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XIAODONG WANG DESIGNING, MODELLING AND TESTING OF JOINTS AND ATTACHMENT SYSTEMS FOR THE USE OF OSB IN UPHOLSTERED FURNITURE FRAMES Thèse présentée à la Faculté des études supérieures de l’Université Laval dans le cadre du programme de doctorat en sciences du bois pour l’obtention du grade de Philosophiae Doctor (Ph.D.) DÉPARTEMENT DES SCIENCES DU BOIS ET DE LA FORÊT FACULTÉ DE FORESTERIE ET DE GÉOMATIQUE UNIVERSITÉ LAVAL QUÉBEC 2007 © Xiaodong Wang, 2007

Transcript of DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une...

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XIAODONG WANG

DESIGNING, MODELLING AND TESTING OF JOINTS AND ATTACHMENT SYSTEMS FOR THE

USE OF OSB IN UPHOLSTERED FURNITURE FRAMES

Thèse présentée à la Faculté des études supérieures de l’Université Laval

dans le cadre du programme de doctorat en sciences du bois pour l’obtention du grade de Philosophiae Doctor (Ph.D.)

DÉPARTEMENT DES SCIENCES DU BOIS ET DE LA FORÊT FACULTÉ DE FORESTERIE ET DE GÉOMATIQUE

UNIVERSITÉ LAVAL QUÉBEC

2007 © Xiaodong Wang, 2007

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Résumé court L'objectif général de l'étude est l’optimisation de la conception structurale des joints utilisés

dans les armatures des meubles rembourrés construites avec des panneaux OSB. Les

propriétés des matières premières OSB, MDF et PB, ont été étudiées. Les résultats

montrent que l'OSB a obtenu la variation de densité la plus élevée dans le plan et en

épaisseur, avec une résistance plus critique avec les vis qu’avec les agrafes. La densité des

panneaux MDF a moins varié, conférant une résistance plus homogène. On a également

déterminé la résistance en flexion des joints de gousset et de plaque métallique avec

différentes configurations sous les charges statique et de fatigue. La présence d’adhésif est

le facteur le plus important affectant l'efficacité des joints. Enfin trois configurations

d'armature de sofa trois-places en OSB avec deux types de joints et trois niveaux de charges

ont été modélisées en utilisant le logiciel SAP2000. Le modèle optimal s’avère utilisable en

chargement léger, moindrement pour un chargement moyen et inutilisable pour un

chargement élevé.

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Résumé long L'objectif de l'étude est de développer l'information requise pour la conception structurale

des joints utilisés dans les armatures des meubles rembourrés construites avec des

panneaux OSB. On présente trois niveaux d'essais: 1) le matériau, avec interaction matériau

/ attaches (vis et agrafe), 2) le joint (plaques gousset et métallique), et 3) modélisation d'une

structure de sofa en OSB.

En premier, les essais des propriétés des matières premières OSB, MDF et PB, notamment

l'effet de la densité localisée sur la performance en résistance de l'attache dans les panneaux

à base de bois, sous les chargements statique et cyclique ont été examinés. Les résultats

montrent que l'OSB a obtenu la variation de densité la plus élevée dans le plan et en

épaisseur, avec une résistance plus critique avec les vis qu’avec les agrafes. La densité des

panneaux MDF a moins varié, conférant une résistance plus homogène.

En second, on a déterminé la résistance en flexion dans le plan et dehors du plan des joints

de gousset et de plaque métallique avec différentes configurations sous les charges statique

et de fatigue. Les résultats indiquent que l'adhésif est le facteur le plus important affectant

l'efficacité des joints. Une augmentation de longueur des goussets de 102 à 203 mm (4 à 8

po) a accru la charge maximale pour le joint collé et pour le joint sans colle. L'utilisation de

deux paires de plaques était le facteur prédominant dans l'efficacité des joints avec métal.

Un rapport de résistance statique-à-fatigue peut être adopté comme rapport de dépassement

pour la conception des armatures de meubles rembourrés avec les joints réalisés avec des

goussets (2,1) et plaques métalliques (2,5). En général, la résistance en flexion dans le plan

était beaucoup plus grande que la résistance en flexion en dehors du plan pour les joints

réalisés avec des plaques métalliques et avec goussets.

Finalement, trois configurations d'armature de sofa trois-places fait en OSB avec deux

types de joints et trois niveaux de charges ont été modélisés en utilisant le logiciel

SAP2000. Le modèle optimal s’avère utilisable en chargement léger, moindrement pour un

chargement moyen et inutilisable pour un chargement élevé.

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Abstract The objective of the study was to develop the information needed for the engineered design

of joints used in upholstered frames constructed of OSB. Presented are three levels of tests:

1) material level, including interaction of material/fasteners (screw and staple), 2) joints

level (gusset-plate and metal-plate), and 3) modeling of a sofa frame made of OSB.

First, tests of basic material properties of OSB, MDF and PB, and localized density

effecting on fastener holding capacities in wood-based panels under static and cyclic

loading were examined. Results showed that in both static and cyclic loads, OSB had the

highest density variation in plane and through thickness, which was more critical to the

screw than to the staple holding capacities. The density of MDF panels varied the least,

leading to a more uniform fastener holding capacity.

Second, in-plane and out-of-plane moment capacities of OSB gusset-plate and metal-plate

joints with different configurations were determined under static and fatigue loads. Results

indicated that application of glue was the most important factor affecting the performance

of the joints. An increase in length of gusset-plate from 102 to 203-mm (4 to 8-in)

increased the peak load for both glued and unglued joints. For metal-plates, the use of two

pairs of plates was the most important factor that affected the performance of the joints. For

fatigue tests, the average values of 2.1 and 2.5 can be used as the passing static-to-fatigue

ratio for design of upholstered furniture frames with OSB gusset-plate and metal-plate

joints, respectively. In general, in-plane moment capacities were found to be 4 to 6 times

higher than out-of-plane moment capacities for both metal-plate and gusset-plate joints.

Finally, three configurations of three-seat sofa frame made of OSB with two types of joints

under three levels of service acceptance loads were modeled using the finite element

program SAP2000. The results demonstrated that the sofa frame model can pass light-

service acceptance level load; there is the limit to pass medium-service acceptance level

load; and it could not serve the heavy-service acceptance level load.

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Foreword

This thesis includes seven scientific papers, which are presented in Chapters III to VI, The

first article has been published in the first issue of 2007 of the Forest Products Journal. The

second and third articles were accepted by the Forest Products Journal in December 2006.

The fourth and fifth articles were submitted to the Forest Products Journal in February

2007, and the sixth and seventh articles were also submitted to the Forest Products Journal

in May 2007. The summary description of these articles is given below:

Chapter 3:

Article 1:

Wang X., A. Salenikovich, and M. Mohammad. 2007. Localized density effects on fastener

holding capacities in wood-based panels. Forest Prod. J. 57(1/2): 103-109.

Article 6:

Wang X., A. Salenikovich, M. Mohammad. Localized density effects on fastener holding

capacities in wood-based panels. Part 2: Cyclic tests. (Submitted to the Forest Products

Journal, May 2007).

Chapter 4:

Article 2:

Wang X., A. Salenikovich, M. Mohammad, C. Echavarria, J. Zhang. Moment capacity of

oriented strandboard gusset-plate joints for upholstered furniture. Part 1. Static Load.

Forest Prod. J. 57(7/8): 39-45.

Article 3:

Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Moment capacity of oriented

strandboard gusset-plate joints for upholstered furniture. Part 2. Fatigue Load. Forest Prod.

J. 57(7/8): 46-50.

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Chapter 5:

Article 4:

Wang X., M. Mohammad, A. Salenikovich, R. Knudson, J. Zhang. Static bending

resistance of metal-plated joints constructed of oriented strandboard for upholstered

furniture frames. (Submitted to the Forest Products Journal, February 2007).

Article 5:

Wang X., M. Mohammad, A. Salenikovich, R. Knudson, J. Zhang. Fatigue bending

resistance of metal-plated joints constructed of oriented strandboard for upholstered

furniture frames. (Accepted by Forest Products Journal, February 2007).

Chapter 6:

Article 7:

Wang X., A. Salenikovich, M. Mohammad. Out-of-plane static bending resistance of

gusset-plate and metal-plate joints constructed of oriented strandboard for upholstered

furniture frames. (Submitted to the Forest Products Journal, May 2007).

The roles of the authors of each article mentioned above are as follows: the first author had

responsibility to do the literature review and to define the methods, conducted all the

experimental and technical work, performed various statistical analyses, interpreted the

results and wrote the manuscripts, Dr. Salenikovich, Dr. Mohammad, Dr. Zhang, Dr.

Echavarria and Dr. Knudson as co-authors defined the overall project at the beginning,

facilitated the sampling and laboratory work, reviewed and revised the manuscripts.

The results of my Ph. D research work were also presented in the following international

conferences:

1. Wang X., M. Mohammad, L. Hu, A. Salenikovich. Evaluation of density distribution

in wood-based panels using x-ray scanning. 14th International Symposium of Non

Destructive Testing of wood. Hannover, Germany (May 2nd- 4th, 2005).

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2. Wang X., M. Mohammad, A. Salenikovich. Localized fastener-material interaction

in panels for upholstered furniture frames. 59th Forest Products Society Annual

Meeting. Quebec, Canada (June 19-22, 2005).

3. Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Capacité de moment de joints

agrafés de goussets construits avec du panneau de plaquettes orientées (OSB) pour les

structures de meubles rembourrés. 74ème Congrès ACFAS, Montréal, Canada. (May

19, 2006).

4. Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Moment capacity of stapled

gusset-plate joints constructed of oriented strandboard for upholstered furniture

frames. 60th Forest Products Society Annual Meeting. Newport Beach, California,

USA (June 25-28, 2006).

