to face

ultimate lateral resistance of two-row-vertically and two-row horizontally-aligned multi-

staple joints for material type for each of two staple alignments. The results were based

on a one way classification with 6 treatments. The protected least significant difference

(LSD) multiple comparisons procedure at the 5 % percent significance level was

performed to determine the mean difference of those treatments using the LSD value of

204 pounds.

Table 2.31 The mean comparisons of face to face ultimate lateral resistance of two-row- vertically and two-row horizontally-aligned multi-staple joints for staple alignment with respect to material type.

Material Staple Alignment type Vertical Horizontal OSB-I 1529 (A) 1616 (A) OSB-II 1747 (A) 1947 (A) OSB-III 1956 (A) 2177 (B)

Table 2.32 The mean comparisons of face to face ultimate lateral resistance of two-row- vertically and two-row horizontally-aligned multi-staple joints for material type with respect to staple alignment.

Staple Material Type Alignment OSB-I OSB-II OSB-III Vertical 1529 (A) 1747 (A) 1956 (B) Horizontal 1616 (A) 1947 (B) 2177 (C)

2.5.3.3.3 Number of Staples by Material Type Tables 2.33 and 2.34 show the mean comparisons of face to face ultimate lateral resistance of two-row-vertically and two-row horizontally-aligned multi-staple joints for material type for each of number of staples and the mean comparisons for number of staples for each of three material types. The results were based on a one way classification with 6 treatments. The protected least significant difference (LSD) multiple comparisons procedure at the 5 % percent significance level was performed to determine the mean difference of those treatments using the LSD value of 130 pounds.

Table 2.33 The mean comparisons of face to face ultimate lateral resistance of two-row- vertically and two-row horizontally-aligned multi-staple joints for material type with respect to number of staples.

Number of Material Type Staples OSB-I OSB-II OSB-III 6 1411 (A) 1552 (B) 1789 (C) 8 1794 (A) 2142 (B) 2344 (C)

Table 2.34 The mean comparisons of face to face ultimate lateral resistance of two-row- vertically and two-row horizontally-aligned multi-staple joints for number of staples with respect to material type.

Material Number of Staples Type 6 8 OSB-I 1411 (A) 1794 (B) OSB-II 1552 (A) 2142 (B) OSB-III 1789 (A) 2344 (B)

2.5.3.3.4 Staple Alignment Effects According to Table 2.30, the mean ultimate lateral resistance of vertical and

horizontal joints with 6 staples is not significantly different. However, the mean ultimate

lateral resistance of vertical with 8 staples is significantly lower than the one horizontal

with 8 staples. According to Table 2.31, Staple alignment is not significant in the joints

made out of OSB-I and OSB-II; however, it is statistically significant in joints made out

of OSB-III. Thus, the staple number of 6 shows the same relationship with the material

types of OSB-I and OSB-II. Likewise, the staple number of 8 shows the same

relationship with the material types of OSB-III.

2.5.3.3.5 Material Type Effects According to Table 2.32, the mean ultimate lateral resistance of vertical joints made out of OSB-I and OSB-II is not significantly different, but they are significantly

lower than the ones made out of OSB-III. The mean ultimate lateral resistance of

horizontal joints made out of OSB-II is significantly higher than the ones made out of

OSB-I and lower the ones made out of OSB-III. According to Table 2.33, the mean ultimate lateral resistance of 6 staples joints made out of OSB-II is significantly higher than the ones made out of OSB-I and is significantly lower than the ones made out of

OSB-III. The same relation is valid for 8 staple joint as shown in Table. Therefore, material type has observable effect on the mean ultimate lateral resistance of the joints.

The number of staples effects shows the same relationship with horizontal staple alignment effects on material type.

2.5.3.3.6 Number of Staples Effects According to Table 2.29, the mean ultimate lateral resistance vertical 6 staples joints is significantly lower than the one with vertical 8 staples joints. The same relationship exists for the horizontal joints. Increasing the staple number has a parallel effect on the mean ultimate resistance of the joints. According to Table 2.34, the mean ultimate lateral resistance of OSB-I joints with 6 staples is significantly lower than the one with 8 staples. The same relationship exists for joints made out of OSB-II and OSB-

III. Thus, the number of staples is also has observable effect on the mean ultimate of lateral resistance of the joints.

2.5.3.4 Estimation Equations To quantify the effect of the number of staples on face lateral resistance of two- row horizontally-aligned multi-staple joints in a given OSB material, Equation (2.1) was fitted to the individual testing data points using the least squares method. To derive the regression constants the both sides of Equation (2.1) were taken log10 which yielded the

Equation (2.2). By setting y = log10 POR; b = log10 K; x = log10 N, the power Equation

(2.1) was converted to a linear equation. A regression was carried out among two-row horizontally-aligned 4-staple, two-row horizontally-aligned 6-staple, and two-row horizontally-aligned 8-staple joints. To run a regression analysis using the individual data point, each of 30 lateral shear test data points was arranged in the format shown in Table

2.35, i.e., three columns representing each specimen number, number of staples used in the numbered specimen, and its ultimate lateral shear load. Then these values were converted to their logarithmic 10 (log 10) values as shown in Table 2.36.

Table 2.35 Each of 30 lateral shear test data points was arranged in the following format for each OSB material, for instance, OSB-I.

Number of Number of Ultimate Load Specimens Staples (N) (P) (lb.) 1 4 842 2 4 787 3 4 909 ...... 11 6 1426 . . . 30 8 1804

Table 2.36 Conversion of number of staples and ultimate lateral load to their Log 10 value for OSB-I.

Number of Log10 N Log10 P Specimens (x) (y) 1 0.60206 2.925312 2 0.60206 2.895975 3 0.60206 2.958564 ...... 30 0.90309 3.256237

Then the regression analysis was run for each OSB group and parameter estimate

numbers were obtained to derive estimation equations. Table 2.37 gives the results from

linear regression analysis of OSB-I data.

Table 2.37 Results of linear regression analysis of OSB-I data.

Variable DF Parameter Pr > |t| Estimate Intercept 1 2.32 < .0001 Log N (a) 1 1.05 < .0001

First log 10 was taken for each side of estimation equations. Accordingly,

log 10 PSR = log 10 K + a log 10 N

2.32=log10K

K=102.32=209

Since b = 2.32, then log10 K = 2.32

Therefore, K = 102.32 = 209

After determining K value, K and a values were used to derive linear P equation for OSB-

I. Accordingly,

P=209× N1.05 (2.8) The same procedure was implemented for OSB-II and OSB-III and obtained their

P estimation equations. Accordingly, K and “a” values of P estimation equations for

OSB-II and OSB-III were listed in Table 2.38.

Table 2.38 Regression constants and associated r2 for derived equations for estimating mean ultimate lateral resistance loads of face-to-face two-row horizontally- aligned multi-staple connected joints in three OSB materials.

Material K a r2 Type OSB-I 209 1.05 0.92 OSB-II 178 1.22 0.90 OSB-III 207 1.2 0.94

To quantify the effects of the number of staples and material density on the face

lateral load resistance of two-row horizontally-aligned multi-staple connected joints in

OSB materials, the power Equation (2.6) was fitted to individual testing data points with

the least squares method. To run the regression of all OSB joints together, logarithmic values of ultimate load, number of staples, and density of OSBs were used. Table 2.39 was obtained from regression analysis among all two-row horizontally-aligned multi- staple joints.

Table 2.39 Results of linear regression analysis of all OSB data.

Variable DF Parameter Pr > |t| Estimate Intercept 1 -0.96 0.0040 Log D (a) 1 1.99 < .0001 Log N (b) 1 1.16 < .0001

The log 10 form of load estimation Equation (2.6) was taken. Accordingly, the

values, K, a, b, and r2 are 0.11, 1.99, 1.16, and 0.92 respectively in Equation (2.6) Table

2.40 summarizes prediction comparisons between observed and predicted mean staple lateral shear resistances of two-row horizontally-aligned multi-staple OSB joints using observed mean lateral shear resistances of two-row horizontally-aligned multi-staple joints and predicted mean lateral resistances of two-row horizontally-aligned multi-staple joints using Equations (2.1), and (2.6).

Table 2.40 Comparison of estimated ultimate lateral shear resistance loads of two-row horizontally-aligned multi-staple joints in OSB using Equations (2.1) and (2.6) with observed values.

Predicted Load Ratio Material Eq. (2.1)/ Eq. (2.6)/ D N Obs. Eq. (2.1) Eq. (2.6) Type Obs. Obs. 40.6 4 886 896 793 1.01 0.90 OSB-I 40.6 6 1405 1372 1269 0.98 0.90 40.6 8 1827 1855 1772 1.02 0.97 43.4 4 990 966 906 0.98 0.91 OSB-II 43.4 6 1585 1584 1450 1.00 0.91 43.4 8 2310 2250 2024 0.97 0.88 46.4 4 1082 1093 1035 1.01 0.96 OSB-III 46.4 6 1883 1777 1656 0.94 0.88 46.4 8 2472 2510 2312 1.02 0.94 aD = density of OSBs; N = number of staples; Obs =observed load values; Eq.= equation.

Results in Table 2.40 indicated that estimation equations Equation (2.1) and (2.6) are reasonable to estimate mean lateral shear resistances of two-row horizontally-aligned multi-staple joints.

2.5.4 Glued Joints

2.5.4.1 Load-Displacement Curve The typical load-displacement curve of glued gusset-plate joint is shown in Figure

2.14. Accordingly, there was always sharp behavior at the point where specimen failure occurred.

Figure 2.14 A typical load-displacement curve for glued joint in OSB.

2.5.4.2 Mean Ultimate Lateral Loads and Comparisons Mean ultimate lateral load values of face-to-face only glue connected joints and

their coefficients of variation are summarized in Table 2.41. Each value represents a

mean value of 10 specimens tested. Mean ultimate lateral loads of the joints with only

glue in the three different OSBs ranged from 1162 to 1198 pounds with coefficients of

variation ranged from 12 to 18 percent.

Table 2.41 Mean ultimate face lateral load values of only glued joints and their COVs.

Material Type OSB-I OSB-II OSB-III Glue 1162 (18) 1177 (12) 1198 (12)

The statistical relationships of mean ultimate lateral load values of face-to-face

only glue connected joints are summarized in Table 2.42. According to table, the mean

lateral load of face-to-face only glue connected joints made out of OSB-I, II, and III are not significantly different from one another.

Table 2.42 Mean comparisons of ultimate lateral load values of face-to-face only glue connected joints.

Material Type OSB-I OSB-II OSB-III Glue 1162 (A) 1177 (A) 1198 (A)

2.5.4.3 Mean Comparison among Only Glue Joints, Two-Row Vertically-Aligned Multi Stapled and Glued Joints Table 2.43 showed that the mean lateral shear resistances of only glue joints are

statistically lower than staple with glue joints in OSB-I and OSB-II but OSB-III. The

mean lateral shear resistances of two-row vertically-aligned 2-staple with glue joints is

significantly lower than the one of two-row vertically-aligned 4-staple with glue joint

while the means lateral shear resistances of two-row vertically-aligned 4-staple with glue

joints and two-row vertically-aligned 6-staple with glue joints are not significantly

different in each type OSB group. The mean lateral shear resistances of two-row

vertically-aligned 8-staple with glue joints are significantly higher than two-row vertically-aligned 6-staples with glue joints.

Table 2.43 The relationship among only-glue and glue-staple joints.

Number of Staples Material Only Glue with Glue with 4 Glue with 6 Glue with 8 Type Glue 2 Staples Staples Staples Staples OSB-I 1162 (A) 1317 (B) 1523 (C) 1578(C) 1761 (D) OSB-II 1177 (A) 1357 (B) 1553 (C) 1670 (C) 1974(D) OSB-III 1198 (A) 1297 (A) 1646 (B) 1590 (B) 2217 (C)

Table 2.44 illustrates the relationship among OSB-I, II, and III materials.

Accordingly, there is no statistical difference among OSB-I, II, and III in only glued

joints, glued joints with 2 staple, glued joints with 4 staple, and glued joints with 6 staple

except glued joints with 8 staple which are significantly different within material type.

Table 2.44 The relationship among OSB-I, II, and III.

Material Type Number of Staples OSB-I OSB-II OSB-III Only Glue 1162 (A) 1177 (A) 1198 (A) Glue with 2 Staples 1319 (A) 1357 (A) 1297 (A) Glue with 4 Staples 1523 (A) 1553 (A) 1646 (A) Glue with 6 Staples 1578( A) 1670 (A) 1590 (A) Glue with 8 Staples 1780 (A) 1939 (B) 2227 ( C)

Figure 2.15 shows typical load-displacement curve for only glue, only 2 staple,

only 4 staple, only 6 staple, and only 8 staple joints. It can be apparently observed that the

maximum load increases when number of staples increase. Increasing staple number made joints stronger, and it also contributed glue connection. Figure 2.15 shows typical load-displacement curve for only glue, 2 staple with glue, 4 staple with glue, 6 staple with glue, and 8 staple with glue joints.

Figure 2.15 Typical load-displacement curve two-row vertically-aligned multi-staple and glued OSB gusset-plate joints and only glued joint.

2.6 Conclusion Material type is statistically significant on the mean lateral resistance of single staple joints. Thus, OSB-II is significantly higher than OSB-I and lower than OSB-III for single staple joints. This situation is slightly different for one-row vertically-aligned multi-staple joint because the mean ultimate lateral resistance of one-row vertically- aligned 2 staple joints is not significantly different among OSB materials; however the mean ultimate lateral resistance of one-row vertically-aligned 3-staple joints in OSB-I is significantly lower than OSB-II and OSB-III which are not significantly different. The 74

mean ultimate lateral resistance of one-row vertically-aligned 4-staple joints is only

different among OSB-I and OSB-III because the one of OSB-II is not significantly

different from the others. For two-row vertically-aligned multi-staple joint, material type

has not significant effect on the mean ultimate resistance of joint. In other words, OSB-I,

OSB-II, OSB-III are not significantly different from one another. This indicated that increasing the staple number in joint, eliminated the material type effect on the lateral resistances of joint. The mean ultimate lateral resistances of two-row horizontally-aligned multi-staple joints indicated that material type has an effect on lateral resistances of joints. Thus, OSB-II is significantly higher than OSB-I and lower than OSB-III for single staple joints. These results indicated that staple alignment affected the mean ultimate lateral resistances of joints. Accordingly, horizontal alignment of staples on gusset-plate in the joints made significant difference among OSB-I, OSB-II and OSB-III while vertical alignment of staple on gusset-plate in the joints did not make significant difference among OSBs. Different distribution of stress could be the major effect on staples that horizontally or vertically placed on gusset-plate. Horizontal alignment of staple may allow OSB type show effects on the mean ultimate lateral resistances of joints. In addition, material type did not influence the mean ultimate lateral resistance of only glued OSB gusset-plate joints.