5. Wang X., A. Salenikovich, M. Mohammad, J. Zhang. Finite element model of sofa

frame made of OSB. Received the 2nd Place Forest Products Society – Eastern

Canadian Section Student Poster Award. Forest Products Society Eastern

Canadian Section Spring Meeting 2007. May 16th and 17th, Pembroke, Ontario,

Canada.

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Acknowledgements

I would like to express my deep appreciation to the individuals and organizations that

helped me in this endeavor. It is an honor and the great delight of my life to be affiliated

with all these wonderful people.

I am deeply grateful to everyone who has helped me in the preparation of my thesis. I will

always be thankful to my supervisor, Prof. Alexandre Salenikovich, whose wide

knowledge and logical way of thinking was invaluable on a number of key issues during

the full course of my study. His understanding, encouraging and personal guidance have

provided a good basis for the present thesis. I wish to express my warm and sincere

appreciation to my co-directors, Dr. Mohammad Mohammad from FPInnovations

Forintek Division, Québec lab, and Prof. Jilei Zhang from Mississippi State University for

their detailed and constructive comments, their tremendous support and encouragement

throughout this work.

I give my special appreciation to my master adviser Prof. Yves Fortin who offered and

made it possible for me to come from Vancouver to Quebec, and who encouraged me to

finish my master and to continue my Ph. D study. Special thanks to Prof. Robert

Beauregard, it was him who brought me this Ph. D subject and financially supported my

study for all these years, it is very important for me. I also would like to give my grateful

thanks to my friend Prof. Tatjana Stevanovic, for her personal advises and cares.

My sincere thanks are to my committee, Prof. Alain Cloutier, from the Wood Research

Center of the Université Laval, Prof. Eva Haviarova from Purdue University for their

detailed review, constructive criticism and excellent advice during the preparation of this

thesis.

First part of the experimental work of localized density effects on fastener holding

capacities was carried out and supported by FPInnovations Forintek Division, Québec lab. I

would like to thank the people in this organization who gave me a lot of help.

Acknowledgements are also to Mr. Richard Desjardin, the manager of the Building System

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Department, and Dr. Lin Hu, for their support and advice towards trial the arrangement and

testing, and so forth.

My warm appreciations are to Dr. Hui Wan and Dr. Tony Zhang, FPInnovations Forintek

Division, for their valuable advices and friendly help. Their extensive discussions around

my work have been very helpful for this study. I wish to express my thanks to Dr.

Chuangming Liu for his kind help on statistical analysis of the experiment results.

Additionally, I would like to express my appreciation for the following personnel for their

technical support, Mr. Jean-Claude Garant, Mr. Anes Omeranovic, Mr. Olivier Bäes, and

Ms. Francine Coté at FPInnovations Forintek Division.

I would like to express my thanks to all members in the Département de sciences du bois et

de la forêt, Centre de recherches sur le bois (CRB) for their help and cooperation. My

sincere appreciations to Mr. Sylvain Auger, Mr. Daniel Bourgault, Mr. Luc Germain, and

Mr. Éric Rousseau, for their technical support during my experimental work. Mr. Etienne

Simard, Mr. Alireza Kaboorani, and Mr. Maxime Bouchard-Deschênes for their help with

some tests. Thanks go to all professors (Bernard Riedl, Michel Beaudoin, and Roger

Hernández), all technologists (Yves Bédard, and David Lagueux), and all staff (Colette

Bourcier, Guylaine Bélanger, Marie-Noël Gagnon, Guillaume Giroud, Aziz Laghdir, and

Virginie St-Onge).

I appreciate a lot the help and encouragement that I received from my friends: Cesar

Echavarria, Alireza Kaboorani, Damien Voinot, Gaspard Houziaux, Williams Manuel

Munoz Toro, Benoit St-Pierre, Myriam Drouin, Julie Cool, Katherina Beck, Étienne

Simard, Maxime Bouchard-Deschênes, Pierre Bossis, Xiaojing Guo, Suying Xing,

Yongmin Zhang, Yan Jiang, Xiaolin Cai, Wenhua Liu and his daughter Yao Liu, etc.

I respectfully acknowledge the financial support given by CIBISA, FPInnovations Forintek

Division and Université Laval (Fonds de soutien au doctorat) for this project.

Last, but not least thanks to my families, relatives both in China and Canada for their

support and encouragement, my boy friend - Francois Magny and my little son Yann who

taught me to be patient.

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Table of Contents Résumé court ...........................................................................................................................i Résumé long .......................................................................................................................... ii Abstract................................................................................................................................. iii Foreword................................................................................................................................iv Acknowledgements.............................................................................................................. vii Table of Contents...................................................................................................................ix List of Tables ....................................................................................................................... xii List of Figures.......................................................................................................................xv Chapter 1 Background.........................................................................................................1

1.1 Introduction.............................................................................................................2 1.1.1 Purposes ..........................................................................................................2 1.1.2 Needs ..............................................................................................................3 1.1.3 Objectives .......................................................................................................3 1.1.4 Significance ....................................................................................................4 1.1.5 Scope and limitation .......................................................................................4 1.1.6 Methodology...................................................................................................5 1.1.7 Overview of the dissertation ...........................................................................6

1.2 Literature Review ...................................................................................................9 1.2.1 Design procedure ............................................................................................9 1.2.2 Loads and design philosophies .....................................................................10 1.2.3 Material properties........................................................................................13 1.2.4 Fatigue life ....................................................................................................15 1.2.5 Properties of fasteners and joints ..................................................................21 1.2.6 Frame construction .......................................................................................47 1.2.7 Structure of sofa frames................................................................................47 1.2.8 Structure of other upholstered furniture frames............................................48

Chapter 2 Load Distribution on a Sofa Frame...................................................................49 2.1 Introduction...........................................................................................................50 2.2 General configuration of loads and the construction of the sofa frame................50

2.2.1 Sofa frame construction ................................................................................50 2.2.2 Frame performance tests...............................................................................51 2.2.3 Simplified Sofa Frame Model.......................................................................52 2.2.4 Simplified Analysis of Sofa Structural Joints...............................................53

2.3 Discussion.............................................................................................................53 2.3.1 Seat System...................................................................................................53 2.3.2 Side Rail System...........................................................................................56 2.3.3 Back System .................................................................................................58

2.4 Summary...............................................................................................................59 Chapter 3 Localized density effects on fastener holding capacities in wood-based panels .. ..........................................................................................................................60

3.1 Localized density effects on fastener holding capacities in wood-based panels. Part 1: Static tests..............................................................................................................61

3.1.1 Résumé..........................................................................................................61 3.1.2 Abstract.........................................................................................................61

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3.1.3 Introduction...................................................................................................62 3.1.4 Materials and Methods..................................................................................64 3.1.5 Results and Discussion .................................................................................66 3.1.6 Conclusions and Recommendations .............................................................75

3.2 Localized density effects on fastener holding capacities in wood-based panels. Part 2: Cyclic tests ............................................................................................................76

3.2.1 Résumé..........................................................................................................76 3.2.2 Abstract.........................................................................................................76 3.2.3 Introduction...................................................................................................77 3.2.4 Materials and Methods..................................................................................78 3.2.5 Results and Discussion .................................................................................83 3.2.6 Conclusions and Recommendations .............................................................93

Chapter 4 Gusset-plate joints.............................................................................................94 4.1 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1: Static load..............................................................................................95

4.1.1 Résumé..........................................................................................................95 4.1.2 Abstract.........................................................................................................95 4.1.3 Introduction...................................................................................................96 4.1.4 Materials and Methods..................................................................................98 4.1.5 Results and discussion ................................................................................105 4.1.6 Conclusion ..................................................................................................110 4.1.7 APPENDIX.................................................................................................110

4.2 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 2: Fatigue load .........................................................................................112

4.2.1 Résumé........................................................................................................112 4.2.2 Abstract.......................................................................................................112 4.2.3 Introduction.................................................................................................113 4.2.4 Materials and Methods................................................................................114 4.2.5 Results and Discussion ...............................................................................119 4.2.6 Conclusions.................................................................................................121 4.2.7 Practicality ..................................................................................................122

Chapter 5 Metal-plate connected joints...........................................................................123 5.1 Static bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames .................................................................124

5.1.1 Résumé........................................................................................................124 5.1.2 Abstract.......................................................................................................124 5.1.3 Introduction.................................................................................................125 5.1.4 Materials and Methods................................................................................127 5.1.5 Results and Discussion ...............................................................................132 5.1.6 Conclusion ..................................................................................................138

5.2 Fatigue bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames .................................................................139

5.2.1 Résumé........................................................................................................139 5.2.2 Abstract.......................................................................................................139 5.2.3 Introduction.................................................................................................139 5.2.4 Materials and Methods................................................................................141

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5.2.5 Results and Discussion ...............................................................................146 5.2.6 Conclusions.................................................................................................150 5.2.7 Practicality ..................................................................................................151

Chapter 6 Out-of-plane static bending resistance of gusset-plate and metal-plate joints constructed of oriented strand board for upholstered furniture frames ..............................152

6.1 Résumé................................................................................................................153 6.2 Abstract...............................................................................................................153 6.3 Introduction.........................................................................................................154 6.4 Materials and Methods........................................................................................156 6.5 Results and Discussion .......................................................................................168 6.6 Conclusion ..........................................................................................................174

Chapter 7 Finite element model of sofa frames made of OSB........................................175 7.1 Introduction.........................................................................................................176 7.2 Methodology.......................................................................................................176 7.3 Results and Discussion .......................................................................................188 7.4 Conclusions and Recommendations ...................................................................195

Summary and Conclusions .................................................................................................197 Recommendations for Future Work ...................................................................................204 Bibliography .......................................................................................................................205 APPENDIX I Visiting Several Upholstered Furniture Companies ..................................212 APPENDIX II Tables in finite element modelling...........................................................223

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List of Tables Table 1.1 The initial load, load increments, and acceptance levels used in GSA upholstered

furniture performance tests (adapted from GSA 1998) ................................................13 Table 1.2 National Furniture Center Upholstered Furniture Performance-acceptance Level

(adapted from GSA “Bare frame”) ...............................................................................14 Table 1.3 Average values of fatigue life (number of cycles to failure) for each joint material

type at each of bending moment level. (from Zhang et al. 2001a)...............................17 Table 1.4 Calculation of the fatigue life for plywood joints using the Palmgran-Miner rule.

(Adapted from Zhang et al. 2001a) ..............................................................................19 Table 1.5 Comparison of predicted fatigue life with average fatigue life from stepped load

tests. (from Zhang et al. 2001a)....................................................................................19 Table 1.6 Withdrawal strength of dowels in the face of OSB (adapted from Eckelman et al.

2002) .............................................................................................................................27 Table 1.7 Withdrawal strength of dowels in edge of OSB (adapted from Eckelman et al.

2002) .............................................................................................................................27 Table 1.8 Bending strength of two-pin moment-resisting dowel joints (adapted from

Eckelman et al. 2002) ...................................................................................................28 Table 1.9 Results for lateral holding capacity of dowels: Test series 1a (adapted from Zhang

et al. 2002a) ..................................................................................................................30 Table 1.10 Results for lateral holding capacity of dowels: Test series 2 a (adapted from

Zhang et al. 2002a) .......................................................................................................30 Table 1.11 Torsional strength per joint, two multi-groove dowel, symmetrically spaced 25-

mm (1 inch) from edge of rail, i.e. all rails 51-mm (2 inches) wider than dowel spacing a (adapted from Zhang et al. 2002b) .............................................................................32

Table 1.12 Face and edge withdrawal resistance (N) of screws in OSB (adapted from Erdil et al. 2002a) ..................................................................................................................35

Table 1.13 Withdrawal force versus pilot hole diameter (adapted from Erdil et al. 2002a) 35 Table 1.14 Withdrawal strength of staples from OSB (adapted from Erdil et al. 2003a) ....38 Table 1.15 Summary of grade properties on OSB panels (adapted from Forintek’s report

(Wang and Knudson 2002))..........................................................................................39 Table 1.16 Lateral holding strength of the staples (adapted from Erdil et al. 2003a) ..........39 Table 1.17 Moment resisting strength of Douglas-fir plywood gusset and stapled joints

(adapted from Erdil et al. 2003a)..................................................................................40 Table 1.18 Bending strength of gusset-plate joints constructed of wood composites

(adapted from Zhang et al. 2001b). ..............................................................................41 Table 1.19 Summary of grade properties on OSb Panels (adapted from Forintek’s report

(Wang and Knudson 2002))..........................................................................................42 Table 1.20 Bending strength of moment resisting through- bolt with dowel nut joints

(adapted from Erdil et al. 2003b)..................................................................................44 Table 1.21 Holding strength of dowel nut in relation to end distance (adapted from Erdil et

al. 2003b) ......................................................................................................................44 Table 1.22 Bending strengths of moment-resisting toothed metal plate connector joints

(adapted from Eckelman and Erdil, 1998)....................................................................46 Table 1.23 Zhang et al. (2005) evaluated the moment capacity of metal-plate-connected

joints in furniture grade pine plywood..........................................................................46

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Table 2.1 Cyclic load schedules of GSA performance tests for bare frame (adapted from GSA 1998) ....................................................................................................................51

Table 2.2 Estimated joints strengths .....................................................................................54 Table 3.1 Screw and staple holding capacities available in literature. .................................63 Table 3.2 Sampling plan to evaluate the static performance of fasteners in wood based

panels. ...........................................................................................................................65 Table 3.3 Fastener performance with localized density for screws. .....................................70 Table 3.4 Fastener performance with localized density for staples. .....................................72 Table 3.5 Sampling plan to evaluate the cyclic performance of fasteners in wood based

panels. ...........................................................................................................................79 Table 3.6 Reference load levels for cyclic loading...............................................................80 Table 3.7 Test results for screw performance in cyclic loading ...........................................84 Table 3.8 Test results for staple performance in cyclic loading. ..........................................85 Table 3.9 Comparisons for screw and staple performances in static and cyclic loadings....86 Table 4.1 Description of the specimens, load capacities, and failure modes of gusset-plate

joints constructed of OSB. ..........................................................................................100 Table 4.2 Performance-acceptance levels of upholstered furniture referencing to GSA

(1998)..........................................................................................................................102 Table 4.3 Average values (COV%) of physical and mechanical properties of joint members

and gusset-plates. ........................................................................................................106 Table 4.4 Test specimen configurations and results for GSA backrest frame schedule.....115 Table 4.5 Test specimen configurations and results for GSA seat load foundation schedule.

....................................................................................................................................116 Table 4.6 Cyclic stepped load schedule using GSA backrest frame testing schedule........118 Table 4.7 Cyclic stepped load schedule for testing using GSA seat load foundation testing

schedule. .....................................................................................................................118 Table 5.1 Moment capacities of metal-plated joints constructed of plywood available in

literature (Zhang et al. 2005). .....................................................................................126 Table 5.2 Moment capacities of gusset-plate joints constructed of OSB available in

literature (Wang et al. 2007b).....................................................................................127 Table 5.3 Acceptance performance level of upholstered furniture in accordance with GSA

(1998)..........................................................................................................................131 Table 5.4 Physical & mechanical properties of OSB. ........................................................133 Table 5.5 Ultimate load capacity and failure modes of metal-plated joints constructed of

OSB.............................................................................................................................133 Table 5.6 Stiffness of six configurations of metal-plate joints. ..........................................137 Table 5.7 Test specimen configurations. ............................................................................144 Table 5.8 Cyclic stepped load levels using GSA backrest frame testing schedule. ...........145 Table 5.9 Cyclic stepped load levels using GSA seat load foundation testing schedule....146 Table 5.10 Test results using GSA backrest frame schedule..............................................148 Table 5.11 Test results using GSA seat load foundation schedule. ....................................149 Table 6.1 In-plane moment capacities of metal-plated joints constructed of OSB available

in literature (Wang et al. 2007d).................................................................................158 Table 6.2 In-plane moment capacities of gusset-plate joints constructed of OSB available in

literature (Wang et al. 2007b).....................................................................................159

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Table 6.3 Out-of-plane moment capacities and stiffness of metal-plate joints constructed of OSB.............................................................................................................................163

Table 6.4 Out-of-plane moment capacities and stiffness of gusset-plate joints constructed of OSB.............................................................................................................................164

Table 6.5 Acceptance performance level of upholstered furniture in accordance with GSA (1998)..........................................................................................................................165

Table 6.6 Distributed loads applied on each springs per seat of sofa (from Tackett and Zhang 2007). ...............................................................................................................165

Table 6.7 Physical and mechanical properties of OSB.......................................................171 Table 7.1 Material properties of members and joints used in the finite element model.....179 Table 7.2 Acceptance performance level of upholstered furniture in accordance with GSA

(1998)..........................................................................................................................181 Table 7.3 Distributed loads applied on each spring of a sofa seat for light, medium, and

heavy-service acceptance levels (from Tackett and Zhang 2007). .............................181 Table 7.4 Specified Strength, Stiffness, and Rigidity Capacities for Type 1 (Standard)

Design OSB (Nominal thickness 18.5mm, Rating grade B) (Adapted from Table 7.3C CSA-O86) ...................................................................................................................183

Table 7.5 The average short-term strength values ..............................................................184 Table 7.6 Joint displacements under light-service acceptance level load...........................190 Table 7.7 Element joint big forces in the links under light-service acceptance level load.191 Table 7.8 Joint displacements under medium-service acceptance level load.....................193 Table 7.9 Joint displacements under heavy-service acceptance level load. .......................194

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List of Figures Figure 1.1 Diagram showing construction of the T-type, two-pin dowel joint specimen in

fatigue test (from Zhang et al. 2001a) ..........................................................................17 Figure 1.2 A specially designed pin rack system with pneumatic cylinder for evaluating

fatigue life of T-shaped joints (from Zhang et al. 2001a) ............................................18 Figure 1.3 Bending moment versus fatigue life (M-N) curve from constant bending tests of

plywood joints (from Zhang et al. 2001a) ....................................................................18 Figure 1.4 Typical configuration of the specimens in the face and edge withdrawal tests of

dowel joints (Eckelman et al. 2002) .............................................................................25 Figure 1.5 General dimensions of the two-pin moment-resisting dowel joints (Eckelman et

al. 2002) ........................................................................................................................26 Figure 1.6 Apparatus for holding specimens in the face and edge withdrawal tests of dowel

joints (Eckelman et al. 2002)........................................................................................26 Figure 1.7 Test apparatus for evaluating the bending strength of the joints (Eckelman et al.