In general, the number of staples positively affected the mean ultimate lateral shear resistances of staple connected gusset-plate joints. The lateral shear resistance of one-row vertically-aligned multi-staple joints significantly increased as the number of staples increased from 2 to 4 with an increment one, and the lateral resistance of two-row vertically-aligned multi-staple joints significantly increased as the number of staples increased from 2 to 8 with an increment two. Increasing the number of staples from 6 to 8

with an increment two also increased the ultimate lateral resistances of two-row horizontally-aligned multi-staple joints.

There different equations Equation (2.1), (2.5), and (2.6) were derived to calculate mean ultimate lateral shear resistance load of one-row vertically-aligned multi-staple joints. In Equation (2.1), K and “a” regression constants were used in the equations. Since

K values are very close to the mean ultimate lateral shear resistances of single-staple joints (FO), FO values were used in Equation (2.5), and only one “a” value were used. The

Equation (2.6) included of number of staples and density of OSBs. All of three equations

yielded reasonable results for estimations of mean ultimate lateral shear resistance of one-

row vertically-aligned multi-staple joint. However, there are some advantages of using

some of these equations to the others. For example, Equation (2.5) has only one “a”

constant instead of having three different “a” constant in equations of Equation (2.1).

Equation (2.6) requires only density of materials instead of determining mean ultimate

lateral resistance of single-staple joints in equations of Equation (2.5).

The ratio of the face lateral resistance of two-row vertically-aligned multi-staple

joint to the face lateral resistance of one-row vertically-aligned multi-staple joint was 2.

Therefore, the estimation of the lateral resistance of two-row vertically-aligned multi-

staple joint is two times the lateral resistance estimation equation of one-row vertically-

aligned multi-staple joints. Therefore, to estimate the mean ultimate lateral resistance of

two-row vertically-aligned multi-staple joints, Equations (2.1), (2.5), and (2.6) were

multiplied with 2 in Equation (2.7). All the equations yielded very close results to the

observed ones. Therefore, using Equation (2.7) to estimate mean lateral resistance of two-

row vertically-aligned multi-staple joints is remarkable.

Equation (2.1) and Equation (2.6) were also used to calculate mean ultimate

lateral shear resistance load of two-row horizontally-aligned multi-staple joints. Equation

(2.6) consisted of number of staples and density of OSBs. Both equations yielded

reasonable results for estimations of mean ultimate lateral shear resistance of two-row horizontally-aligned multi-staple joint.

CHAPTER III

STATIC BENDING MOMENT CAPACITY OF GUSSET-PLATE JOINTS

3.1 Material and Methods

3.1.1 Approach This part of study evaluated and compared static bending moment resistances of

L-type and T-type, stapled, one-side, two gusset-plate joints constructed of three different

OSB materials. Mechanical analysis models of L-type and T-type gusset-plate joints were developed to predict their static moment resistances.

3.1.2 Specimen Configurations and Materials The general configuration of the joint in this part of study is shown in Figure 3.1.

Each joint consisted of a rail and a stump assembled with two narrower gusset plates that stapled to the upper and lower part of the same side of two connected members. Both members were constructed of OSB-I, OSB-II, and OSB-III. Gusset plates were constructed of one type ¾ inch 5-ply plywood.

Figure 3.1 Configuration of joint specimens for evaluating moment capacity of gusset- plate joints in OSB, a) L-type, end-to-side joints, b) T-type, end-to-side joints.

3.2 Experimental Design

3.2.1 L-type Joints A complete 2×3×3 factorial experiment with 10 replications per cell was conducted to evaluate significance of factors on moment capacity of the L-type, end-to- side, stapled, one-side, two gusset-plate joints. Factors are the number of staples (8 and

12), rail width (6, 7, and 8 inches), and material type (OSB-I, OSB-II, and OSB-III).

3.2.2 T-type Joints A complete 2×3×3 factorial experiment with 10 replications per cell was

conducted to evaluate significance of factors on moment capacity of the T-type, end-to-

side, stapled, one-side, two gusset-plate joints. Factors are the number of staples (8 and

12), stump width (4.5, 6, 7 inches), and material type (OSB-I, OSB-II, and OSB-III).

3.3 Model Development

3.3.1 L-type Joint Figure 3.2 illustrates mechanical analysis models used for deriving equation

predicting of the moment resistance load at proportional limit of L-type, end-to-side, staple-connected, one-side, two gusset-plate joints. It is assumed that the distance from the center line to the neutral axis is “e”. Distributions of multi-staple gusset plate joint stresses along lower compression side are assumed as shown in Figure 3.2.

Figure 3.2 Mechanical analysis model for deriving ultimate moment resistance loads of L-type, end-to-side joints.

By summing the forces in the horizontal direction as shown in Figure 3.2, the force at lower compression side can be obtained:

Σ F = 0 (3.1)

FC = FT - P (3.2)

where P = moment resistance load (lb.); FT = tensile force, acting along center line of the

top gusset plate (lb.); FC = compression force, acting along the center line of the

compression area (lb.).

By summing the moments at the point B as indicated in Figure 3.2, the ultimate load capacity prediction equation for L-type gusset-plate joints can be obtained:

Σ M = 0 (3.3)

Pd-( FT d1+FC d2) = 0 (3.4) Substituting Equation (3.2) into Equation (3.4) yielded Equation (3.5).

P = FT (d1+d2)/ (d+d2) (3.5) where d =distance between moment resistance load to neutral axis; d1 = distance between tensile force to neutral axis; d2 = distance between compression force to neutral axis (in.).

d1= (WR-WG)/2 + e (3.6)

d2 = [(WR/2) – e]/2 (3.7) where WR = rail width (in.); WG = gusset-plate width (in.).

Substituting Equations (3.6) and (3.7) into Equation (3.5) yielded Equation (3.8).

(3W − 2W + 2e) P = F R G (3.8) T (4d + W − 2e) R

FT value in Equation (3.8) comes from the lateral shear resistance load of the two- row vertically-aligned multi-staple joint at proportional limit. FT value is the lateral shear resistance load of the two-row vertically-aligned 4-staple joint at proportional limit for L- type joint with 8 staple, and it is the lateral shear resistance load of the two-row vertically-aligned 6-staple joint at proportional limit for L-type joint with 12 staple gusset-plate joints. Figure 3.3 shows two-row vertically aligned multi-staple joints and its proportional limit proportional limit load (FT).

Figure 3.3 a) two-row vertically-aligned 4 staples gusset-plate joint; b) Load- displacement curve of the joint.

3.3.1.1 e-value e values were determined by using the displacement of load head of L-type joints at proportional limit point and the displacement of load-displacement of the 4 and 6 staple lateral resistances of gusset plate joints at proportional limit point as shown in

Figure 3.4.

Figure 3.4 Diagram showing the position of e, load-head displacement, and multi- staple joint displacements.

a R = b (3.9) where a = load head displacement at proportional limit; b = multi-staple joint displacement at proportional limit; R = the ratio of a to b; d=distance between load head to rail.

W e +R + d R = 2 W W e +R − G 2 2 (3.10)

W W R (1 − R) + G R + d e = 2 2 − (R 1) (3.11)

3.3.2 T-type Joint Figure 3.5 shows mechanical analysis models used for deriving prediction

equation of the moment resistance load at proportional limit of T-type, end-to-side staple- connected, one-side, two gusset-plate joints. It is assumed that the distance from the center line to the neutral axis is “e”. Distributions of multi-staple gusset-plate joint stresses

along lower compression side are assumed as shown in Figure 3.5.

Figure 3.5 Mechanical analysis model for deriving ultimate moment resistance loads of T-type, end-to-side joints.

By summing the forces in the vertical direction as indicated in Figure 3.5, the force at lower compression side can be obtained:

Σ Fy = 0 (3.12)

FC = FT (3.13)

where FT = tensile force (lb.); FC = compression force (lb.)

By summing the moments at point B as indicated in Figure 3.5, the ultimate

moment resistance load prediction equation for T-type gusset-plate joints can be

obtained:

Σ M = 0 (3.14)

Substituting Equation (3.13) into Equation (3.4) yielded Equation (3.15).

P= FT (d1+d2)/d (3.15)

where d =distance between moment resistance load to neutral axis; d1 = distance

between tensile force to neutral axis; d2 = distance between compression force to neutral

axis (in.).

d1= (WS-WG)/2 +e (3.16)

d2= (WS/2-e)/2 (3.17)

where WS =Stump width; WG= gusset plate width;

Then, substituting Equations (3.16) and (3.17) into Equation (3.15) yielded

Equation (3.18).

(3Ws − 2WG + 2e) P = FT (3.18) 4d

3.3.2.1 e-value The calculation of e value for T-type end-to-side joint was based on the

assumption of angle (θ) between center line of the stump and displacement of load-head.

It is assumed that the same angle existed for multi-staple lateral joint displacement as

shown in Figure 3.6. The displacement of the load head at proportional limit and multi- staple joints at proportional limit yielded e-value. Accordingly,

Figure 3.6 Diagram showing the θ displacement angle of T-type end-to-side joints.

The similar triangles have the same angle θ, yielded Equation (3.20) for e calculation.

a d R = = b WW (e +SG − ) (3.19) 2 2

W W d − R( S − G ) e = 2 2 (3.20) R where d= distance between load head to rail (in.); a= the displacement of load head at proportional limit(in.); b= the displacement of the multi-staple joint at proportional limit(in.); R= ratio of a to b.

3.4 Specimen Preparation

3.4.1 L-type Joints A rail and a stump were the two principal members that comprised an L-type joint. These two members were connected by a pair of gusset-plates attached to one side of the joint. The gusset plates were constructed of one type of frame, ¾ inch thick 5-ply southern yellow pine plywood. The full-size sheet (4 by 8 foot) was constructed with one center ply placed to parallel to the face and two plies placed perpendicular to the face, and two surface plies placed parallel to the sheet 8-foot direction. The stumps were 23 inches long, 4.5 inches wide. There were three different widths for rails which were 6, 7, and 8 inches and the length of the rail was 7 inches. All joints made out of OSB-I, II, and

III, and total 180 L-type specimens for bending test. To prepare these members, Rip saw for parallel cut to the direction of full size sheet and the Radial arm saw for perpendicular cut to the direction of full size sheet were used. The gusset-plate size is 2x6 inches, and staple numbers are 8 and 12. The staple were SENCO 16-gage galvanized chisel-end- point types with a crown width of 7/16 inches. The leg width of the staples was 0.062 inch, and thickness was 0.055 inch. The staple were coated with Sencote coating, nitro- cellulose based plastic.

(a) (b)

(e) (f)

Figure 3.7 L-type joints with: a) 6 in. wide rail with 8-staple joint, b) 7 in. wide rail with 8-staple joint, c) 8 in. wide rail with 8-staple joint, d) 6 in. wide rail with 12-staple joint, e) 7 in. wide rail with 12-staple joint, and e) 8 in. wide rail with 12-staple joint.

Figure 3.7 shows all L-type joint groups made out of OSB-II. Each group has 10 replications. All cut members and gusset plates were conditioned in an equilibrium moisture content chamber at 65± 4ºF and 41±1 relative humidity. The staple were driven into the specimens with air staple guns with 70 psi pressure. Staple crown orientation at an angle of 45 degrees to gusset plate face grain was considered in all specimens. All tests were conducted immediately after staples were driven into gusset plate joint members.

3.4.2 T-type Joints As in L-type joints, a rail and a stump were the two principal members that comprised a T-type joint. These two members were connected by a pair of gusset-plates attached to one side of the joint. The specimens were constructed with the same type plywood with L-type joints. The rails were 11.5 inches long, 7 inches wide. There were three different widths for stump which were 4.5, 6, and 7 inches and the length of the stump was 16 inches. All joints made out of OSB-I, II, and III, and total 180 T-type specimens were prepared. The cutting, preparation, and conditioning procedure of the joints was the same with ones of L-type joints. Figure 3.8 shows all joint groups made out of OSB-I for T-type joints. Each group has 10 replications.

(a) (b)

(e) (f)

Figure 3.8 T-type joints with: a) 4.5 inch wide stump with 8-staple joint, b) 6 inch wide stump with 8-staple joint, c) 7 inch wide stump with 8-staple joint, d) 4.5 inch wide stump with 12-staple joint, e) 6 inch wide stump with 12- staple joint, and e) 7 inch wide stump with 12-staple joint.

3.5 Testing Static bending test specimens were tested on a hydraulic SATEC universal testing machine at a load rate of 0.10 in/min. The placement of L-type and T-type gusset-plate joint is shown in Figure 3.9. The joints were bolted to the metal apparatus to be fixed during the bending test. The load was calibrated to not leave a gap between the load head and specimen before initiation of loading specimens. Vertical load were applied on the stump 12 inches away from rail of the joint for each rail of the joints. The test continued until the joints were disabled. The ultimate bending load, displacement, and failure modes were recorded.

(a)

(b)

Figure 3.9 Test set-up for evaluation of bending moment resistances of a) L-type; b) T-type gusset-plate joints.

3.6 Results and Discussion

3.6.1 L-type Joints

3.6.1.1 Load-Displacement Curve Figure 3.10 shows a typical load-displacement curve of L-type joints. When loading the L-type bending specimen, in the beginning of the process, a rising loading occurred until proportional limit. Beyond proportional limit, a low-rate loading occurred until maximum load point. After the maximum point, the loading gradually decreased.

The load-displacement curves of L-type joints are similar to the curves of one-row and two-row vertically aligned multi-staple lateral withdrawal joints.

Figure 3.10 A typical load-displacement curve of L-type, end-to-side, staple-connected gusset-plate joints in OSB.