2002). ............................................................................................................................26 Figure 1.8 General configuration of specimens used in lateral dowel strength tests with the

centre rail in: a) flat position b) edge position (adapted from Zhang et al. 2002a) ......28 Figure 1.9 Dimensions of the specimens used in lateral shear strength of dowel joints tested

in edge and flat positions (adapted from Zhang et al. 2002a) ......................................29 Figure 1.10 Methods of testing the lateral face and edge strength of dowels (adapted from

Zhang et al. 2002a) .......................................................................................................29 Figure 1.11 Configurations of the joints tested with the rail in the flat and edge positions

(adapted from Zhang et al. 2002b) ...............................................................................31 Figure 1.12 Apparatus used to test joints in the flat and edge positions (adapted from Zhang

et al. 2002b) ..................................................................................................................31 Figure 1.13 Configuration of screw withdrawal test (adapted from Erdil et al. 2002a).......34 Figure 1.14 Screw withdrawal from edge and face (adapted from Erdil et al. 2002a).........34 Figure 1.15 Specimens with screw embedded to full depth (a) and with tip protruding (b)

(adapted from Erdil et al. 2002a)..................................................................................34 Figure 1.16 General configuration of face (left) and edge (right) withdrawal specimens

(from Erdil et al. 2003a) ...............................................................................................37 Figure 1.17 Geometric dimensions of face and edge staple withdrawal specimens (adapted

from Erdil et al. 2003a).................................................................................................38 Figure 1.18 Apparatus for evaluating face and edge withdrawal strength of staples (adapted

from Erdil et al. 2003a).................................................................................................38 Figure 1.19 Configuration and apparatus of staple lateral holding strength (adapted from

Erdil et al. 2003a) .........................................................................................................39 Figure 1.20 Configuration and apparatus for staple bending strength (adapted from Erdil et

al. 2003a) ......................................................................................................................40 Figure 1.21 Through-bolt with dowel-nut (from Erdil et al. 2003b)....................................43 Figure 1.22 Dimensions of specimens for dowel-nut withdrawal test (from Erdil et al.

2003b) ...........................................................................................................................43 Figure 1.23 Dimensions of moment resisting through-bolt with dowel-nut specimens

(adapted from Erdil et al. 2003b)..................................................................................44

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Figure 1.24 Typical sofa frame construction (from Chen 2003). .........................................48 Figure 2.1 Structural performance test loads of three-seat sofa frames................................52 Figure 2.2 Simplified three-seat sofa frame structural model ..............................................52 Figure 2.3 Front rail to stump joint under vertical loading...................................................55 Figure 2.4 Front rail to stump joint under horizontal sidethrust loading.............................55 Figure 2.5 Front rail to stump joint under out of plane loading............................................56 Figure 2.6 Side rail system under vertical loading ..............................................................57 Figure 2.7 The side rail system under horizontal front to back loading ...............................58 Figure 2.8 Horizontal loads on the top rail to back post joints.............................................59 Figure 3.1 Typical images of horizontal density variation in panels: a) OSB; b) MDF; and

c) PB. ............................................................................................................................67 Figure 3.2 Vertical density profiles of OSB, MDF and PB specimens. ...............................67 Figure 3.3 Average screw withdrawal resistance of OSB, MDF and PB specimens. ..........69 Figure 3.4 Screw head pull-through resistance of OSB panels in relation to average

localized density. ..........................................................................................................74 Figure 3.5 A test set-up for carrying out static (left) and cyclic (right) lateral loading

resistance of screws ......................................................................................................80 Figure 3.6 An example of typical cyclic loading regime for fastener holding capacity tests

of screw face withdrawal on 11-mm OSB panels.........................................................82 Figure 3.7 Example of load-displacement curves of static and cyclic tests of screw head

pull-through on 15-mm OSB panels. ............................................................................87 Figure 3.8 Average cyclic withdrawal resistance of screws in OSB, MDF and PB panels. 87 Figure 3.9 Cyclic head pull-through resistance of staples in OSB panels in relation to

average localized density. .............................................................................................92 Figure 4.1 Schematic of a three-seat sofa frame (Critical joints—Side rail to back post joint

& Back rail to back post joint)......................................................................................97 Figure 4.2 Configuration of a typical staple-glued gusset-plate joint...................................99 Figure 4.3 Placement of staples in gusset-plates of unglued joints (Configurations a-i). ..101 Figure 4.4 GSA load applied on the back rail of a three-seat sofa frame (back rail to back

post joint). ...................................................................................................................103 Figure 4.5 Schematic of a moment-resisting connection....................................................105 Figure 4.6 Forces in fasteners of a moment-resisting connection. .....................................105 Figure 4.7 Typical failure modes of gusset-plate joints......................................................107 Figure 4.8 Experimental reference resistance vs. predicted peak loads of stapled gusset-

plate joint assemblies with/without glue.....................................................................108 Figure 4.9 Schematic of a three-seat sofa frame: a) side rail to back post joint; b) back rail

to back post joint.........................................................................................................117 Figure 4.10 Setup for the fatigue test of gusset-plate connected joint assemblies. ............119 Figure 5.1 An example of metal-plated joint with two LVDTs’ points A and B. ..............128 Figure 5.2 Configurations of metal-plated joints................................................................130 Figure 5.3 Measurement of the angle of rotation, α. ..........................................................131 Figure 5.4 Typical moment-rotation curves of metal-plated joints. ...................................132 Figure 5.5 Typical failure modes of metal-plated joints.....................................................134 Figure 5.6 Experimental mean ultimate loads of metal-plated joints. ................................136 Figure 5.7 Rotational stiffness of metal-plated joints.........................................................137 Figure 5.8 Configurations of metal-plated joints for fatigue tests. .....................................143

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Figure 5.9 Schematic of a three-seat sofa frame. a) side rail to back post joint; b) back rail to back post joint.........................................................................................................144

Figure 5.10 Setup for fatigue test of metal-plate connected joints. ....................................146 Figure 6.1 Configurations of metal-plate joints for out-of-plane moment tests. ................160 Figure 6.2 Configuration of a typical staple-glued gusset-plate joint for out-of-plane

moment tests. ..............................................................................................................161 Figure 6.3 Placement of staples in gusset-plates of unglued joints (Configurations a-i) for

out-of-plane moment tests. .........................................................................................162 Figure 6.4 Schematic of the out-of-plane bending carried by the front rail. ......................165 Figure 6.5 An example of out-of-plane bending test joint with a LVDT point A. .............166 Figure 6.6 Measurement of the angle of rotation, α. ..........................................................166 Figure 6.7 Typical out-of-plane moment-rotation curves: (a) gusset-plate, and (b) metal-

plate joints...................................................................................................................167 Figure 6.8 Typical failure modes of test joints. ..................................................................172 Figure 6.9 Experimental mean ultimate out-of-plane loads of gusset-plated and metal-plated

joints............................................................................................................................173 Figure 6.10 Stiffness of all configurations of gusset-plated and metal-plated joints. ........173 Figure 7.1 Typical three-seat sofa frame. ...........................................................................178 Figure 7.2 Two of 2 x 6 metal-plate joint in-plane and out-of-plane rotation-moments (R3

and R2). .......................................................................................................................180 Figure 7.3 Light-service acceptance level loads distributed on a sofa frame model. .........182 Figure 7.4 Configurations (a), (b) and (c) of a three-seat sofa made of OSB.....................185 Figure 7.5 Types of connections used in sofa frame model. ..............................................187 Figure 7.6 OSB sofa frame with torsion stress bars for configurations (a), (b) and (c). ....189

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Chapter 1 Background

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1.1 Introduction

1.1.1 Purposes Upholstered furniture manufacturers are always looking for ways to cut down on the cost

of the raw material. They always search for a new less expensive material, which of course,

have to be as strong and reliable as the traditional ones. Recently, upholstered furniture

manufacturers are exploring new alternatives to solid wood, especially with the

development of CNC technology, where panels are becoming the good alternative for solid

wood. Oriented Strand Board (OSB) is one of those panel products that have a good

potential in such applications.

OSB is a wood-based flake board product that emerged in the early 1980s. Water resistant

exterior-type resin is applied to long narrow flakes to form a mat of three to five layers.

OSB has only recently started to be investigated for use in furniture framing. There are not

many published reports on the use of OSB in furniture frames. FPInnovations Forintek

Division published a technical report on the “Suitability of OSB for usage in upholstered

furniture” (Wang and Knudson 2002). The results of the study indicate that some

upholstered furniture manufacturers use a limited amount of OSB in their furniture frames.

The main advantages of OSB are the low cost, product consistency, availability, and low

labour requirement. This indicates that OSB deserves careful consideration as a frame

stock for upholstered furniture. On the other hand, the major disadvantages of the product

cited by the furniture manufacturers are a low staple withdrawal resistance on edges, lower

perpendicular to grain strength compared to lumber, rougher surface and faster saw blade

and tool wear. Moreover OSB lacks the bending strength of solid wood (Erdil, 1998),

hence one should be careful with the construction of front rails in sofas, where substitution

for solid wood on a one-to-one basis could lead to serious structural problems.

There is no reason to assume that sound frames cannot be constructed of OSB. We should

further investigate the characteristics and capacities of OSB in order to ensure its rational

use through appropriate design. Upholstered furniture manufacturers are looking for an

alternative to hardwood lumber and plywood, combining low cost, consistent high strength

and a good fastener holding capacity. If OSB manufacturers are able to supply products

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with those attributes, there will be an opportunity to expand the use of OSB in the

upholstered furniture market.

1.1.2 Needs The upholstered furniture industry is in need for technical information on rational design

sofa frames with OSB, especially the joints design with OSB, since most failures occur at

joints. Joints are the weakest part in the frame. Also, strength design of upholstered

furniture frames should take into account information about joints fatigue strength

properties since most service failures appear to be fatigue related (Eckelman and Zhang

1995). However, the strength properties currently available for the design of upholstered

furniture frames have mostly been determined using static load tests. Research to

determine the fatigue properties of joints subjected to cyclic loads in furniture application

has so far been minimal. Although, fatigue studies have been done in the area of material

(wood and composites) for structural design of furniture frame, studies are rarely

concerning joint fatigue. So, the research of joint fatigue is quite new and we have to carry

out in detail research on this topic.