3.6.1.2 Failure Modes Specimen failure always first occurred at the gusset plate in the tension side. The failure modes for specimen were recorded. In general, five different types of failure modes were observed in the specimens. They are: the staples legs lateral shear withdrawal from rail (wr); the staples legs lateral shear withdrawal from stump (ws); the staples legs lateral shear withdrawal the same amount from rail and stump (both); gusset plate rupture (g.p.r.); stump rupture, respectively. Among 180 tested specimens, 49 % percent of specimens showed ws type of failure, 24 % percent of specimens showed wr type of failure, 8 % percent of specimens showed both type of failure, 13 % percent of specimens showed g.p.r. type of failure, and 6 % percent of specimens showed p.r. type of failure. Figure 3.11 illustrates the five failure modes.

(a)

Figure 3.11 The failure modes : a) the staples legs lateral shear withdrawal from rail (wr); b) the staples legs lateral shear withdrawal from stump (ws); c) the staples legs lateral shear withdrawal the same amount from rail and stump (both); d)gusset plate rupture (g.p.r.); e)stump rupture.

(b)

(d)

(e) Figure 3.11 (Continued)

3.6.1.3 Mean Comparisons Table 3.1 summarizes the mean ultimate static moment resistance load of L-type

joints and their cov values. A three factor ANOVA general linear model procedure was performed for individual joint data to analyze main effects and their interactions on the

mean ultimate moment resistance loads of L-type joints and its results were summarized in Table 3.2.

Table 3.1 Mean ultimate static bending moment resistance loads and their coefficients of variation of L-type, end-to-side, staple-connected gusset-plate joints in OSB for ten observations of each combination of material type, number of staples, and rail width.

Number of Staples Material 8 12 Type Rail Width (in.) 6 7 8 6 7 8 OSB-I 245 (12) 271 (14) 297 (13) 365 (6) 387 (11) 430 (9) OSB-II 237 (12) 276 (11) 314 (10) 388 (7) 413 (11) 402 (19) OSB-III 264 (11) 302 (6) 403 (10) 410 (8) 412 (22) 467 (16)

Table 3.2 General linear model procedure output for main effects and interactions of 2 by 3 by 3 L-type gusset-plate joint factorial experiment with 10 replication of each combination.

Source DF F Value Pr > F MT 2 17.34 <.0001 S NOS 1 310.84 <.0001 S RW 2 33.85 <.0001 S MT* NOS 2 0.58 0.5637 NS MT*RW 4 2.62 0.0372 MS NOS*RW 2 3.69 0.0270 MS MT*NOS*RW 4 1.70 0.1525 NS aS = significant; NS = not significant; MS = marginally significant; MT = material type; NOS = number of staples; RW = rail width.

The ANOVA results indicated that the three-factor interaction was not statistically

significant at the 5 percent significance level. Among the three two-factor interactions,

two of them, material type by rail width and the number of staples by rail width, were

statistically significant at 5 percent significance level. Therefore, these two significant

two-factor interactions were analyzed.

3.6.1.3.1 Material Type by Rail Width Interaction A one way classification was created with nine treatment combination of material type by rail width. The least significant difference (LSD) multiple comparison procedure at a 5 percent significant level was performed to determine the mean differences of those treatment combinations. The LSD value was 48. Table 3.3 and 3.4 summarize the mean comparison of ultimate bending load of L-type joints for rail width for each of three materials and the mean comparisons of the ultimate bending load of L-type joints for material type for each of the three rail widths.

Table 3.3 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, stapled, one-side, two gusset-plate joints for rail width for each material type.

Material Rail Width(in.) Ratio Type 6 7 8 7/6 8/6 8/7 OSB-I 306 (A) 330 (AB) 363 (B) 1.08 1.19 1.10 OSB-II 313(A) 344 (AB) 358 (B) 1.10 1.14 1.04 OSB-III 335 (A) 364 (A) 434 (B) 1.09 1.30 1.19 Average 1.09 1.21 1.11

Table 3.4 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, stapled, one-side, two gusset-plate joints for material type for each rail width.

Rail Material Type Ratio Width OSB-I OSB-II OSB-III II/I III/I III/II (in.) 6 306 (A) 313(A) 335 (A) 1.02 1.09 1.07 7 330 (A) 344 (A) 364 (A) 1.04 1.1 1.06 8 363 (A) 358 (A) 434 (B) 0.98 1.20 1.21 Average 1.01 1.13 1.11

3.6.1.3.2 Number of Staples by Rail Width Interaction A one way classification was created with six treatment combination of material

type by rail width. The least significant difference (LSD) multiple comparison at a 5

percent significant level was 26. Table 3.5 and 3.6 summarize mean comparisons of L- type joints for rail width with respect to number of staples and mean comparison of L- type joints for number of staples with respect to rail width.

Table 3.5 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, stapled, one-side, two gusset-plate joints for each rail width for each number of staples.

Number Rail Width (in.) of Staples 6 7 8 8 248(A) 283 (B) 338 ( C) 12 386 (A) 409(AB) 432 (B)

100

Table 3.6 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, stapled, one-side, two gusset-plate joints for number of staples for each rail width.

Rail Number of Staples Width (in.) 8 12 6 248 (A) 386 (B) 7 283 (A) 409 (B) 8 338 (A) 432 (B)

3.6.1.3.3 Rail Width Effects In accordance with Table 3.3, the mean moment resistance loads of 6 inch rail L-

type joints are not significantly different from the ones of 7 inch rail L-type joints in

OSB-I. Likewise, the mean moment resistance loads of 7 inch rail L-type joints are not significantly different from the ones of 8 inch rail L-type joints in OSB-I. However, the mean moment resistance loads of 6 inch rail L-type joints are significantly lower from the ones of 8 inch rail L-type joints in OSB-I. The same relationship exists among L-type joints in OSB-II. This may cause by number staple of 12 because L-type joints with 12 staple shows the same relationship among different rail width as shown in Table 3.5. The mean moment resistance loads of 6 and 7 inch rail of L-type joints are not significantly different, but they are significantly lower than ones of 7 inch rail of L-type joints in OSB-

III. As shown in Table 3.5, the mean moment resistance loads of 6, 7, and 8 inch rail L- type joints with 8 staple are significantly different from one another. Table 3.7 also summarizes rail width effects and their ratios with respect to number of staples and material type.

101

Table 3.7 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, stapled, one-side, two gusset-plate joints for rail width for each number of staples and material types.

Number Material Rail Width (in.) Ratio of Type 6 7 8 7/6 8/6 8/7 Staples I 245 271 297 1.11 1.21 1.10 8 II 237 276 314 1.16 1.32 1.14 III 264 302 403 1.14 1.53 1.33 I 365 387 430 1.06 1.18 1.11 12 II 388 413 402 1.06 1.04 0.97 III 410 412 465 1.01 1.14 1.13 Average 1.09 1.24 1.13

3.6.1.3.4 Material Type Effects According to Table 3.4, the mean moment resistance loads of 6, 7, and 8 inch rail

L-type joints with is not significantly different from one another among OSB materials

except the mean moment resistance loads of OSB-III 8 inch rail L-type joints which are significantly higher than the others. These results are similar to the ones in Table 2.25.

Likewise, the mean lateral shear resistances of two-row vertically-aligned 2, 4, and 6 staples joints are not significantly different in material type; however, two-row 8 staple joints in OSB-III are significantly higher than ones in OSB-I and OSB-II. Therefore these two different joints group can be related. Table 3.8 also summarizes material type effects and their ratios with respect to number of staples and rail width.

102

Table 3.8 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, one sided, two gusset-plate joints for material type for each number of staples and rail widths.

Number Rail Material Type Ratio of Width I II III II/I III/I III/II Staples (in.) 6 245 237 264 0.97 1.08 1.11 8 7 271 276 302 1.02 1.11 1.09 8 297 314 403 1.06 1.36 1.28 6 365 388 410 1.06 1.12 1.06 12 7 387 413 412 1.07 1.06 0.99 8 430 402 465 0.93 1.09 1.16 Average 1.02 1.14 1.12

3.6.1.3.5 Number of Staples Effects Table 3.6 shows the interaction between rail width and number of staples. The

mean moment resistance loads of 6 inch rail L-type joints with 8 staples are significantly lower from the ones of 6 inch rail L-type joints 12 staples. Likewise, the same relationships exits for 7 and 8 inch width rail L-type joints. Mean comparisons of ultimate moment resistance loads of L-type, end-to-side, one sided, two gusset-plate joints for number of staples for each material type and rail widths. Table 3.9 also summarizes mean comparisons of ultimate moment resistance loads of L-type gusset- plate joints for number of staples for each material type and rail widths.

103

Table 3.9 Mean comparisons of ultimate moment resistance loads of L-type, end-to- side, one sided, two gusset-plate joints for number of staples for each material types and rail widths.

Material Rail Width Number of Staples Ratio Type (in.) 8 12 12/8 6 245 365 1.49 OSB-I 7 271 387 1.43 8 297 430 1.45 6 237 388 1.64 OSB-II 7 276 413 1.50 8 314 402 1.28 6 264 410 1.55 OSB-III 7 302 412 1.36 8 403 465 1.16 Average 1.43

3.6.2 T-type Joint

3.6.2.1 Load-Displacement Curve Figure 3.12 shows a typical load-displacement curve of T-type joints. Although some of the load-displacement curve of individual data of T-type joints shows similarity with the typical load-displacement curve of L-type joints, Figure 3.11 type curve is more general one among all of the T-type data curves.

104

Figure 3.12 A typical load-displacement curve of T-type, end-to-side, staple-connected, one-side, two gusset-plate joints in OSB.

3.6.2.2 Failure Modes For T-type end-to-side gusset-plate joints, the same failure modes were observed

with L-type gusset-plate joints. Accordingly, among 180 tested specimens, 45 % percent

of specimens showed wr type of failure, 34 % percent of specimen failed showed ws type of failure, 13 % percent of specimens showed both type of failure, 5 % percent of specimens showed g.p.r. type of failure, and 3 % percent of specimens showed p.r. type

of failure. Figure 3.11 shows five different failure modes. In addition to these, bottom

failure was observed at gusset plate in the compression side for T-type of specimens. This

type of failure was classified as bottom failure, little bottom failure, and no bottom

failure. Among 180 specimens, 70 % percent of specimen showed bottom failure, 25 %

105

percent of specimens showed little bottom failure, and 5 % percent of specimen showed no bottom failure. Figure 3.13 shows bottom failure modes.

(a)

(b)

Figure 3.13 Typical failure modes of T-type joints: a) Bottom failure, b) little bottom failure, and c) no bottom failure.

106

(c)

Figure 3.13 (Continued)

3.6.2.3 Mean Comparisons Table 3.10 summarizes the mean ultimate load of T-type end-to-side gusset-plate joints and their coefficients of variation (COV). The ultimate moment resistance loads T- type, end-to-side, staple-connected gusset-plate joints in OSB were statistically analyzed with 3 ways ANOVA table and checked whether there are interaction effects among factors which are material (OSB-I, OSB-II, OSB-III), staple number (8 and12), and stump (4.5, 6, and 7 in.).

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Table 3.10 Mean ultimate moment resistance loads and their coefficients of variation of T-type, end-to-side, staple-connected, one-side, two gusset-plate joints in OSB for ten observations of each combination of material type, number of staples, and stump width.

Number of Staples Material Type 8 12 Stump Width (in.) 4.5 6 7 4.5 6 7 OSB-I 220 (5) 314 (5) 386 (10) 301 (4) 445 (5) 562 (6) OSB-II 220 (6) 334 (9) 461 (10) 297 (8) 485 (7) 642 (7) OSB-III 297 (7) 460 (7) 534 (8) 373 (6) 609 (8) 706 (10)

Table 3.11 General linear model procedure output for main effects and interactions of 2 by 3 by 3 T-type gusset-plate joint factorial experiment with 10 replication of each combination.

Source DF F Value Pr > F MT 2 202.63 <.0001 S NOS 1 637.11 <.0001 S SW 2 853.44 <.0001 S MT*NOS 2 0.15 0.8569 NS MT*SW 4 12.05 <.0001 S NOS*SW 2 30.52 <.0001 S MT*NOS*SW 4 0.22 0.9267 NS aS = significant; NS = not significant; MT = material type; NOS = number of staples; SW = stump width.

Table 3.11 indicates the 3-way interaction (Material Type × Number of Staples ×

Stump Width) is not significant, and the 2-way interaction, material type by number of

staples, is not significant at 5 percent significance level. The other 2-way interactions,

material type by stump width and number of staples by stump width, are statistically

significant. Therefore, these two interactions were analyzed.

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3.6.2.3.1 Number of Staples by Stump Width Interaction Tables 3.12 and 3.13 show mean comparisons of ultimate bending loads of T-type

joints for stump width for each of staple number and mean comparisons of ultimate

bending loads of T-type joints for number of staples for each of stump width, respectively. The results were based on a one way classification with 6 treatments. The protected least significant difference (LSD) multiple comparisons procedure at the 5 % percent significance level was performed to determine the mean difference of those treatments using the LSD value of 34 pounds.

Table 3.12 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for stump width for each number of staples.

Number Stump Width (in.) of 4.5 6 7 Staples 8 246 (A) 369 (B) 460 (C) 12 323 (A) 513 (B) 637 (C)

Table 3.13 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for number of staples for each stump width.

Stump Number of Staples Width (in.) 8 12 4.5 246 (A) 323 (B) 6 369 (A) 513 (B) 7 460 (A) 637 (B)

3.6.2.3.2 Material Type by Stump Width Interaction The results were based on a one way classification with 9 treatments. The least

significant difference (LSD) multiple comparisons procedure at the 5 percent significance

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level was performed to determine the mean difference of those treatments using the LSD

value of 49 pounds. Tables 3.14 and 3.15 show mean comparisons of ultimate bending

loads of T-type joints for stump width with respect to material type and mean

comparisons of ultimate bending loads of T-type joints for material type with respect to

stump width.

Table 3.14 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for stump width for each material type.

Material Stump Width (in.) Type 4.5 6 7 OSB-I 260 (A) 379 (B) 474 (C) OSB-II 258 (A) 409 (B) 551 (C) OSB-III 345 (A) 535 (B) 620 (C)

Table 3.15 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for material type for each stump width.

Stump Material Type Width (in.) OSB-I OSB-II OSB-III 4.5 260 (A) 258 (A) 345 (B) 6 379 (A) 409 (A) 535 (B) 7 474 (A) 551 (B) 620 (C)

3.6.2.3.3 Stump Width Effects As can be seen in Table 3.12, the ultimate bending loads of T-type joints attached with 8 staples are significantly different among stump width 4.5, 6, and 7 inches. The same relationship is valid for the ultimate bending loads of T-type joints attached with 12

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staples. The same relation among three different size stump width can be seen in Table

3.14. Thus, T-type joints made out of OSB-I, OSB-II, and OSB-III with 4.5, 6 and 7 inch stump width are significantly different from one another. Additionally, Table 3.16 also indicates stump width effects and their ratios in accordance with number of staples and material type.

Table 3.16 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for stump width for each combination of number of staples and material types.

Number Material Stump Width (in.) Ratio of Staples Type 4.5 6 7 6/4.5 7/4.5 7/6 I 220 314 386 1.43 1.75 1.23 8 II 220 334 461 1.52 2.10 1.38 III 297 460 534 1.55 1.80 1.16 I 301 445 562 1.48 1.87 1.26 12 II 297 485 642 1.63 2.16 1.32 III 373 609 706 1.63 1.89 1.16 Average 1.54 1.93 1.25

3.6.2.3.4 Number of Staples Effects According to Table 3.13, the ultimate bending resistances of 12 staples T-type

joints are significantly higher than the ones of 8 staple T-type joints in 4.5 inch stump.

The same relationship exists for 6 and 7 inch stump width. Table 3.17 also summarizes

number of staples effects and their ratios with respect to material type and stump width.

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Table 3.17 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for number of staples for each combination of material types and stump widths.

Stump Number of Ratio Material Width Staples Type (in.) 8 12 12/8 4.5 220 301 1.37 OSB-I 6 314 445 1.42 7 386 562 1.46 4.5 220 297 1.35 OSB-II 6 334 485 1.45 7 461 642 1.39 4.5 297 373 1.26 OSB-III 6 460 609 1.32 7 534 706 1.32 Average 1.37

3.6.2.3.5 Material Type Effects As shown in Table 3.15, the ultimate mean loads of 4.5 inch stump T-type joints made out of OSB-I and OSB-II are not significantly different, but they are significantly lower than those which were made out of OSB-III. The same relationship exists among 6 inch width stump T-type joint in OSB-I, OSB-II, and OSB-III. These results show similarity with the mean lateral load of two-row vertically-aligned 8 staple joints in Table

2.25, but the ones with two 2, 4, and 6 staples are not significantly different. However, the mean ultimate loads of 7 inch stump T-type joints in OSB-II is significantly higher than those in OSB-I and lower than those in OSB-III, respectively. This relationship is the same relationship with the ultimate lateral withdrawal load of single staple joints in

OSB-I, OSB-II, and OSB-III as shown Table 2.3. In addition to these, Table 3.18 also summarizes material type effects and their ratios with respect to each combination of number of staples and stump width.

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Table 3.18 Mean comparisons of ultimate moment resistance loads of T-type, end-to- side, one-side, two gusset-plate joints for material type for each number of staples and stump widths.

Number Stump Material Type Ratio of Staples Width (in.) I II III II/I III/I III/II 4.5 220 220 297 1.00 1.35 1.35 8 6 314 334 460 1.06 1.46 1.38 7 386 461 534 1.19 1.38 1.16 4.5 301 297 373 0.99 1.24 1.26 12 6 445 485 609 1.09 1.37 1.26 7 562 642 706 1.14 1.26 1.10 Average 1.08 1.34 1.25

3.6.3 Ratio of Proportional Limit to Ultimate Moment Load The loads at proportional limit point and maximum point were determined for all individual L-type and T-type joints. The ratio of moment load at proportional limit to its corresponding ultimate moment load was calculated for all individual data points.

Eventually an overall ratio value was obtained as shown in Table 3.19.

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Table 3.19 Mean ratios of proportional limit moment resistance load to its corresponding maximum moment resistance load of L-type and T-type joints.

Rail Width (in.) and Number of Staples Over all Material 6 7 8 Type 8 12 8 12 8 12 OSB-I 0.46 (15) 0.59 (12) 0.5 (14) 0.57 (9) 0.52 (8) 0.56 (9) 0.53 (9) OSB-II 0.49 (10) 0.48 (7) 0.48 (11) 0.51 (9) 0.56 (13) 0.51 (12) 0.51 (6) OSB-III 0.51 (8) 0.48 (8) 0.53 (12) 0.5 (13) 0.48 (8) 0.49 (9) 0.50 (4) Over all 0.51 (3) Stump Width (in.) and Number of Staples Over all Material 4.5 6 7 Type 8 12 8 12 8 12 OSB-I 0.56 (7) 0.56 (7) 0.54 (9) 0.55 (8) 0.56 (6) 0.56 (9) 0.56 (2) OSB-II 0.54 (9) 0.56 (10) 0.5 (7) 0.55 (6) 0.51 (7) 0.46 (10) 0.52 (7) OSB-III 0.53 (6) 0.51 (7) 0.49 (8) 0.51 (8) 0.5 (9) 0.5 (12) 0.51 (3) Over all 0.53 (5) Over all for L-type and T-type joint 0.52 (3)

As shown in Table 3.19, the overall ratio of proportional limit moment resistance

load to maximum moment resistance load is 0.52. This means the maximum point load is

approximately two times greater than the proportional limit load. Accordingly,

PMax=2×PPL (3.21)

where, PMax = the maximum moment resistance load; PPL = the proportional limit moment resistance load.

3.6.4 Model Verification

3.6.4.1 L-type Joints To obtain the ratio of predicted P value of the L type joints at proportional limit point to observed P load value of the L-type joints, first of all e values were determined

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by using displacement of load head of L-type joints at proportional limit and

displacement of the two-row vertically-aligned 4 and 6 staples gusset plate joints at

proportional limit point as it was previously mentioned. To calculate e values of L-type joints, displacement of two-row vertically-aligned multi-staple joint at proportional limit were averaged in Table 3.20. Then e values were calculated.

Table 3.20 Average value two-row vertically-aligned multi staple displacement at proportional limit (displacement 1) and of load head displacement at proportional limit (displacement 2).

Material Type 8 staple Disp.1 Disp.2 6 0.074 0.24 OSB I 7 0.074 0.27 8 0.074 0.25 6 0.068 0.46 OSB II 7 0.068 0.44 8 0.068 0.45 6 0.073 0.44 OSB III 7 0.073 0.41 8 0.073 0.46 average 0.07 0.45 12staple Disp.1 Disp.2 6 0.090 0.34 OSB I 7 0.090 0.37 8 0.090 0.40 6 0.081 0.42 OSB II 7 0.081 0.42 8 0.081 0.47 6 0.086 0.50 OSB III 7 0.086 0.54 8 0.086 0.55 average 0.09 0.45

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As shown in Table 3.20, displacement 1 and displacement 2 were averaged within

8 staple and 12 staple joints, and these averaged numbers were utilized to calculate e value. The reason averaging the displacement is because the interactions of 6 inches rail

L-type joints is not significant for OSB-I, OSB-II, and OSB-III as shown in Table 3.4.

The same relationship exists for 7 and 8 inches rail L-type joints when they are compared among OSB-I, OSB-II, and OSB-III. Table 3.21 lists the variables to calculate the e value.

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Table 3.21 Two-row-vertically-aligned 4 and 6 staple joint displacement values at proportional limit and load head displacement values of the L-type gusset- plate joints at proportional limit.

Number Material of W Dis 1 Dis2 R d W e Type R G Staple 6 0.07 0.45 6.43 12 2 0.39 OSB I 7 0.07 0.45 6.43 12 2 -0.11 8 0.07 0.45 6.43 12 2 -0.61 6 0.07 0.45 6.43 12 2 0.39 8 OSB II 7 0.07 0.45 6.43 12 2 -0.11 8 0.07 0.45 6.43 12 2 -0.61 6 0.07 0.45 6.43 12 2 0.39 OSB III 7 0.07 0.45 6.43 12 2 -0.11 8 0.07 0.45 6.43 12 2 -0.61 6 0.09 0.45 5.00 12 2 1.25 OSB I 7 0.09 0.45 5.00 12 2 0.75 8 0.09 0.45 5.00 12 2 0.25 6 0.09 0.45 5.00 12 2 1.25 12 OSB II 7 0.09 0.45 5.00 12 2 0.75 8 0.09 0.45 5.00 12 2 0.25 6 0.09 0.45 5.00 12 2 1.25 OSB III 7 0.09 0.45 5.00 12 2 0.75 8 0.09 0.45 5.00 12 2 0.25 aDis 1= the displacement of lateral shear resistance of two-row vertically-aligned 4- staple joints for 8 staple L-type joints at proportional limit point and of lateral shear resistance of two-row vertically-aligned 6-staple joints for 12 staple L-type joints at proportional limit point; Dis 2= the displacement of L-type joints at proportional limit point; WR= rail width; WG= gusset-plate width; d= distance between moment resistance load to rail; R= ratio of Dis.2 to Dis.1.

For 6 inch rail L-type 8 staple joints in OSB-I, R ratio and e value were calculated as following.

a 0.45 R = = = 6.43 b 0.07 6 2 (1 − 6.43) + 6.43 + 12 e = 2 2 − (6.43 1) 117

e = 0.39 inch.

Figure 3.14 Diagram showing the load arm of L-type end-to-side gusset-plate joint.

The load arm “d” used in P calculations was calculated with respect to different rail width and e values. As shown in Figure 3.14, the load arm consisted of the summation of e, the rail width, and 12 inches. Accordingly, the load arm d for 6 inch rail

L-type joints; d = 12+WR/2+e (3.22) d = 12+3+0.3947 = 15.39

To calculate the predicted P load for 8 stapled L-type joints, i.e., Equation (3.8) was used. For 6 in. rail: WR = 6 in., WG = 2 in., e = 0.39, and d = 15.39 inches. Then all the numbers was substituted to the Equation (3.8).

(3* 6 − 2* 2 + 2* 0.39) P = 502 + − (4*15.39 5 2* 0.39)

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P =111 lb. The observed P load value of 6 inch rail L-type joint is 116 lb. Then,

Ratio = 111/111= 1.00

Table 3.22 lists the all variables to estimate static moment resistance of L-type joints. As shown in Table 3.22, the ratios of L-type joints are ranking between 0.70- 1.07 with an average 0.92. Therefore, the model to estimate static bending moment resistances of L-type gusset-plate joint is reasonable.

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Table 3.22 The ratio of predicted P value of the L type end-to-side, one sided, two gusset-plate joints at proportional limit point to observed P load value of the L-type end-to-side, one sided, two gusset-plate joints.

Number Material of W W e F d P P . Ratio Type R G T pre. obs Staples 6 2 0.39 502 15.39 111 111 1 OSB-I 7 2 -0.11 502 15.39 123 139 0.88 8 2 -0.61 502 15.39 133 155 0.86 6 2 0.39 502 15.39 111 116 0.96 8 OSB-II 7 2 -0.11 502 15.39 123 132 0.93 8 2 -0.61 502 15.39 133 154 0.86 6 2 0.39 505 15.39 112 133 0.84 OSB-III 7 2 -0.11 505 15.39 124 159 0.78 8 2 -0.61 505 15.39 134 191 0.7 6 2 1.25 804 16.25 194 217 0.89 OSB-I 7 2 0.75 804 16.25 211 221 0.95 8 2 0.25 804 16.25 227 241 0.94 6 2 1.25 776 16.25 187 187 1 12 OSB-II 7 2 0.75 776 16.25 204 190 1.07 8 2 0.25 776 16.25 219 210 1.04 6 2 1.25 805 16.25 194 193 1.01 OSB-III 7 2 0.75 805 16.25 211 224 0.94 8 2 0.25 805 16.25 228 236 0.97 a WR= rail width; WG= gusset-plate width; d= distance between moment resistance load to

the neutral axis; FT =the lateral resistance load of two-row vertically-aligned 4 and 6 staple joint load at proportional limit point; Ppre.=the predicted load of L-type end-to-side,

one sided, two gusset-plate-joint; P obs.=the moment resistance load of L-type end-to-side, one sided, two gusset-plate-joint at proportional limit point.

3.6.4.2 T-type Joints As it formerly mentioned, the calculation of e value for T-type joints was based the displacement of load head T-type gusset-plate joint at proportional limit and

displacement of the two-row vertically aligned multi-staple joints. Equations (3.20) were

used to calculate e value. Accordingly,

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For 8 staple 4.5 inch stump size T-type gusset-plate joints made of OSB-I, a R = = 5.46in. b

4.5 2 12 − 5.46( − ) e = 2 2 5.46

e = 0.95 in.

Table 3.23 lists all variable to calculate each e value for each type of T-type gusset-plate joint.

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Table 3.23 Two-row-vertically-aligned 4 and 6 staple joint displacement values at proportional limit and load head displacement values of the T-type gusset- plate joints at proportional limit.

Number Material of W Disp.1 Disp.2 R W d e Type S G Staple 4.5 0.07368 0.4025 5.46 2 12 0.95 OSB I 6 0.07368 0.4125 5.60 2 12 0.14 7 0.07368 0.4103 5.57 2 12 -0.35 4.5 0.06824 0.4302 6.30 2 12 0.65 8 OSB II 6 0.06824 0.4285 6.28 2 12 -0.09 7 0.06824 0.5238 7.68 2 12 -0.94 4.5 0.07254 0.4258 5.87 2 12 0.79 OSB III 6 0.07254 0.4515 6.22 2 12 -0.07 7 0.07254 0.4091 5.64 2 12 -0.37 4.5 0.09044 0.4688 5.18 2 12 1.07 OSB I 6 0.09044 0.4616 5.10 2 12 0.35 7 0.09044 0.5531 6.12 2 12 -0.54 4.5 0.08071 0.4968 6.16 2 12 0.70 12 OSB II 6 0.08071 0.5829 7.22 2 12 -0.34 7 0.08071 0.4715 5.84 2 12 -0.45 4.5 0.08613 0.3911 4.54 2 12 1.39 OSB III 6 0.08613 0.4713 5.47 2 12 0.19 7 0.08613 0.4207 4.88 2 12 -0.04 aDis 1= the displacement of lateral shear resistance of two-row vertically-aligned 4- staple joints for 8 staple T-type joints at proportional limit point and of lateral shear resistance of two-row vertically-aligned 6-staple joints for 12 staple T-type joints at proportional limit point; Dis 2= the displacement of T-type joints at proportional limit point; WS= stump width; WG= gusset-plate width; d= distance between moment resistance load to rail; R= ratio of Dis.2 to Dis.1.

e value was used to calculate observed P value for T-type end-to-side gusset-plate

joints in Equation (3.18). FT value is the proportional limit load of two-row vertically

aligned 4 and 6 staples joints for this test group. To calculate predicted P value for 8 staples 4.5 inch stump T-type joints made of OSB-I are WS = 4.5 in., WG = 2 in., d = 12

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in., e = 0.95, and FT = 502 as included in Table 3.22. Then all the numbers were substituted to the Equation (3.18).