1.1.3 Objectives This study was focused on issues associated with designing, modelling, and testing of

joints and attachment systems for the use of OSB in upholstered furniture frames. The

primary purpose of this study was to develop technical information needed for strength and

durability design of joints used in upholstered frames constructed of OSB. This study was

intended to add to the previous studies and supplement the results with additional

experimental and mathematical investigations to improve the methodology of joints design

for upholstered sofa frame. The following complementary objectives comprise the purpose

of the study:

1) Examine basic material physical and mechanical properties of OSB, Medium density

fiberboard (MDF) and Particle board (PB), and interaction of material/fastener, including

screw and staple face and edge direct withdrawal resistance, screw lateral resistance, and

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screw and staple head pull-through resistance under static and cyclic loads, and these

resistances correlations with material localized density.

2) Determine in-plane and out-of-plane bending moment capacities of OSB joints,

including gusset-plate and metal-plate joints under static and fatigue loadings.

3) Estimate load distribution on joints of a full-size structural three-seat sofa frame using

numerical modeling. Different configurations of sofa frames made of OSB with different

types of joints under three levels of service acceptance loads were modeled using finite

element method (SAP2000). Two types of connections were used in the model: rigid and

semi-rigid (with real connectors’ properties).

4) Provide recommendations and improvements based on testing and modeling.

1.1.4 Significance It is postulated that findings from this study will help the upholstered furniture companies

to improve their designs and produce reliable products with good performance/cost ratios

by providing better designs for sofa frames made of OSB and, in particular, for joints made

of OSB.

This study provides tools to support the development of OSB frames for upholstered

furniture and foster the development of niche market for OSB.

1.1.5 Scope and limitation A literature review has been carried out in addition to a study of the various types of joints

for upholstered sofa frame made of OSB. Four upholstered furniture manufacturers in

Quebec area have been visited to learn more about the framing and jointing systems and

potential problems associated with the usage of OSB in such frames.

The material properties and fastener material localized density relationships were studied

using OSB of various thickness and various types of fasteners. The static tests were carried

out according to ASTM standards, and fatigue tests were conducted in accordance with

GSA standard (GSA 1998).

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The frame structural modeling was limited to a three seats standard sofa frame, other

types of frames, such as recliners, should be the subject of future studies, after validation of

the model.

1.1.6 Methodology To achieve the objectives, the following steps have been done:

1) Based on the literature review of pertinent research and visits of furniture manufacturers,

the decisions on the types of joints and frame configuration to be studied were made.

2) Structural analysis of a typical sofa frame:

This part of study provides background information on how to estimate load distribution on

the joints of a full-size three-seat sofa frame. A simplified three-seat sofa frame structural

model was proposed, including the most critical members needed to resist service loads.

Structural analyses were performed on this frame using the various General Service

Administration (GAS 1998) loading cases (i.e. light duty, medium duty and heavy duty)

and boundary conditions. Internal forces at each connection and stresses in each structural

member were evaluated in two different ways. First, the analysis was performed using

basic structural analysis techniques assuming rigid joints, magnitudes and directions of

internal forces at each connection in the frame model were determined, i.e., type of forces

that those connections were subjected to such as tension and shear force, and bending

moments. Second, finite element analysis software (SAP 2000) was used to analyze the

furniture frame with real joint performance parameters considering semi-rigid joint effect.

3) OSB panel properties and localized fastener characteristics:

Material localized density / fastener holding capacities were studied in this part. Basic

material tests, such as density profile, internal bond, modulus of elasticity (MOE), and

modulus of rupture (MOR) were performed. These data was used as input for the

modelling of the joints and for the sofa frame. The fastener holding capacity and, localized

density, were evaluated. Screws and staples were chosen since they are the common types

of fasteners in the upholstered furniture industry. The fastener experiments under static and

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cyclic regimes were carried out. These tests were screw and staple face and edge direct

withdrawal, screw lateral, and screw and staple head pull-through. Such information is

crucial for the final model and it is also important in providing some suggestions to the

OSB industry as to how they could improve their panel properties specifically for

upholstered furniture usage.

4) Tests and analysis of joints identified

After identifying the connection points subjected to maximum internal forces in the frame

model, joint configurations were proposed for connecting those being highly stressed

connections. Joint specimens of finally determined configurations were built using OSB

and tested. Two types of joints were investigated, including staple gusset-plate with or

without glue, and metal-plate. In-plane moment capacities of OSB gusset-plate and metal-

plate joints under static and fatigue loads were examined. Then the static out-of-plane

moment capacity of these joints with gusset-plates and metal-plates were determined

experimentally for different configurations. The comparisons between in-plane and out-of-

plane moment capacities were performed.

5) Modeling of sofa frames made of OSB

Three OSB sofa frame configurations were designed. The finite element analysis software

(SAP2000) was used to analyze the sofa frames under three levels of service acceptance

loads. The performances of each frame and joint were studied, and then through analysis,

any possible weaknesses due to OSB properties were identified. Recommendations and

improvements were proposed based on those observations.

1.1.7 Overview of the dissertation Background presented in Chapter 1 continued with a literature review including furniture

frame design procedure; loads and design philosophies. In this study, GSA performance

test loads were used as design loads. Material properties, such as fatigue life were reviewed

based on most recent publications on member and joints fatigue research. Also,

experimental studies that have been completed in the past were discussed for the properties

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of different types of fastener and joints, including dowel, screw, staple, gusset-plate,

through bolt with dowel nuts, toothed metal connector plates, tenon-mortise, and T-nuts.

Chapter 2 provided information on how to estimate load distribution on the joints of a full-

size three-seat sofa frame. A simplified three-seat sofa frame structural model was

analyzed. Internal forces at each connection were evaluated using structural analysis

techniques. Finite element analysis (SAP 2000) would be performed later, in Chapter 7,

using parameters determined during the experimental study.

In Chapter 3, the material localized density effects on fastener holding capacities in wood-

based panels were discussed. Some basic materials tests, such as density profile, internal

bond, and bending MOE and MOR, and localized density / fastener holding capacities

were investigated. Fastener holding capacities - localized density relationship tests were

presented in this chapter, including screw and staple face and edge withdrawal, screw

lateral resistance, and screw and staple head pull-through under static and cyclic regimes.

Two journal articles were written based on the test results in this chapter. Article 1:

localized density effects on fastener holding capacities in wood-based panels; Article 6:

localized density effects on fastener holding capacities in wood-based panels. Part 2:

Cyclic tests.

In Chapter 4, tests and analysis of gusset-plate joints made of OSB were reported. Joints

most commonly used and/or with the most potential use in industry, e.g. stapled gusset-

plate with/without glue were selected. Such joints were tested using static and fatigue

loadings. Experiments of OSB stapled gusset-plate with/without glue joint static and

fatigue bending tests were performed. Two articles were written in this part. Articles 2 and

3 described static and fatigue tests of critical joints of sofa frame made of OSB. 1) Moment

capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1: Static

Load; 2) Moment capacity of oriented strandboard gusset-plate joints for upholstered

furniture. Part 2: Fatigue Load.

Similar to Chapter 4, Chapter 5 studies OSB metal-plate joints under static and fatigue

bending tests. Two articles were written in this part (Article 4 and 5) that discussed static

and fatigue tests of metal-plate joints of sofa frame made of OSB. The article 4 titled static

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bending resistance of metal-plate joints constructed of oriented strandboard for upholstered

furniture frames. The article 5 titled fatigue bending resistance of metal-plate joints

constructed of oriented strandboard for upholstered furniture frames.

Chapter 6 demonstrated the test results of static out-of-plane moments capacity of T-

shaped joints with gusset-plate and metal-plate joints made of OSB for different

configurations. The results from out-of-plane were compared with in-plane moment

capacities. Out-of-plane moment capacities were needed for modeling of the sofa frame.

This chapter yielded the last article from the thesis.

Chapter 7 discussed the finite element model of a typical sofa frame made of OSB. Three

configurations of a three-seat sofa frame made of OSB with two types of joints under three

levels of service acceptance loads were modeled using the finite element method

(SAP2000). Two types of connections are used in the model: rigid (fixed) and semi-rigid

(with real connectors’ properties). Comparing the results of experimental test and finite

element analysis for three-seat sofa frame could be a future project.

In the summary and conclusions section, an overview of the research and achieved results

are presented and some conclusions are provided. This section also included

recommendations and improvements based on research findings, and suggestions for future

research.

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1.2 Literature Review Although there is much literature pertaining to various aspects of furniture design, there are

very few publications related the structural analysis and design of upholstered furniture

frames. Nevertheless, the last fifty years saw valuable studies related to the structural

analysis and design of furniture and its components, which can be applied to OSB as well.

It is worthwhile to review these studies in order to develop basic guidelines for the

structural design of upholstered furniture frames of OSB. Studies of interest may be

divided into the following subgroups according to the major topics covered:

1.2.1 Design procedure At the early age in recorded history, man had already developed furniture design and

constructions differing little from those in use today. In 1963, chairs, cabinets and even a

folding bed were found in the tomb of the Ancient Egyptian King Tutankhamen's tomb

(Desroches-Noblecourt, 1963). After the 10th century, as a result of innovations borrowed

from the field of architecture, both the aesthetic and functional design of furniture vastly

improved. Immediately after the Middle Age, almost every new idea introduced in

architecture was incorporated into furniture, especially in Europe. In other words, the

renaissance affected both architecture and furniture design in Europe (Erdil 1998).

There are actually 3 areas of furniture design (In the text book of Eckelman 1991, Chapter

I, p. 1-2). The first is aesthetic design, that is, the artistic development of a structural form

that is appealing to consumers and which will culturally enrich their lives. This area is still

of most importance today. The second is function design, planning the structure so that it

will perform its intended function as efficiently as possible. The third one is engineering

design which involves devising the structure so that it can safely resist the load imposed

upon it in service.

Engineering design of a piece of furniture, just as that of any other structures, consists of

carrying out the following procedures:

1) Determining the loads which will be imposed upon the structure in service

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2) Designing the size of the members or parts required to carry these loads and “draw

up” a “prototype” structure

3) Analyzing the magnitude and distribution of the internal forces arising in this trial

structure under the action of the external loads

4) Redesigning the trial structure and repeating steps 2 through 4, until no part is

overstressed

5) Designing the joints so that they can safely carry the internal and external loads

acting upon them in service

The real situation is a little different from the above in that the aesthetic design of an artist

constitutes the first step in the design procedure. In fact the artist’s sketch corresponds to

the first attempt at a trial structure. Nonetheless, the formerly described procedure will

form the basis of the computer-aided design system not taking into account the aesthetic

design step.

1.2.2 Loads and design philosophies The first step in any design procedure involves the determination of the external loads

which the piece of furniture must be able to withstand in service. Such loads are not always

predictable, and determining them is often more difficult than the design of the structure

itself. In order to select these loads, the designer must have a thorough knowledge of the

conditions the furniture will encounter in service. We must know not only how it is used,

but also how it is abused. To be more exact, we need to know the nature of the static and

dynamic forces that will be encountered in service, i.e., their magnitude, direction and

frequency of occurrence. In the case of sofas, for instance, we need to know the forces

arising when users sit down, lean backwards, and then move around as they settle. We also

need to know which forces are imposed on the sofas when they are transported or moved.

Such forces could be quite high, and furniture is often damaged in transit. We also need to

know whether the sofa will be shoved across a floor, or whether if it will be lifted and

carried from one location to the next, whether it is to be moved in an upright position or

standing on end. Obviously, it is important that we anticipate as many potential uses of the

furniture as possible. Many failures occur in service simply because the ways the furniture

were to be used were not foreseen.

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Structural design can be defined as a procedure for determining member and joint

configurations to ensure that external loads do not exceed the resistance of a structure.

Safety, function, and economy are the three major goals of design. Normally, a factor of

safety of 3 is assumed (Eckelman 1970a, 1974) for allowable design stresses in furniture

designs. This may be increased to 6 if fatigue and creep conditions are considered.

There are two philosophies applied in current structure (Geschwindner et al. 1994; Salmon

and Johnson 1990). The first is Allowable Stress Design (ASD), also called “working

stress design”. ASD is a classical approach to structural design, not only for wood

structures, but also for the design of reinforced concrete and steel structures. ASD is based

on the concept that the maximum stress in a member will not exceed an allowable stress,

which incorporates a factor of safety (FS) under normal service conditions. All load effects

are determined by elastic analysis of the structure. Both the factor of safety and the

resulting allowable stress depend on the governing limit stress, with allowable stress

expressed as follows:

Governing limit stress

Allowable stress = ------------------------------ (1.1) Factor of safety The governing limit stress depends on the structural element type and stress condition

being considered. Importantly, there may be limit stresses which must be checked

individually for each element.

ASD has been the primary philosophy used for over a century, but it has been replaced by

Limit States Design (LSD) in many countries, including Canada. The actual level of safety

is not known, however. During the past 20 years, structural design has been developing a

more rational, probability-based, economic design procedure called “limit state” design.

Load and resistance factor design (LRFD) is an example of such recently developed limit

state design in the USA.

In the United States, LRFD has been accepted for steel design with the adoption of the

1986 AISC Load and Resistance Factor Design Specification. For engineered wood

construction both formats (ASD and LRFD) are currently in use. LRFD explicitly

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incorporates the effects of the random variability of strength and load. The basic LRFD

design criterion can be summarized as follows:

Φ Rn ≥ Σ Γi Qi (1.2)

Where

Φ: resistance factor (strength reduction factor)

Rn: nominal resistance

Γi: overload factors

Qi: various load effects

The quantity of Φ Rn (called resistance or strength) must be more than the load effects, i.e.,

Qi multiplied by Γi, to fulfill the safety requirement.

Rosowsky and Hunt (1995) also showed that structural wood composites benefit from the

introduction of LRFD concepts into wood design, especially in the potential for the control

of material property distributions through product design, manufacturing process control,

and quality control.

Unfortunately, a systematic scientific investigation of the loads that act on a sofa frame has

never been undertaken. Therefore, relatively few service loads have been thoroughly

evaluated, and there is a scarcity of pertinent quantitative data. At this time, the

information required to design furniture on a scientific basis is still too imperfect to rely

totally on strength design methods. For instance, design loads are simply not available for

the design of a sofa frame.

Fortunately, furniture frame performance test standards such as General Services

Administration (GSA 1998) and the Business and Institutional Furniture Manufacturer’s

Association (BIFMA) are available to evaluate the durability of a furniture frame

construction including components such as joints and members. Therefore, the loads used

for the performance tests could be the best available candidates for the determination of

design loads for furniture frame components. Efforts in determining design loads based on

available engineering design information for a sofa frame to meet specified frame

performance test requirements, for instance GSA performance test, were explored in this

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study. Tables 1.1 and 1.2 show the initial load, load increments, and acceptance levels used

in GSA general upholstered furniture performance and “BARE” frame tests.

1.2.3 Material properties Because of the particular structure of OSB, bending properties of oriented strand board (in

the direction of alignment) are generally superior to those of a randomly oriented flake

board. As with any particle panel product, the properties of OSB depend strongly on the

manufacturing process. It has been manufactured primarily for structural purposes such as

wall sheathing, floors, and roofs of conventional buildings. However, recently, OSB

products are increasingly used in upholstered furniture frame construction in place of solid

wood and plywood as some studies have demonstrated (Wang and Knudson 2002).

Even though, many studies have examined and evaluated properties of OSB, most of those

have dealt with the use of OSB as structural materials in conventional structures (i.e.,

sheathing). If its mechanical properties are closely controlled, and structurally evaluated as

a furniture framing material, OSB may find more use in the furniture industry.

From furniture engineering design point of view, research relating the structural

performance of OSB to its properties is limited. Eckelman (1987) carried a study to

determine the bending strength, fatigue strength, stiffness and allowable design stresses for

engineered strand-lumber (ESL), engineered strand-panel (ESP) and OSB.

Table 1.1 The initial load, load increments, and acceptance levels used in GSA upholstered furniture performance tests (adapted from GSA 1998)

Acceptance levels light Medium Heavy

Description of test No. of loads

Initial load (N)

Load increment

(N) (N) (N) (N) Seat Load

Foundation 3 667 167 1334 1668 1835

Backrest Foundation 3 222 56 500 556 667 Backrest Frame 3 334 111 334 445 667

Front to Back on Leg 1 667 222 667 890 1334 Sidethrust on Arm 1 222 111 334 667 890 Sidethrust on legs 1 890 222 890 1112 1557

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Table 1.2 National Furniture Center Upholstered Furniture Performance-acceptance Level (adapted from GSA “Bare frame”)

Test Initial load (N)

Load increments

(N)

Number of loads

Light- service

acceptance level (N)

Medium-service

acceptance level (N)

Heavy-service

acceptance level (N)

Cyclic Front to Back Load Test on Top

Rails 334 111 3 334 445 667

Cyclic Sidethrust

Load

Test on Arm -- Inward 222 111 1 334 778 1001

-- Outward 222 111 1 334 667 890

Cyclic Vertical Load 445 445 2 1779 2669 3558 Test on Arm

Cyclic Vertical Load Test on -- Front Rail 445 445 3 1334 1779 2669

-- Back Rail 445 445 3 890 1334 2224

Cyclic Torsional Inward 445 445 3 1334 1779 2669

Pull Test on Seat Rails

Cyclic Frame Racking Test 445 445 1 445 890 1779

Cyclic Front to Back Load Test on Legs 445 222 2 667 890 1334

Cyclic Sidethrust

Load

Test on Legs -- Inward 445 222 1 890 1112 1557

-- Outward 445 222 1 445 667 1112

Cyclic Vertical Load Test on Legs 667 667 4 2002 2669 4003

In that study, tests were carried out to determine the allowable design stress of such

materials when they are used as furniture framing components. Particularly, lateral and

withdrawal strength of dowels and screws were investigated for these materials. In

addition, Eckelman evaluated the impact and long term performance of bending specimens.

Based on the results, it was concluded that ESL, ESP and OSB could be used to build

sound furniture frames.

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Similar research was carried out ten years later by Erdil (1998) for plywood and OSB. The

withdrawal, lateral, torsional and bending strength of dowels and the holding strength of

screws, staples and T-nuts in such materials were determined for upholstered furniture

frames. The study concluded that plywood and OSB could be used in the construction of

upholstered furniture frames. Models were developed in that study, which could be used in

the engineering design of such frames.

1.2.4 Fatigue life In carrying out a structural design, a furniture designer, like any other structural designer,

must select a material and choose the size of structural members to perform a specified

function without failure. Safety is one of the most important considerations. Failure of

material under fluctuating or cyclic loading conditions is known as fatigue failure.

Importantly, such failure can occur well below the ultimate static strength of the material

(Eckelman, 1987). Therefore, knowing the behaviour of the furniture parts under both

static and cyclic loading and having a set of allowable design stresses for wood composites

are fundamental to the design of furniture. That is true for both wood material and joint

fatigue strength. Studies on joint fatigue strength include joints with different types of

fasteners (i.e. staple, staple-glue-block, dowel, screw, gusset-plate and metal plate).