(3* 4.5 − 2* 2 + 2 *0.9475) P = 502 = 119lbs. 4 *12 Accordingly, the ratio (R) between observed P and predicted P was calculated.

R = Predicted P / Observed P (3.23) The ratio for this group

R = 119/124 = 0.96

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Table 3.24 The ratio of predicted P value of the L type end-to-side, one sided, two gusset-plate joints at proportional limit to observed P load value of the T- type end-to-side, one sided, two gusset-plate joints.

Number Material of W W e F d P P . Ratio Type S G T pre. obs Staples 4.5 2 0.95 502 12 119 124 0.96 OSB-I 6 2 0.14 502 12 149 169 0.88 7 2 -0.4 502 12 171 217 0.79 4.5 2 0.65 502 12 113 118 0.96 8 OSB-II 6 2 -0.1 502 12 145 168 0.86 7 2 -0.9 502 12 158 233 0.68 4.5 2 0.79 505 12 117 159 0.74 OSB-III 6 2 -0.1 505 12 146 224 0.65 7 2 -0.4 505 12 171 267 0.64 4.5 2 1.07 804 12 195 168 1.16 OSB-I 6 2 0.35 804 12 246 243 1.01 7 2 -0.5 804 12 267 315 0.85 4.5 2 0.7 776 12 176 167 1.05 12 OSB-II 6 2 -0.3 776 12 215 268 0.8 7 2 -0.5 776 12 260 239 1.09 4.5 2 1.39 805 12 206 190 1.08 OSB-III 6 2 0.19 805 12 241 308 0.78 7 2 -0 805 12 284 350 0.81 a WS= stump width; WG= gusset-plate width; FT =the lateral resistance load of two-row vertically-aligned 4 and 6 staple joint load at proportional limit point; d= distance between moment resistance load to rail; Ppre. = the predicted P load of T-type stump-to-

front-rail joints; Pobs. = the observed moment resistance load of T-type end-to-side joints at proportional limit point.

Table 3.24 summarizes the variables to predict static bending moment resistance

load of each configuration of T-type joints at proportional limit and its ratio value of

predicted P to observed P loads. The ratios are ranking from 0.64 to 1.16 with an average

0.88 which mean predicted P values and observed P values from the experiments are

quite close one another. Therefore, the model and equation to estimate P predicted load

are plausible.

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3.6.5 Conclusions The ultimate bending moment resistance capacity of L-type and T-type end-to- side, one sided, two gusset-plate joints were investigated. The moment resistances of L- type joints ranged from 237 to 467 lb. The rail width affected moment resistance of L- type joints. Accordingly, the mean ultimate bending load of 8 inch rail L-type joints was averaged 20 percent higher than one of 6 inch rail L-type joints. However, in general, 7 inch rail width joints are not significantly different either from 6 inch rail or 8 inch rail joints in all OSB groups. The mean ultimate bending loads of 6, 7, and 8 inch rail width

L-type joints with 8 staple are significantly different for all OSB groups. However, increasing the staple number from 8 to 12, made no significant difference between the ultimate bending moment resistances of 6 and 7 inch and 7 and 8 inch rail width. This could be explained by the increment of the number of staples. Material type had no effect on mean ultimate moment resistance of L-type gusset-plate joints. Number of staples increased mean ultimate moment resistance of L-type gusset-plate joints. Accordingly, the mean ultimate bending moment resistances of 12 staple L-type joints were averaged

43 percent higher than those of 8 staple L-type joints.

The ultimate bending moment resistance loads of T-type joints ranged from 220 to 706 lb. The stump width affected moment resistances of T-type joints. Accordingly, the mean ultimate bending loads of 6 inch stump T-type joints were averaged 54 percent higher than the ones of 4.5 inch stump T-type joints and 25 percent lower than the ones of

7 inch stump T-type joints. The mean ultimate bending loads of 7 inch stump T-type joints were averaged 93 percent higher than the ones of 4.5 inch stump width T-type joints. Number of staples also affected moment resistance of T-type joints. In accordance with this, the mean ultimate bending loads of 12 staple T-type joints were averaged 37

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percent higher than the mean ultimate bending loads of 8 staple T-type joints. In contrast

to L-type joints, material type influenced the mean ultimate bending resistances of T-type

joint. In general, the mean ultimate bending loads of OSB-III T-type joints were averaged

34 and 25 percent higher than the ones of OSB-I and OSB-II, respectively, however; the

mean ultimate bending loads of OSB-I and OSB-II were not significantly different.

In tested L-type and T-type joints, ws was the most common failure mode among

L-type joint while wr was the most common failure mode among T-type joints. The

reason that L-type showed mostly ws was because stump was the weaker member of L-

type joints. Likewise, rail was the weaker member of T-type joint, so the wr was the most

observed failure mode for T-type joints. The least observed failure mode for both L-type

and T-type joints was pr. Besides these type failure modes, bottom type failure mode was

also observed for T-type joints. Accordingly, total 95 percent of T-type specimen

exhibited this type failure.

The mechanical analysis model to predict bending moment resistance of L-type yielded the ratio of predicted to observed moment resistance of 8-staple L-type joints ranged from 0.70 to 1.00 and the same ratio of 12-staple L-type joints ranged from 0.89-

1.07, respectively. Results indicated that using the mechanical model for prediction equation of static bending moment resistance capacity of L-type gusset-plate joint is reasonable. The mechanical analysis model to predict bending moment resistance of T- type yielded the ratio of predicted to observed moment resistance of 8-staple T-type joints ranged from to 0.64 to 0.96, and the same ratio of 12-staple T-type joint ranged from 0.78 to 1.16. Results pointed that using the mechanical model for prediction equation of static bending moment resistance capacity of T-type gusset-plate joint is

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remarkable. In general, the bending moment resistance capacities of L-type and T-type joints could be predicted by means of the Equations (3.8) and (3.18).

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CHAPTER IV

LATERAL SHEAR RESISTANCE OF L-TYPE, GUSSET-PLATE JOINTS

CONSTRUCTED OF OSB

4.1 Material and Method

4.1.1 Joint Configurations and Materials There is only one configuration of OSB joint, L-type. OSB-I, OSB-II, and OSB-

III were also used as three different materials. MOE and MOR values were the same with materials that were used in Chapter III.

4.2 Experimental Design A complete 2×3×3 factorial experiment with 10 replications per cell was conducted to evaluate significance of factors on lateral shear resistance of the L-type, end-to-side, one-side, two gusset-plate joints. Factors are the number of staples (8 and

12), rail width (6, 7, and 8 inches), and material type (OSB-I, OSB-II, and OSB-III).

4.3 Specimen Preparation The L-type lateral shear resistance specimens were prepared with the same way with the L-type moment resistance specimens in Chapter III. The only difference is the stump width. In this test, for 6 inch rail width, 4.5 inch wide and 10 inch long stump, for

7 inch rail width, 4.5 inch wide and 11 inch long stump, and for 8 inch, 4.5 inch wide and

12 inch long stump were used.

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4.3.1 Testing This test was carried out in SATEC Universal Testing Machine. As shown in

Figure 4.1 (a), specimens were bolted to metal loading fixture, and a cylindrical load head was used for loading. The specimens were loaded at a load rate of 0.10 in/min.

Vertical load was applied on rail of specimen as shown in the figures. A piece of square metal was placed between loading head and specimen to prevent rail rupture during the

test as shown in Figure 4.1 (b). The ultimate lateral shear loads, load-displacement curves

and specimen failure modes were recorded.

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(a)

(b)

Figure 4.1 Lateral shear resistance test a) specimen attachment and loading; b) metal piece between specimen and cylindrical load head.

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4.4 Results and Discussion

4.4.1 Mean Ultimate Lateral Load Comparisons

4.4.1.1 Load-Displacement Curve Figure 4.2 shows a typical load-displacement curve of lateral shear resistance of

L-type joint. As shown in the curve, a low-rate loading occurred after proportional limit until maximum load point. After the maximum point, the loading gradually decreased.

Figure 4.2 A typical load-displacement curve of L-type staple-connected gusset-plate joints subjected to lateral shear loads.

4.4.1.2 Failure Modes Staple legs lateral shear withdrawal failure mode was observed in all specimens in this test as shown in Figure 4.3.

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Figure 4.3 Typical failure mode of lateral shear resistance of L-type, end-to-side, one- side, two gusset-plate joint.

4.4.1.3 Mean Comparisons Mean ultimate lateral shear loads of L-type end-to-side, one-side, two gusset-plate joints and their coefficient of variations are summarized in Table 4.1.

Table 4.1 Mean ultimate lateral resistance load values and their coefficients of variation of L-type, staple-connected gusset-plate joints in OSB.

Rail Width (in.) Material 6 7 8 Type Number of Staples 8 12 8 12 8 12 OSB-I 908 (7) 1345 (7) 963 (6) 1390 (4) 991 (6) 1407 (6) OSB-II 1068 (12) 1548 (4) 1052 (12) 1551 (5) 1164 (11) 1556 (6) OSB-III 1161 (7) 1586 (5) 1145 (5) 1790 (5) 1088 (4) 1788 (7)

A three-factor ANOVA general linear model procedure was performed for individual joint data to analyze main effects and the interaction on the mean ultimate lateral shear loads of L-type joints. Table 4.2 gives the ANOVA result. 132

Table 4.2 General linear model procedure output for main effects and interactions of 2 by 3 by 3 L-type gusset-plate joint factorial experiment with 10 replication of each combination.

Source DF F Value Pr > F MT 2 129.01 <.0001 S NOS 1 1373.70 <.0001 S MT*NOS 2 14.34 <.0001 S RW 2 8.07 0.0005 S MT *RW 4 1.96 0.1029 NS NOS*RW 2 2.96 0.0548 NS MT *NOS*RW 4 6.34 <.0001 S aS = significant; NS = not significant; MT = material type; NOS = number of staples; RW = rail width.

The ANOVA results indicated that the three-factor interaction, material type ×

number of staples × rail width, was statically significant at the 5 percent significance

level. Therefore, the tests for main effects and two-factor interactions were ignored, and

the significant three factor interaction was analyzed.

Table 4.3 shows the mean comparisons of ultimate lateral shear loads for material type effect for each combination of number of staples and rail width. Table 4.4 gives the mean comparisons of ultimate lateral shear loads for number of staples for each combination of material type and rail width. Table 4.5 lists the mean comparisons of ultimate lateral shear loads for rail width for each combination of material type and number of staples. The results were based on a one way classification with 18 treatment combinations. The protected least significant difference (LSD) multiple comparisons procedure at the 5 percent significance level was performed to determine the mean difference of those treatments using the LSD value of 79 pounds.

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Table 4.3 Mean comparisons of ultimate lateral shear loads of L-type joints for material type.

Number Rail Material Type Ratio of Width Staples (in) OSB-I OSB-II OSB-III II/I III/I III/II 6 908 (A) 1068 (B) 1161 (C) 1.18 1.28 1.09 8 7 963 (A) 1052 (B) 1145 (C) 1.09 1.19 1.09 8 991 (A) 1164 (B) 1088 (B) 1.17 1.1 0.93 6 1345 (A) 1548 (B) 1586 (B) 1.15 1.18 1.02 12 7 1390 (A) 1551 (B) 1790 (C) 1.12 1.29 1.15 8 1407 (A) 1556 (B) 1788 (C) 1.11 1.27 1.15 Average 1.14 1.22 1.07

Table 4.4 Mean comparisons of ultimate lateral shear loads of L-type joints for number of staples.

Rail Material Number of Staples Ratio Width Type (in) 8 12 12/8 6 908 (A) 1345 (B) 1.48 OSB-I 7 963 (A) 1390 (B) 1.44 8 991 (A) 1407 (B) 1.42 6 1068 (A) 1548 (B) 1.45 OSB-II 7 1052 (A) 1551 (B) 1.47 8 1164 (A) 1556 (B) 1.33 6 1161 (A) 1586 (B) 1.37 OSB-III 7 1145 (A) 1790 (B) 1.56 8 1088 (A) 1788 (B) 1.64 Average 1.46

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Table 4.5 Mean comparisons of ultimate lateral shear loads of L-type joints for rail width.

Number Material Rail Width (in.) Ratio of Type Staples 6 7 8 7/6 8/6 8/7 8 908 (A) 963 (AB) 991 (B) 1.06 1.09 1.03 OSB-I 12 1345 (A) 1390 (A) 1407 (A) 1.03 1.05 1.01 8 1068 (A) 1052 (A) 1164 (B) 0.99 1.09 1.11 OSB-II 12 1548 (A) 1551 (A) 1556 (A) 1.01 1.01 1 8 1161 (A) 1145 (A) 1088 (A) 0.99 0.94 0.95 OSB-III 12 1586 (A) 1790 (B) 1788 (B) 1.13 1.13 1 Average 1.04 1.05 1.02

4.4.1.4 Material Type Effect Table 4.3 indicates that the mean ultimate lateral shear load of L-type joints in

OSB-II is significantly lower than the ones in OSB-III and significantly greater than the ones in OSB-I. This would be explained by the fact that the density of OSB-II is significantly lower than the ones of OSB-III and significantly higher than the ones of

OSB-I. The mean ultimate lateral shear load of 8 inch rail L-type joints with 8 staple and

6 inch rail with 12 staples in OSB-II is not significantly different than the ones in OSB-

III.

4.4.1.5 Number of Staples Effect According to Table 4.4, the mean ultimate lateral shear load of the joint with 8

staples is significantly lower than the ones with 12 staples in all OSB groups.

4.4.1.6 Rail Width Effect According to Table 4.5, the mean ultimate lateral shear load of 6 inch rail L-type

joints with 8 staples is not significantly different than the mean ultimate lateral shear load

of 7 inch rail L-type joints with 8 staples. Likewise, the mean ultimate lateral shear load 135

of 7 inch rail L-type joints with 8 staples is not significantly different than the mean ultimate lateral shear load of 8 inch rail L-type joints with 8 staples; however, the mean ultimate load of 6 inch rail L-type joints with 8 staples is significantly lower than the

mean ultimate load of 8 inch rail L-type joints with 8 staples in OSB-I. The mean

ultimate lateral shear load of L-type joints with 12 staple in OSB-I, L-type joints with 12

staple in OSB-II, and L-type joints with 8 staple in OSB-III are not significantly different

for rail width 6, 7, and 8 inches, respectively. The mean ultimate lateral shear load of 7

inch rail L-type joints with 8 staples is significantly lower than the mean ultimate lateral

shear load of 8 inch rail L-type joints with 8 staples in OSB-II. The mean ultimate lateral

shear load of L-type joints with 8 staples is significantly lower than the one of 8 inch rail

L-type joints with 8 staples. The mean ultimate load of 6 inch rail L-type joints with 12

staples is significantly lower than the mean ultimate load of 7 and 8 inch rail L-type joints

with 12 staples; however the mean ultimate load of 7 inch rail L-type joints with 12

staples is not significantly different than the mean ultimate load of 8 inch rail L-type

joints with 12 staples in OSB-III.

4.5 Estimation Equations Table 4.6 shows that the overall lateral shear resistance ratio of L-type joints to

two-row horizontally-aligned multi-staple gusset-plate joints is 1.02, or approximately 1.

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Table 4.6 Mean lateral shear resistance ratios of L-type OSB stapled gusset-plate joints to two-row horizontally-aligned multi-staple gusset plate joints.

OSB-I Number of Number of Staples Over all Plates 4 6 1-plate 886 1405 8 12 2-plate 954 1381 Rate 1.08 0.98 1.03 OSB-II Number of Staples 4 6 1-plate 990 1585 8 12 2-plate 1095 1552 Rate 1.11 0.98 1.04 OSB-III Number of Staples 4 6 1-plate 1082 1883 8 12 2-plate 1131 1721 Rate 1.05 0.91 0.98 Over all 1.02

Therefore, Equation (2.1) and (2.6) of two-row horizontally-aligned multi-staple joints were used to estimate lateral shear resistance of L-type joints.

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Table 4.7 Comparison of estimated ultimate lateral shear resistance loads of L-type OSB gusset-plate joints using Equations (2.1) and (2.6) with observed values.

Predicted Load Ratio

Material Eq.(2.1)/ Eq.(2.6)/ D N Obs. Eq.(2.1) Eq.(2.6) Type Obs. Obs. 40.6 8 954 896 793 1.01 0.90 OSB-I 40.6 12 1381 1372 1269 0.98 0.90 43.4 8 1095 966 906 0.98 0.91 OSB-II 43.4 12 1552 1584 1450 1.00 0.91 46.4 8 1131 1093 1035 1.01 0.96 OSB-III 46.4 12 1721 1777 1656 0.94 0.88 aD = density of OSBs; N = number of staples; Obs = observed load values, Eq.= equation.

Equation (2.1) was used for OSB-I, OSB-II, and OSB-III, respectively to estimate

the lateral shear resistances of L-type joints. According to these equations, the ratios of predicted to observed loads were ranged from 0.94 to 1.01 in Table 4.7. Therefore, it is reasonable that the Equation (2.1) equations can be used to predict mean ultimate lateral resistance of L-type joints. Equation (2.6) was used as all OSBs. Accordingly, the ratios of predicted to observed loads ranged from 0.88 to 0.96. Similar to Equation (2.1),

Equation (2.6) yielded plausible results to estimate mean ultimate lateral shear resistance of L-type joint.

4.6 Conclusions The ultimate lateral shear resistances of L-type end-to-side, stapled, one-side, two gusset-plate joints were investigated. Material type had an increasing effect on the mean lateral resistance capacity of joints. In general, the mean ultimate lateral resistances of L- type joints constructed of OSB-II were significantly averaged 14 percent higher than

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those constructed of OSB-I and significantly 7 percent lower than OSB-III. The mean

ultimate lateral resistances of L-type joints constructed of OSB-III were significantly 22

percent higher than those constructed of OSB-I. The number of staples also increased the

mean ultimate lateral resistance of L-type joints. The mean ultimate lateral shear

resistances of 8-staple L-type joints were significantly 46 percent lower than those of 12-

staple L-type joints. The rail width increased the lateral shear resistance capacity of L-

type joints. In general, the ultimate lateral shear of 6 inch rail width L-type joints was

significantly 5 percent lower than those of 8 inch rail width L-type joints. The mean

ultimate lateral shear resistances of 7 inch rail of L-type joints were between those of 6

inch rail and 8 inch rail L-type joints. The rail width effect on the lateral shear resistance

of L-type joints was similar to the rail width effect on bending moment resistance of L-

type joints.

The ratio of the lateral shear resistance of L-type one-side, stapled two gusset-

plate joints to the lateral shear resistance of two-row horizontally-aligned multi-staple

joint was 1. Therefore, to estimate the mean ultimate lateral resistance of L-type joints

Equation (2.1) and Equation (2.6) were used. Both equations yielded very close results to

the observed ones. Therefore, using Equations (2.1) and (2.6) to estimate mean lateral

resistance of L-type joints is remarkable. Staple legs lateral shear withdrawal was the

only failure mode that observed on tested specimen for the lateral shear test of L-type joint.

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CHAPTER V

FATIGUE BENDING MOMENT RESISTANCES OF L-TYPE AND T-TYPE

GUSSET-PLATE JOINTS IN OSB

5.1 Materials and Methods

5.1.1 Approach This part of study was the continuation of bending moment resistance evaluation of stapled, end-to-side, one-side-two-gusset-plates connected joints constructed of OSB.

In this study, the L-Type and T-type gusset-plates joints in OSB were subjected to a stepped cyclic loading schedule following the same schedule of GSA outward arm test

(GSA 1998) to evaluate and compare the fatigue bending moment resistance of the gusset-plates joints in different OSB materials.

5.2 Experimental Design Table 5.1 shows the detailed cyclic stepped load schedule for testing sofa frame arms. The acceptance load for each of light, medium, and heavy levels is 75, 150, and

200 lb., respectively. Previous studies (Zhang et al. 2001, 2003, 2006, Wang et al. 2007a, and Wang 2007c) on the bending fatigue resistance of various types of furniture joints indicated that the average ratio of the static to passing fatigue moment capacity ranged from 1.6 to 3.1. In this study, a minimum ratio of 2 was considered. Therefore, static bending moment resisting load capacity of joints should be 150, 300, and 400 lb. for passing light, medium, and heavy level, respectively, as shown in Table 5.1.

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Table 5.1 GSA cyclic stepped loading schedule for arm test.

Loads 50 75 100 125 150 175 200 No. of cycles 25,000 50,000 75,000 100,000 125,000 150,000 175,000 Service A-L Light Medium Heavy Static M-load 150 300 400 a A-L= acceptance level; M = moment.

Accordingly, the following L-type and T-type test groups were chosen and

constructed for joint fatigue performance evaluation based on the results from static

bending moment evaluation of the joints. Tables 5.2 and 5.3 were the summary of static

bending moment resisting load capacities of L-type and T-type gusset-plate joints, respectively. For each type of the joint, three circled groups, I, II, and III were chosen for fatigue resistance evaluation because their bending resisting load values were at least twice higher than their corresponding fatigue acceptance load levels 75, 150, and 200 lb., respectively. For each testing group, there were five replications evaluated for each type of OSB materials.

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Table 5.2 Static bending moment resisting load capacities of L-type gusset-plate joints subjected to a testing load 12 inches in front of the rail.

Number of Staples 8 12 Material Type Rail Width (in.) 6 7 8 6 7 8 Group I Group II Group III OSB-I 245 (12) 271 (14) 297 (13) 365 (6) 387 (11) 430 (9) OSB-II 237 (12) 276 (11) 314 (10) 388 (7) 413 (11) 402 (19) OSB-III 264 (11) 302 (6) 403 (10) 410 (8) 412 (22) 465 (16)

Table 5.3 Static bending moment resisting load capacities of T-type gusset-plate joints subjected to a testing load 12 inches in front of the rail.

Number of Staples 8 12 Material Stump Width (in.) Type 4.5 6 7 4.5 6 7 Group I Group II Group III OSB-I 220 (5) 314 (5) 386 (10) 301 (4) 445 (5) 562 (6) OSB-II 220 (6) 334 (9) 461 (10) 297 (8) 485 (7) 642 (7) OSB-III 297 (7) 460 (7) 534 (8) 373 (6) 609 (8) 706 (10)

5.3 Testing A specially designed air cylinder and pipe rack system as shown in Figure 5.1 was

set up for evaluating bending fatigue resistance capacity of gusset-plates joints. In all test, a one-sided, vertical fatigue load was applied to the stump 12 inches in front of the rail by an air cylinder at a rate of 20 cycles per minutes. The loading schedule was given in

Table 5.1. Tests were started at the 50 pound load level. After 25,000 cycles, the load was increased by an increment of 25 pounds. The test was continued for another 25,000

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cycles, and then the procedure was repeated until joints failed to resist the applied load.

A Programmable Logic Controller and electrical re-settable counter system (Figure 5.2 a, b) recorded the number of cycles completed. Limit switches were attached on the specimens (Figure 5.2c) to stop the test when the specimen disabled.

Figure 5.1 A specially designed air cylinder and pipe rack system for evaluating fatigue bending moment resistance capacity of gusset-plate joints in OSB materials.

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(a)

(b)

Figure 5.2 Setup details: a) electrical re-settable counter, b) a Programmable Logic Controller, and c) limit switch.

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5.4 Results and Discussion

5.4.1 Failure Modes Four types of failure modes occurred in the tests: staple legs lateral shear

withdrawal from rails (Figure 5.3a), staple legs lateral shear withdrawal from stumps

(Figure 5.3b), staple legs lateral shear withdrawal from rail and staple break-off (Figure

5.3c), and staple legs lateral shear withdrawal from stump and staple break-off (Figure

5.3d). Figure 5.3 illustrates all four types of failure modes.

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(a)

(b)

Figure 5.3 Failure modes of L-type and T-type gusset-plate joints in OSB materials: a) staple legs lateral shear withdrawal from rail; b) staple legs lateral shear withdrawal from stump; c) staple legs lateral shear withdrawal from rail and staple break-off d) staple legs lateral shear withdrawal from stump and staple break-off.

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(c)

(d) Figure 5.3 (Continued)

Tables 5.4 and 5.5 summarize the failure modes for L-type and T-type gusset

plate joints, respectively. In general, the joints with lower static moment resistance

capacity such as 6 inch wide rail joints had the failure mode of staple legs lateral shear withdrawal from stump and rail, which was similar to the failure mode in static test.

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Joints with higher static moment resistance tended to have staple leg break-off mode since they suffered more fatigue cycles than joints with lower static moment resistance.

Table 5.4 Failure mode summary of five tested L-type gusset-plate joints for each combination of material type and number of staples, and rail widths.

Number Rail Material of Width WR WS WR&SR WS&SR Type Staples (in.) 6 2 3 8 OSB-I 8 1 2 2 12 8 5 6 5 8 OSB-II 8 1 4 12 8 3 2 6 5 8 OSB-III 8 5 12 8 5 aWR= staple legs withdrawal from rail; WS= staple legs withdrawal from stump; WR & SR= staple legs withdrawal from rail and staple break-off; WS & SR= staple legs withdrawal from stump and staple break-off.

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Table 5.5 Failure mode summary of five tested T-type gusset-plate joints for each combination of material type and number of staples, and stump widths.

Number Stump Material of width WR WS WR&SR WS&SR Type Staples (in.) 8 4.5 1 3 1 OSB-I 4.5 1 4 12 6 3 2 8 4.5 4 1 OSB-II 4.5 5 12 6 2 3 8 4.5 1 1 2 1 OSB-III 4.5 4 1 12 6 4 1 aWR= staple legs withdrawal from rail; WS= staple legs withdrawal from stump; WR & SR= staple legs withdrawal from rail and staple break-off; WS & SR= staple legs withdrawal from stump and staple break-off.

5.4.2 Mean Comparison

5.4.2.1 L-type Joints Mean passed fatigue moment resistance load values and their coefficients of variation of tested L-type gusset-plate joints are summarized in Table 5.6. A two-factor

ANOVA general linear model procedure was performed for individual joint data to analyze main effects and their interaction on the mean passed fatigue moment resistance loads of L-type gusset-plate joints in OSB materials.

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Table 5.6 Mean passed fatigue moment resistance load values and their coefficients of variation of L-type, staple-connected gusset-plate joints in OSB.

Static Fatigue Number Rail Average Material Cumulative Cycles to of Width Static Load Passed Type Failure Staples (in.) Load 6 245 125 (25) 100,000+16,337 8 OSB-I 8 297 120 (17) 100,000+6,700 12 8 430 190 (7) 150,000+22,855 6 237 110 (26) 75,000+17,761 8 OSB-II 8 314 160 (18) 125,000+21,291 12 8 402 210 (7) 175,000+13,538 6 264 110 (20) 75,000+18,753 8 OSB-III 8 403 120 (9) 100,000+9,867 12 8 467 190 (12) 175,000+8,033

Table 5.7 summarizes the ANOVA results, which indicated that the two-factor interaction was marginally not significant at the 5 percent level. The two-factor interaction was further analyzed to explore the main effects on the passed fatigue moment resistance load capacity of gusset-plates joints in OSB materials.

Table 5.7 General linear model procedure output for main effects and interactions of 3 by 3 L-type gusset-plate joint factorial experiment with 5 replication of each combination.

Source DF F Value Pr > F MT 2 3.25 0.0504 MS SML 2 55.08 <.0001 S MT*SML 4 2.08 0.1033 NS a MT= material type; SML = static moment level; S = significant; NS = not significant; MS = marginally significant.