Material studies include plywood, Timberstrand, Engineered Strand Lumber (ESL),

oriented strand board (OSB), particleboard, oak and yellow poplar (Zhang 2000).

1.2.4.1 Wood material fatigue life Bao and Eckelman (1995) studied the fatigue life and allowable design stresses for wood

composites used in furniture. They tested MDF, OSB, and particleboard in edgewise in

order to determine their resistance to fatigue. They concluded that the relationship between

the level of stress and fatigue life was in inverse proportion. An anticipated, fatigue life

was found to decrease as the level of stress increases. Fatigue life amounted to over a

million cycles when the stress level was 30 percent of MOR, but decreased to about 400

cycles for MDF, and to about 11,000 cycles for OSB respectively at a stress level of 70

percent of MOR. The result of the study suggests that allowable design stress for the

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composite materials included in the study could likely be derived from a consideration of

their fatigue resistance at various load levels.

1.2.4.2 Wood joints fatigue life Strength design of upholstered furniture frames requires information about joint fatigue

strength properties since most service failures of such frames appear to be fatigue related

and the most common failure to the frames occurs at the joints (Eckelman and Zhang

1995).

Eckelman (1970a) studied the fatigue life of two-dowel joints subjected to a constant cyclic

loading. He tested sugar maple joints with an average ultimate static bending load of 359

N-m (3,180 lbf-in) under two different cyclic load schedules, alternating fully-reversed

loads and one sided loads. Fatigue loads were applied to joints at a rate of 40 cycles per

minute. No failures were found at the 56.5 N-m (500 lbf-in) load level in either set of

specimens after 1,000,000 cycles. At the 113.0 N-m (1,000 lbf-in) load level (about 30% of

ultimate static bending capacity), joints failed at about 200,000 cycles, and at 169.5 N-m

(1,500 lbf-in) level (about 50% of ultimate static bending capacity), the value was about

12,000 cycles. Results clearly demonstrated that specimens were subject to fatigue damage,

and an endurance limit existed for the joints. The suggested design strength for two-pin

dowel joints should be limited to no more than one-third of joint ultimate static bending

capacity.

Few studies were found on the fatigue life of furniture frame joints subjected to cyclic

stepped loads. Zhang et al. (2001a) studied the fatigue strength properties of furniture

frame joints subjected to one-sided constant and stepped cyclic bending loads. In that

study, T-shaped, two-pin moment-resisting dowel joints constructed of red oak, yellow-

poplar, southern yellow pine plywood, aspen engineered strand lumber, and particleboard

subjected to constant and stepped cyclic bending loads were evaluated. Table 1.3

summarizes average values of fatigue life (number of cycles to failure) for each joint

material type at each of the bending moment levels. Joint fatigue life was below 25,000

cycles at the bending moment level of 70 percent of joint ultimate bending capacity. It is

expected that at 30 percent, the joint could have a fatigue life over 1 million cycles.

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Regression of M-N data (moment versus log number of cycles to failure) of each joint

material type subjected to constant cyclic bending loads resulted in linear equations for M-

N curves. Figures 1.1 and 1.2 demonstrate the configuration and special testing system for

fatigue tests of dowels. Figure 1.3 shows the results of constant load fatigue tests of

plywood as a log-linear plot, i. e. M-N curve, the following regression equation was used

to fit individual representation of it:

M = C + D log10 Nf (1.3) Where,

M = bending moment (lb.-in.);

Nf = number of cycles to failure;

C, D = fitting constants.

Table 1.3 Average values of fatigue life (number of cycles to failure) for each joint material type at each of bending moment level. (from Zhang et al. 2001a)

Bending moment level

(%) Red oak Yellow-

poplar Plywood ESL Particleboard

90 286 (109)a 5,406 (92) 72 (43) 318 (132) 1,406 (64)

70 1,013 (114) 17,011 (100) 1,088(112) 5,263 (90) 7,491 (132)

50 82,382 (121) 301,026 (82) 84,633 (73) 121,705 (37) 152,307 (66)

30 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

a Values in parentheses are coefficients of variation, in percent.

Figure 1.1 Diagram showing construction of the T-type, two-pin dowel joint specimen in fatigue test (from Zhang et al. 2001a)

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Figure 1.2 A specially designed pin rack system with pneumatic cylinder for evaluating fatigue life of T-shaped joints (from Zhang et al. 2001a)

Figure 1.3 Bending moment versus fatigue life (M-N) curve from constant bending tests of plywood joints (from Zhang et al. 2001a)

To predict the fatigue life of a joint subjected to cyclic stepped bending loads based on its

M-N curve, the Palmgren-Miner rule may be used with the following unity summation of

life fractions (Zhang et al. 2001a):

13

3

2

2

1

1 ==⋅⋅⋅+++ ∑fj

j

fff NN

NN

NN

NN

(1.4)

Where

Nj = number of cycles applied to a joint at the bending moment Mj;

Nfj = number of cycles to failure from the joint M-N curve for the bending moment Mj.

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The proposed equation indicates that for a given stepped load schedule and a known M-N

curve, joint failure is expected when the life fractions sum to unity, that is, when 100

percent of life is exhausted. The fatigue life of a joint under a given stepped bending load

schedule could be estimated from its M-N curve.

Table 1.4 shows fatigue life calculations for plywood joints subjected to cyclic stepped

loads Mj. According to the regression equation of the M-N curve for plywood joints, M =

2991 - 338 log10 Nf, the number of cycles to failure Nfj for each bending moment level is

first calculated. Then the life fractions Nj/Nfj are determined based on a known number of

cycles applied to the joint Nj. Finally, the sum of Nj/Nfj ratios is determined and made equal

to unity, the number of cycles applied (N4) at the bending moment of 169.5 N-m (1,500

lbf-in) can be calculated, which is 22,065. So the total number of cycles applied to joint

failure is 97,065 with summation of column Nj. Table 1.5 summarizes fatigue life of both

predicted and tested results of joints subjected to cyclic stepped loads.

Table 1.4 Calculation of the fatigue life for plywood joints using the Palmgran-Miner rule. (Adapted from Zhang et al. 2001a)

J Mj Nfj Nj Nj/Nfj (N-m)

1 68 11,856,718 25,000 0.002 2 102 1,535,998 25,000 0.016 3 136 198,983 25,000 0.126 4 170 25,778 N4 N4/25,778

Table 1.5 Comparison of predicted fatigue life with average fatigue life from stepped load tests. (from Zhang et al. 2001a)

Red oak Yellow-poplar Plywood ESL Particleboard

Average number of cycles to

failure 102,537(21)a 103,557 (4) 102,242(9) 88,167 (13) 71,232 (12)

Predicted number of cycles

to failure 102,068 107,440 97,065 79,945 64,739

Means difference (%) -0.5 3.6 -5.3 -10.3 -10.0

a Values in parentheses are coefficients of variation, in percent.

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Zhang et al. (2001a) found that for fatigue life of dowel joints subjected to a given stepped

cyclic bending schedule, joints constructed of particleboard had significantly lower fatigue

life than joints made of red oak, yellow poplar, plywood, and ESL. No evidence of

significant differences existed in fatigue life among joints constructed of red oak, yellow-

poplar, plywood, and ESL. Results of static bending tests, however, showed significant

differences in bending capacity among them. They suggest that joint resistance to fatigue

failure should be taken into account in strength design of furniture frames that are

subjected to repeated loading. Fatigue strength property data such as M-N curves should be

obtained for joints commonly used in the furniture frame construction so that analyzing

and designing furniture frames for fatigue failure would be made possible.

Later on, Zhang et al. (2003) investigated the bending fatigue behaviour of T-shaped, end

to side, two-pin dowel joints constructed of furniture grade, 19.1 mm (3/4 in) thick 5-ply

southern yellow pine plywood under one-sided constant and stepped fatigue load

conditions. Results indicated that the fatigue life of dowel joints averaged 131,253; 78,122;

31,617; 11,023; 4,161; and 329 cycles for load levels of 40; 50; 60; 70; 80; and 90 percent

of their ultimate static bending capacity, respectively. Also fatigue life comparisons among

joint groups with different static bending capacity indicated that a significant increase in

ultimate static bending capacity might not yield a significant fatigue life increase when

joints were subjected to cyclic stepped loads. Joint resistance to fatigue failure should be

taken into account in strength design of furniture frames that are subjected to repeated load.

Most recently, Zhang et al. (2006) studied bending fatigue life of metal-plate-connected

(MPC) joints in furniture-grade pine plywood. Tested joints were subjected to one-sided

cyclic stepped bending loads. The purpose of the study was to obtain joint static to fatigue

moment capacity ratios. Performance test results showed that a MPC plywood joint would

fail within 25,000 cycles when a stepped load level reached 46 percent of the static

moment capacity of the tested joint. Joints failed mainly due to tooth fatigue shear at the

roots. The static to fatigue moment capacity ratio for tested joints averaged 2.5 with a

coefficient of variation of 11 percent and a range of 2.2 to 3.1.