Tables 5.8 and 5.9 summarize mean comparisons of fatigue moment resistance

loads of L-type, one-side, stapled, two-gusset-plate joints for material type effect and static moment resistance effect, respectively. The results were based on a one-way

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classification created with 9 treatment combinations using the single LSD value of 29

pounds. In addition to fatigue data, the corresponding static moment resistance load values were also given in the tables for comparison purposes.

Table 5.8 Mean comparisons of passed fatigue moment resistance loads of L-type, one-side, stapled, two gusset-plate joints for material type for each static moment resistance.

Static Test Material Type Ratio Moment Type Level OSB-I OSB-II OSB-III II/I III/I III/II Fatigue 125 (A) 110 (A) 110 (A) 0.88 0.88 1 I Static 245 (A) 237 (A) 264 (A) 0.97 1.08 1.11 Fatigue 120 (A) 160 (B) 120 (A) 1.33 1.00 0.75 II Static 297 (A) 314 (A) 402 (B) 1.06 1.35 1.28 Fatigue 190 (A) 210 (A) 190 (A) 1.11 1.00 0.90 III Static 430 (A) 402 (A) 465 (B) 0.93 1.08 1.16

Table 5.9 Mean comparisons of passed fatigue moment resistance loads of L-type, one-side, stapled, two gusset-plate joints for static moment resistance for each material type.

Material Test Static Moment Levels Ratio Type Type I II III II/I III/I III/II Fatigue 125 (A) 120 (A) 190 (B) 0.96 1.52 1.58 OSB-I Static 245 (A) 297 (B) 430 (C) 1.21 1.76 1.45 Fatigue 110 (A) 160 (B) 210 (C) 1.45 1.91 1.31 OSB-II Static 237 (A) 314 (B) 402 (C) 1.32 1.70 1.28 Fatigue 110 (A) 120 (A) 190 (B) 1.09 1.73 1.58 OSB-III Static 264 (A) 403 (B) 465 (C) 1.53 1.76 1.15

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5.4.2.1.1 Material Type Effect Table 5.8 indicated that for the light level joint group, there were not significant differences in fatigue moment resistance capacity among the joints constructed of three

OSB materials. There were no significant differences in static moment resistance capacity among the joints in three OSB materials. For the medium level joint, the mean static resistance of OSB-II L-type joints is significantly higher than others, and the mean fatigue resistance of OSB-III is significantly higher than other OSB materials. For the heavy level joint, the mean static resistance of OSB-III L-type joints is significantly higher than other OSB materials whereas the mean fatigue resistance of L-type joints is not significant among three different materials.

5.4.2.1.2 Static Moment Levels Table 5.9 lists static and fatigue resistance relationship of L-type joins for static moment level. Accordingly, the static resistance of OSB-I L-type joints is significantly different among all static moment levels, and the fatigue resistance of OSB-I L-type joints at heavy level is significantly greater than the ones at light and medium levels. The same relationship is available for OSB-III L-type joints. On the other hand, both static and fatigue resistances of OSB-II L-type joints are significantly different among all service acceptance levels.

5.4.2.2 T-type Joints Mean passed fatigue moment resistance load values and their coefficients of variation of tested T-type gusset-plate joints are summarized in Table 5.10. A two-factor

ANOVA general linear model procedure was performed for individual joint data to

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analyze main effects and their interaction on the mean passed fatigue moment resistance loads of T-type gusset-plate joints in OSB materials in Table 5.11.

Table 5.10 Mean passed fatigue moment resistance and their coefficients of variation of T-type, staple-connected gusset-plate joints in OSB.

Static Fatigue Number Stump Average Material Static Cumulative Cycles to of Width Passed Type Load Failure Staples (in.) Load 8 4.5 220 115 (19) 100,000+1,753 OSB-I 4.5 301 135 (10) 100,000+20,085 12 6 445 210 (7) 175,000+18,967 8 4.5 220 90 (25) 50,000+20,428 OSB-II 4.5 297 140 (10) 100,000+24,446 12 6 485 220 (10) 200,000+6,318 8 4.5 297 145 (14) 125,000+1,515 OSB-III 4.5 373 145 (22) 125,000+7,000 12 6 609 220 (5) 200,000+1,350

Table 5.11 summarizes the ANOVA results, which indicated that the two-factor interaction was marginally significant at the 5 percent level. Therefore, the significant

two-factor interaction (material type by load acceptance level) was further analyzed to

explore the main effects on the passed fatigue moment resistance load capacity of T-type gusset-plates joints in OSB materials.

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Table 5.11 General linear model procedure output for main effects and interactions of 3 by 3 T-type gusset-plate joint factorial experiment with 5 replication of each combination.

Sources DF F Value Pr > F

MT 2 4.28 0.0216 MS SML 2 101.93 <.0001 S MT* SML 4 2.93 0.0339 MS aMT= material type; SML = static moment level; S = significant; MS = marginally significant.

Tables 5.12 and 5.13 summarize mean comparisons of fatigue moment resistance loads of T-type, one-side, stapled, two-gusset-plate joints for material type effect and static moment resistance effect, respectively. The results were based on a one-way classification created with 9 treatment combinations using the single LSD value of 26 pounds. In addition to fatigue data, the corresponding static moment resistance load values were given.

Table 5.12 Mean comparisons of passed fatigue moment resistance loads of T-type, one-side, stapled, two gusset-plate joints for material type for each static moment resistance.

Static Test Material Type Ratio moment Type Levels OSB-I OSB-II OSB-III II/I III/I III/II Fatigue 115 (A) 90 (A) 145 (B) 0.78 1.26 1.61 I Static 220 (A) 220 (A) 297 (B) 1.00 1.35 1.35 Fatigue 135 (A) 140 (A) 145 (A) 1.04 1.07 1.04 II Static 301 (A) 297 (A) 373 (B) 0.99 1.24 1.26 Fatigue 210 (A) 220 (A) 220 (A) 1.05 1.05 1.00 III Static 445 (A) 485 (B) 609 (C) 1.09 1.37 1.26

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Table 5.13 Mean comparisons of passed fatigue moment resistance loads of T-type, one-side, stapled, two gusset-plate joints for static moment resistance for each material type.

Material Test Static Moment Levels Ratio Type Type I II III II/I III/I III/II Fatigue 115 (A) 135 (A) 210 (B) 1.17 1.83 1.56 OSB-I Static 220 (A) 301 (B) 445 (C) 1.37 2.02 1.48 Fatigue 90 (A) 140 (B) 220 (C) 1.56 2.44 1.57 OSB-II Static 220 (A) 297 (B) 485 (C) 1.35 2.20 1.63 Fatigue 145 (A) 145 (A) 220 (B) 1.00 1.52 1.52 OSB-III Static 297 (A) 373 (B) 609 (C) 1.26 2.05 1.63

5.4.2.2.1 Material Type Effect Table 5.12 illustrates that, for static level-I joint group, the static and fatigue

resistances of OSB-III T-type joints are significantly higher than the ones of OSB-I and

OSB-II T-type joints. For static level-II joint group, the static resistance of OSB-III T-

type joints is significantly higher than the ones of other OSB materials while the fatigue

resistance of joints is not significantly different among OSB materials. For level-III joint group, the static resistance of all OSB joints is significantly different from one another while the fatigue resistance of joints is not significantly different among materials.

5.4.2.2.2 Static Moment Effect Table 5.13 lists static and fatigue relationship of T-type joins for static moment level. According to the table, the static resistances of OSB-I and OSB-III T-type joints are significantly different among all three static moment levels while the fatigue resistances of those at III are significantly higher than the ones in I and II levels.

However, both static and fatigue resistances of OSB-II T-type joints are significantly different among all three static moment levels.

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5.4.3 Static to Fatigue Moment Resistance Capacity Ratio

5.4.3.1 L-type Gusset-Plate Joints Table 5.14 summarizes the mean static moment resistance load, passed fatigue

load, and failed fatigue load of each tested joint group. The ratios of the mean static

moment resistance load of each tested joint group to its corresponding passed and failed

fatigue moment load were calculated and listed in “Ratio” section of Table 5.14.

Table 5.14 Summary of dimension and static moment resistance load values of L-type gusset-plate joints and their corresponding fatigue performance results.

Static Fatigue Ratio Number Rail Static Material Passed Failed Static/ Static/ of Width Load Type Load Load Passed Failed Staples (in.) (lb.) 6 245 125 150 1.96 1.63 8 OSB-I 8 297 100 125 2.97 2.38 12 8 430 175 200 2.46 2.15 6 237 100 125 2.37 1.9 8 OSB-II 8 314 150 175 2.09 1.79 12 8 402 200 225 2.01 1.79 6 264 100 125 2.64 2.11 8 OSB-III 8 403 100 125 4.03 3.22 12 8 467 175 200 2.67 2.34 Average 2.58 (25) 2.15 (22)

aNumber in parenthesis = coefficient of variation

The ratio of “static load” to “passed load” of all OSB joints averaged 2.58, with a

COV of 25 percents and a range of 1.96 to 4.03. The ratio of “static load” to “failed load” of all OSB joints averaged 2.15, with a COV of 22 percents and a range of 1.63 to 3.22.

Therefore, the average static to fatigue moment ratio for the design of one-side gusset- plate joints in OSB would be set to 2.6. It might be advisable to design the gusset-plate joints in OSB materials so that their static moment resistance should be 2.6 times of the

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fatigue moment load expected to pass. Other studies indicated that the average static to passed fatigue moment ratios were 2.1 for gusset-plate joint in OSB (Wang et al. 2007c);

2.5 for metal-plate joints in OSB materials (Wang et al. 2007a), 2.6 for two-pin dowels in plywood (Zhang et al. 2003); 2.5 for metal-plate joints in plywood (Zhang et al. 2006)

1.6 to 2.1 for two-pin dowel joints in selected solid wood and wood composites (Zhang et al. 2001), respectively.

5.4.3.2 T-type Gusset-Plate Joints Table 5.15 summarizes the static moment resistance load, passed fatigue load, failed fatigue load of each tested joint group. The ratios of the static moment resistance load of each tested joint group to its corresponding passed and failed fatigue moment load were calculated and listed in “Ratio” section of Table 5.15. The ratio of “static load” to

“passed load” of all OSB joints averaged 2.55, with a COV of 13 percents and a range of

2.20 to 3.05. The ratio of “static load” to “failed load” of all OSB joints averaged 2.14, with a COV of 14 percents and a range of 1.76 to 2.71. Therefore, the average static to fatigue moment ratio for the design of T-type, one-side gusset-plate joints in OSB would be also set to 2.6

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Table 5.15 Summary of dimension and static moment resistance load values of T-type gusset-plate joints and their corresponding fatigue performance results.

Static Fatigue Ratio Number Rail Static Material Passed Failed Static/ Static/ of Width Load Type Load Load Passed Failed Staples (in.) (lb.) 8 4.5 220 100 125 2.2 1.76 OSB-I 4.5 301 125 150 2.41 2.01 12 6 445 200 225 2.23 1.98 8 4.5 220 75 100 2.93 2.2 OSB-II 4.5 297 125 150 2.38 1.98 12 6 485 200 225 2.43 2.16 8 4.5 297 125 150 2.38 1.98 OSB-III 4.5 373 125 150 2.98 2.49 12 6 609 200 225 3.05 2.71 Average 2.55 (13) 2.14 (14)

aNumber in parenthesis = coefficient of variation

5.5 Conclusions Fatigue performances of L-type and T-type end-to-side, stapled, one-side, two gusset-plate joints were investigated by subjecting them to cyclic stepped bending test. In general the static moment resistance of L-type joints in OSB-III is significantly higher than the ones of others and the other ones are not significantly different in their service level. On the other hand, the fatigue moment resistances of L-type joints is not significantly different among material in all service level except the one of L-type joint in

OSB-II which is significantly higher than others at medium level. The static moment resistance of T-type joints is significantly different at heavy service among OSB materials, and it is only significantly different between OSB-II and OSB-III at light and medium service levels. The fatigue moment resistance of T-type joint is not significantly different among material except T-type joints in OSB-III which is significantly higher than others at light service level. In addition, the proposed design ratio of static to fatigue moment ratio of both L-type and T-type joints should be 2.6.

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Four different type failure modes were observed: staple legs lateral shear withdrawal from rails; staple legs lateral shear withdrawal from stump; staple legs lateral shear withdrawal from rails and staple break-off; and staple legs lateral shear withdrawal from stump and staple break-off. Staple legs lateral shear withdrawal from stump and staple break-off mostly and withdrawal from rail rarely occurred in L-type joints. In T- type joints, staple legs lateral shear withdrawal from rail and staple break-off mostly and staple legs lateral shear withdrawal from stump rarely occurred. In general, both L-type and T-type joints showed staple legs withdrawal from joint members at lower load level and fatigue cycle while they showed staple break-off at higher load levels and fatigue cycles.

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CHAPTER VI

FATIGUE PERFORMANCE OF OSB AS UPHOLSTERED FURNITURE FRAME

STRUCTURAL MEMBERS

6.1 Material and Methods

6.1.1 Materials Three OSB materials, OSB-I, OSB-II, and OSB-III were tested. All OSB materials were 23/32 inch thick panels with face strands oriented in the direction parallel to the 8-foot direction of 4-by 8-foot full-size sheet. The MOR values of OSB-I, OSB-II and OSB-III were 2,529, 3,279, and 3,848 psi (Zhang and Quin 2010), respectively. The length of tested beam specimens was 80 inches long. All specimens were simply- supported at two ends with a span of 72 inches.

6.1.2 Experimental Design

6.1.2.1 Cyclic Stepped Load Tests Three OSB materials were subjected to the cyclic stepped load schedule as shown in Table 6.1. For each OSB material, three member depths were considered, which were calculated based on passing three GSA testing acceptance levels, light, medium, and heavy (Table 6.1). Five replications were tested for each combination of material type and member depth. Therefore, a total of 45 members were subjected to backrest frame test loading schedule.

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Table 6.1 Cyclic stepped loading schedule for 72-inch-long back top rail fatigue tests and calculated maximum moments in back top rail for each fatigue load level.

j P (lb) No. of Loads Cumulative Cycles Service Acceptance Level Mj 1 75 3 25,000 Light Service 2,250 2 100 3 50,000 Medium Service 3,000 3 125 3 75,000 3,750 4 150 3 100,000 Heavy Service 4,500

The Palmgren-Miner rule was used to estimate the fatigue life of back top rails in

OSB materials when they were subjected to cyclic stepped loads (Zhang et al. 2005).

The Palmgren-Miner rule expresses unity summation of life fraction.

NN N N j 1 =1 + 2 +3 + .... = ∑ (6.1) NNN N f 1 f 2 f 3 fj

where Nj = number of cycles applied to a member at the bending moment Mj and Nfj = number of cycles to failure from the member material S-N curve for the bending moment

Mj.

Therefore, the fatigue life of a back top rail can be predicted with Equation (6.2).

25000 25000 25000 25000 1 = + + + (6.2) NNNN f 1 f 2 f 3 f 4 For OSB materials, the low 5 percent limit S-N curve equation is (Dai and Zhang

2007):

σ = MOR (0.85 – 0.08 x log10 Nf) (6.3) where σ = applied nominal stress (psi); and MOR = modulus of rupture for each member

material (psi).

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For a rectangular cross section beam member subjected to an edgewise bending

moment, the relationship between stress and moment can be expressed with the formula:

6M σ = j 2 (6.4) bh

where Mj = nominal applied maximum moment in beam member (lb.-in.); b = beam

member thickness (in.); and h = beam member depth (in.).

The maximum bending moment, Mj, in a beam member subjected to three

identical loads, P, at the center-point and at 1/6 the span, L, from each supporting end,

can be calculated with the formula (Dai and Zhang 2007):

5PL M j = (6.5) 12 Substituting the stress-moment equation into the S-N curve equation yielded the following relationship:

0.85 6M ( − 1 ) N = 10 0.08 MOR× 0.08×b×h2 (6.6) fj

Then, substituting Nfj into the Palmgren-Miner rule equation yielded the

following equation:

25000 25000 = + 1 0.85 6M 0.85 6M ( − 1 ) ( − 2 ) 0.08 × × × 2 0.08 × × × 2 10 MOR 0.08 b h 10 MOR 0.08 b h

25000 25000 + + 0.85 6M 0.85 6M (6.7) ( − 3 ) ( − 4 ) 10 0.08 MOR× 0.08×b×h2 10 0.08 MOR× 0.08×b×h2

Therefore, the depth of a specimen passing the light service acceptance, hL , can

be calculated with Equation (6.8):

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25000 = 1 0.85 6M (6.8) ( − 1 ) 0.08 × × × 2 10 MOR 0.08 b h

The depth of a specimen passing the medium service acceptance level, hM , can

be calculated with Equation (6.9):

25000 25000 = + 1 0.85 6M 0.85 6M (6.9) ( − 1 ) ( − 2 ) 0.08 × × × 2 0.08 × × × 2 10 MOR 0.08 b h 10 MOR 0.08 b h

The depth of a specimen passing the heavy service acceptance level, hH , can be calculated with Equation (6.10).

25000 25000 = + 1 0.85 6M 0.85 6M ( − 1 ) ( − 2 ) 10 0.08 MOR× 0.08×b×h 2 10 0.08 MOR ×0.08×b×h2

25000 25000 + 0.85 6M + 0.85 6M (6.10) ( − 3 ) ( − 4 ) 10 0.08 MOR× 0.08×b×h2 10 0.08 MOR× 0.08×b×h2 Table 6.2 lists the depths of each OSB material for passing three fatigue

acceptance levels. In calculation of the depth of a back top rail passing the heavy

acceptance level using OSB-I, the equation (6.10) was used by substituting MOR=2,529

psi, b = 23/32 inches and the moment, Mj, for each fatigue loading level (Table 6.1)

calculated using Equation (6.5). A minimum rail depth of 5.469 inches was resulted.

Table 6.2 Depths of 72-inch-long back top rail specimens for each OSB material passing three stepped cyclic load acceptance levels.

Material Service Acceptance Level Type Light Medium Heavy 3-7/8 4-7.5/16 5-7.5/16 OSB-I (3.875) (4.469) (5.469) 3-3/8 3-15/16 4-13/16 OSB-II (3.375) (3.938) (4.813) 3-1/8 3-5/8 4-7/16 OSB-III (3.125) (3.625) (4.438)

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6.1.2.2 Constant Cyclic Load Test There OSB materials were subjected to the constant cyclic load schedule as shown in Table 6.3. Substituting Equation (6.6) into Equation (6.1) yielded Equation

(6.11) to calculate depths of the test members.

Table 6.3 BIFMA horizontal backrest loading schedule.

Load Cycle 75 (lb.) 120,000

120,000 1 = 0.85 6M ( − 1 ) 0.08 MOR× H×b×h2 10 (6.11) Substituting MOR values = 2,529, 3,279, and 3,848 psi for each OSB-I, OSB-II,

and OSB-III, respectively, b = 23/32, and the moment value of 2,250 (lb.-in.) calculated

using Equation (6.5). Table 6.4 yielded the calculated depth for each OSB material.

Table 6.4 Depths (in.) of back top rails subjected to BIFMA constant cyclic load test for each OSB material.

Material Type

OSB-I OSB-II OSB-III 4-1.5/16 3-9.5/16 3-5/16 Depth (4.094) (3.594) (3.313)

6.1.3 Specimen Preparation Testing members, 23/32 inch thick and 72 inches span full size, were cut from

OSB-I, OSB-II, and OSB-III sheets, and measured 80 inches long with their direction parallel to the full size sheet 8 foot direction. The depth of specimens differed according to service acceptance levels (light, medium, and heavy) for cyclic stepped test. For each

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level, there were 5 replications, and total numbers of test member were 45 for cyclic

stepped load tests and 15 for constant cyclic load tests, respectively.

6.1.4 Testing A specially designed air cylinder and pipe rack system as shown in Figure 6.1 was

used to evaluate the fatigue life of OSB subjected to cyclic stepped loads. This set-up

mainly consists of pneumatic air cylinder, air regulator, electrical resettable counters,

limit switches, Universal flasher instead of PLC which makes cycles, and air pipes. This setup allowed 5 specimens to be tested simultaneously. The specimens were simply supported with a support span of 72 inches. Three identical loads were applied by the air cylinders at the center point of the rail and at points 1/6 of the span from the support end

(Figure 6.2). A wooden fixture and transfer roller system as shown in Figure 6.3 was built to keep member straight and prevent members from turning. A programmable logic controller and electrical resettable counter system recorded the number of cycles completed.

For GSA loading schedule, the test began at the 75 pound load of each air cylinder. Each of three loads was increased by 25 pounds after 25,000 cycles had been completed at each preceding load level. This process was repeated, and testing was continued until the tested member broke. After 25,000 cycles had been completed at a prescribed load level, or when the tested specimens completely broke, limit switches actuated and stopped the test.

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Figure 6.1 An air cylinder-pipe rack system for cyclic fatigue load tests.

Figure 6.2 Diagram showing the locations of three cyclic loads applied to a tested specimen.

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Figure 6.3 A wooden fixture and transfer roller system used to prevent tested members from turning.

For BIFMA backrest horizontal loading schedule, 75 lb. load (Table 6.3) at a rate of 20 cycles per minutes was applied to the members to complete 120,000 cycles for the constant fatigue test. There is no load increment in this method. After 120,000 cycles were completed, the constant fatigue test continued to complete 255,000 cycles unless the members did not break.

6.1.5 Results and Discussion

6.1.5.1 Failure Modes In general, two type failure modes were observed on tested OSB members. They were splintering tension failure and brush tension failure (Figure 6.4). OSB-I and OSB-II members exhibited splintering tension failure while OSB-III exhibited brush tension failure. This indicated that OSB-III was more brittle than OSB-I and OSB-II. This could be related to its higher MOR value. This might imply that OSB with higher MOR value shows brittle behavior. 167

(a)

(b)

Figure 6.4 Failure modes of OSB members subjected to cyclic fatigue bending loads: a) splintering tension mode; b) brush tension mode.

6.1.5.2 Cyclic Stepped Load Test Table 6.5 indicates average fatigue life results of back top rail OSB members as observed cycles. Mean difference between estimated and observed fatigue life cycles were obtained and presented as a percentage of estimate cycles. According to Table 6.5,

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the fatigue life of OSB-II medium and heavy and the fatigue life of OSB-III heavy was

perfectly estimated. On the other hand, the fatigue life of the OSB-I light-medium-heavy members, OSB-II light members, and OSB-III light members was overestimated value by

Palmgren-Miner rule with S-N curve equations derived from 5 percent data points. The fatigue life of OSB-III medium members was the only underestimated test group.

Table 6.5 The ratio of Estimated to observed mean fatigue life of full-size back top rail specimens for each combination of material type and service acceptance level.

Material Type Service Estimated Acceptance OSB-I OSB-II OSB-III (cycle/load) Level Observed Diff Observed Diff Observed Diff (cycle/load) (%) (cycle/load) (%) (cycle/load) (%) Light 25,000/75 32,558/95 0.77 43,418/90 0.58 38,166/155 0.66 Medium 50,000/100 74,190/115 0.67 54,117/80 0.92 34,520/175 1.45 Heavy 100,000/150 131,594/80 0.76 118,350/94 0.84 101,876/150 0.98 aDiff= the ratio of estimated to observed cycles.

Table 6.6 summarizes averaged MOR-stress ratio of OSB members tested in this

study. The stress for each OSB member was calculated by substituting its maximum

moment (calculated by Equation (6.5)) and depth value into the Equation (6.4). For

instance, the formerly determined depth for OSB-I light service was 3.875 inches. This

OSB member passed 75 lb. at light service level. Then substituting the depth and load into Equation (6.4) resulted with stress value 1251 psi at the load level of 75 pounds.

Since MOR value of OSB-I member is 2,529 psi, the individual passed stress ratio of

MOR to stress at the passed load level was 2.02.

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Table 6.6 Summary of the stress ratios ranges for service acceptance level for each OSB group in this study.

Service Acceptance Level Material Light Medium Heavy Type MOR/stress MOR/stress MOR/stress MOR/stress MOR/stress MOR/stress at passed at failed at passed at failed at passed at failed load level load level load level load level load level load level OSB-I 2.17 1.70 1.69 1.31 1.99 1.70 OSB-II 1.77 1.45 1.92 1.46 1.74 1.52 OSB-III 2.56 1.94 1.63 1.42 2.06 1.76 Average 2.17 (6) 1.70 1.75 (9) 1.40 1.93 (18) 1.66 acov= coefficient of variance.

The averaged passed stress ratios of MOR to passed stress of OSB members are

2.17, 1.75, and 1.93 for light, medium, and heavy service, respectively. For design of

upholstered furniture frame, the stress ratio of OSB should be greater than 2.17, or the proposed design stress of OSB member should be less than 46 % percent of its MOR.

These results were compared with the results: from fatigue performance of wood composites subjected to bending stresses study (Dai et al. 2007) of OSB specimens, which had a stress ratio of MOR to passed stress of OSB ranged from 1.10 to 2.08 and a stress ratio of MOR to failed stress of OSB ranged from 0.93 to 1.56 for all three acceptance levels. The stress ratio for design of upholstered furniture frame members using tested OSB should be higher than 1.56. In other words, the allowable design stress for OSB should be less than 64 percent of its MOR.

6.1.5.3 Constant Cyclic Load Test 4.094, 3.594, and 3.313 inches wide 80 inches long 15 OSB-I, OSB-II, and OSB-

III members which their span is 72 inches were tested in pipe-rock system according to constant cyclic BIFMA backrest test standard. All OSB-I and OSB-II members completed 255,000 cycles and they passed 120,000 cycles BIFMA backrest horizontal

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standard. Therefore, these two OSB groups meet BIFMA backrest test standard; however,

OSB-III members 2 and 3 were broken without meeting the standard while OSB-III

members 1, 3, and 4 completed 255,000 cycles and meet BIFMA backrest test standard.

Table 6.7 shows the ratio of OSB MOR to fatigue stress of members in this study.

The stress for each OSB member was calculated by substituting its maximum moment

(calculated by Equation (6.5)) and depth value into the Equation (6.4). For the formerly

determined depth for OSB-I, OSB-II, and OSB-III were 4.094, 3.594, and 3.313 inches,

and the load was 75 lb. for all OSB members. Accordingly, the maximum moment is

2,250 lb.-in., and the thickness of material is 23/32 inch. Then substituting the depth and

the moment value into Equation (6.4) resulted with stress value 1,120, 1,454, and 1,711

psi at the load level of 75 pounds. Since MOR value of all OSB members were previously

stated, the overall stress ratio of MOR to stress at the passed load level was 2.25 for

constant cyclic fatigue member, and the proposed design stress of OSB member should

be less than 44 % percent of its MOR. Splintering tension failure mode was mostly

observed in OSB-I and OSB-II while brush tension failure mode was mostly observed in

OSB-III materials.

Table 6.7 The ratios of OSB MOR to bending fatigue stress of OSB member that were subjected to constant cyclic fatigue load.

Material Stress MOR Ratio Type OSB-I 1120 2,529 2.26 OSB-II 1454 3,279 2.25 OSB-III 1711 3,848 2.25 Overall Ratio 2.25

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6.2 Conclusion In general, all OSB members that were subjected to GSA cyclic stepped bending fatigue test had an averaged stress ratio of MOR to passed stress was around 2.17, and the proposed stress design of all members in each OSB type and for each service acceptance level should be less than 46 percent of their MOR. Likewise GSA test members, all OSB members that were subjected to BIFMA constant cyclic fatigue test had an averaged stress ratio of MOR to stress was 2.25. It is proposed stress design of members for

BIFMA standard should be less than 44 percent of their MOR.

Most of OSB-I and all OSB-II members passed their service load and meet GSA standard. However; almost half of OSB-III members failed in their service level.

Especially, most of OSB-III members for medium services were broken at medium level.

All OSB-I and OSB-II members that were subjected to constant cyclic bending fatigue test meet BIFMA standard. However; two out of five OSB-III members failed.

In GSA and BIFMA test, OSB-I and OSB-II members meet standard while some of OSB-III members failed. Failure may cause by having higher MOR for material. Since

OSB-III has the highest MOR value, this material was more brittle than the other two materials which were more flexible. This conclusion were also inferred from failure modes that OSB-III members showed brush tension mode whereas OSB-II and OSB-I members showed splintering tension mode.

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