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1.2.5 Properties of fasteners and joints The design of joints in a furniture frame is the most important step in the whole design

process. The strength and stiffness of joints used in the construction normally determine

the strength and rigidity of the furniture frame. Structural failure in furniture is often

associated with weak joints. It is very important that the joints used in the construction of a

particular piece of furniture are properly designed, so that they can safely carry the forces

imposed upon them in service. Current advances in furniture mechanics and design have

now made it possible to relate joint strength requirements to service loads in furniture

(Eckelman 1968). Some important joints and fasteners have been studied during the past

half century. Eckelman (1978a) developed design formulas for one-pin dowels (Eckelman

1969), two-pin dowels (Eckelman 1971a), and tenon-mortise joints (Hill and Eckelman

1973) for both bending and withdrawal strength of typical mechanical fasteners such as

screws, staples, and nails. Eckelman (1989a) also carried out tests to determine the bending

strength of through-bolts and dowel-nuts and developed expressions to predict their

strength. Erdil (1998) developed design formulas for dowel screws, staples and T-nuts used

with plywood and OSB to predict the withdrawal and holding strength. The characteristics

of some joints and fasteners along with studies of their design formulas are given below:

1.2.5.1 Dowel joints A dowel is a small diameter wooden pin used to fasten two furniture components together

with or without the help of other fasteners and glue. Dowels are among the most commonly

used connectors to assemble furniture. Because of their favourable cost and production

characteristics, dowels have long been a favourite connector in the furniture industry and

good for both mass and small shop productions of furniture. They are simple in design and

require only a drilling operation to form a joint. They have high initial strength, are self-

aligning and can also be used to joint parts of almost any shape that come together at

nearly any angle. Dowels are often used as the primary connectors in furniture frames

constructed of both solid wood and composite materials, including plywood and OSB.

Ideally, we would like to be able to design all types of dowel joints on the basis of the axial

and shear properties of the individual dowels used in their assembly (Eckelman 1991). The

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strength of a dowel depends on the wood it is made of. The other factors affecting dowel

joint strength are the strength of the wood in shear, the internal bond of connected

members, the glue type, gluing conditions, diameter and length of the dowel, and precision

of dowel pin installation (Eckelman 1989b).

In the case of solid wood, substantial research provided the basis for the rational design of

the dowel-based joints used in such frames. Some basic formulae that could be used to

obtain reasonable estimates of their properties have been developed. Eckelman (1969)

proposed the following expression to predict average direct withdrawal strength of a dowel

pin from the side grain surface of a piece of solid wood:

F = 0.834 D L 0.89 (0.95S1 + S2) a b c (1.5)

Where:

F = ultimate withdrawal strength of the dowel, lbf;

D = diameter of the dowel, in;

L = depth of penetration of the dowel in the wooden piece, in;

S1= shear strength of the member parallel to the grain, psi;

S2= shear strength of the dowel parallel to the grain, psi;

a = 1.0 for polyvinyl resins with at least 60 percent solids content;

= 0.9 for polyvinyl resins with less than 60 percent solids content;

= 0.85 for animal glue;

b = correction factor for dowel-hole clearance;

c = 1.0 for plain (smooth surface) dowel;

= 0.9 for spiral-groove and multi-groove dowel (Eckelman and Hill 1971).

It can be clearly seen from this equation, that a strong relationship exists between the

withdrawal strength of a dowel and the shear strength parallel to grain of the solid wood

used in the construction of the joint. In other words, high withdrawal strength is obtained

when dowels are constructed of a high shear strength wood.

Moreover, in modern furniture constructions, two-pin moment-resisting dowel joints are

used more than any other type to give strength and rigidity to furniture frames. The most

common example of the use of these joints is probably the side rail to back post joint in

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sofas. In the textbook of Eckelman (1991, Chapter VI, p.11) describes the bending strength

and moment rotation characteristics of T-shaped end-to-side grain two-pin moment

resisting dowel joints. Findings indicated that the bending strength of such joints increased

as their shear strength, rail width and dowel spacing increased. According to his

recommendations, the bending moment strength of these joints can be predicted by means

of the expression:

F4 = F2 (d1 + d2 / 2) (1.6)

Where:

F4 = ultimate bending moment strength of the joint, lbf-in;

F2 = withdrawal strength of the dowel loaded in tension, lbf;

d1 = spacing between dowel hole centers, in;

d2 = distance from the centre of the dowel loaded in compression to the corresponding

outside edge of the rail, in.

Using sufficient glue is an important factor for dowel holding strength. Eckelman and

Cassens (1985) carried out a study to determine the withdrawal strength of dowels from

wood composites used in furniture construction. They realized that when an excess amount

of glue was applied and subsequently forced into the substrate as the dowels were inserted

into the holes, the strength increased. They also emphasized the importance of surface

configuration of dowels. Findings indicated that the plain dowel and spiral-groove dowels

provided greater strength than multi-grooved dowels when an excess amount of glue was

applied, as can be seen in equation 1. In addition, they pointed out that the face withdrawal

strength of the dowels was closely related to the internal bond strength of the composite

used in the test.

Eckelman et al. (1979) were first to make a direct study of specific dowel joint strength

related to the upholstered furniture frame construction. They evaluated the utilization of

red oak press-lam as upholstered furniture frame stock. It was found that the shear strength

of press-lam was only 53 percent of frames made of solid red oak. Its dowel withdrawal

strength on the face and edge was found to be 69 percent of solid red oak.

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Erdil (1998) carried out a study on joint design for upholstered furniture constructed of

plywood and OSB. Zhang et al. (2002a, 2002b), and Eckelman et al. (2002) studied the

fundamental lateral holding, torsional, withdrawal and bending resistances of dowel joints

for plywood and OSB constructions. Figures 1.4 to 1.12 show the configurations and

apparatus used for all dowel tests. They found that equations 1 and 2 provide good

predictions of the withdrawal resistance and bending moment, respectively for dowel joints

made of plywood and OSB. As can be seen in Tables 1.6 to 1.11, results from withdrawal

tests were incorporated into predictive expressions allowing designers to estimate

withdrawal strength as a function of the diameter of the dowels, their embedment depth,

and the density of the composite material. Results from two-pin moment-resisting joint

tests indicate that the bending strength of two-pin dowel joints constructed of plywood and

OSB could be estimated by means of the same expression developed for solid wood.

Results from lateral shear strength tests of dowel joints constructed of plywood and OSB

are sufficiently strong for several frame applications such as top rail to back post joints in

sofa frames. However, joints subjected to high levels of lateral force need to be reinforced.

Such case can be found in the case of a sofa with its front rail equipped with sinusoidal

type spring or other seat foundation materials that impose high front to back loads on the

rails. Results have indicated that torsional strength of the dowel joints increased linearly

with the dowel spacing and rail width. Joints subjected to high torsional forces such as

front rail to stump joints in smooth-front sofas or to side rails in T-front sofas should be

reinforced with glued blocks or gusset plates in order to develop the strength needed to

resist in-service loads.

Summary of predictive expressions developed to calculate the strength of dowel joints in

OSB joints of upholstered frames can be expressed as: (Erdil 1998, Eckelman and Erdil

1998)

1) Withdrawal strength

• On face: Y = 87 D 1.19 L 0.9 W 0.93 (1.7)

Where:

W = density of OSB, lb/ft3.

A simplified form of the expression has been used and is written as: Y = 55 DLW (1.8)

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• On edge: Y = 0.41 D 1.71 L 0.9 W 2.48 (1.9)

A simplified form is written as: Y = 1.2 DW2 (1.10)

or F2 = 179 D2 L0.5 W (1.11)

2) Bending resistance of two-pin moment resisting dowel joints

Withdrawal strength of a dowel embedded in the edge of OSB may be predicted by means

of expression:

F2 = 179 D2 L0.5 W (1.12)

Then, the bending strength of the joint maybe found by means of expression:

F4 = F2 (d1 + d2 / 2) (1.13)

Figure 1.4 Typical configuration of the specimens in the face and edge withdrawal tests of dowel joints (Eckelman et al. 2002)

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Figure 1.5 General dimensions of the two-pin moment-resisting dowel joints (Eckelman et al. 2002)

Figure 1.6 Apparatus for holding specimens in the face and edge withdrawal tests of dowel joints (Eckelman et al. 2002)

Figure 1.7 Test apparatus for evaluating the bending strength of the joints (Eckelman et al. 2002).

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Table 1.6 Withdrawal strength of dowels in the face of OSB (adapted from Eckelman et al. 2002)

Mean face withdrawal strength/standard deviation Material Dowel Depth of embedment in face (mm)

Code Replications Diam. 9.5 12.7 14.3 15.9 19.1 22.2 Density Thick. (mm) ------------------------------------------(N)-------------------------------------------- (kg/m3) (mm)

OSB–1b 8 6.4 1,975/445 2,082/325a 751.3 19.1 8 7.9 1,850/374 2,144/400a 8 9.5 2,905/89 3,407/138a

OSB - 2 8 6.4 1,503/209 2,051/276a 626.3 19.1 8 7.9 1,268/285 2,246/165a 8 9.5 1,882/169 3,158/191a

OSB - 3 20 9.5 2,406/196 3,091/560a 776.9 22.2 5 9.5 4,506/182a

OSB - 4 20 9.5 2,286/151 3,260/520a 680.8 22.2 5 9.5 3,874/480a

OSB - 5 20 9.5 2,317/173 2,887/596a 752.9 19.1 5 9.5 3,821/342a

aThe dowel hole was drilled completely through the specimen bOSB -1 to 5 are oriented strandboard made of Southern pine (Pinus elliottii)

Table 1.7 Withdrawal strength of dowels in edge of OSB (adapted from Eckelman et al. 2002)

Mean edge withdrawal strength/standard deviation Depth of penetration (mm)

Material Dowel 19.1 25.4 31.8 Code Rep. Diam. Random or

end and side

combined

End Side Random or end and

side combined

End Side Random or end and

side combined

End Side

(mm) ----------------------------------------------------(N)------------------------------------------------------ OSB–1b 8 6.4 2,193

/431 2,206 /374

2,180 /543

8 7.9 3,385 /556

3,514 /645

3,260 /512

8 9.5 2,931 /1,010

2,753 /1,023

3,109 /1,116

24 9.5a 4,559 /503

4,533 /672

4,581 /360

5,716 /712

5,738 /898

5,693 /609

5,831 /885

5,640 /116

6,027 /565

OSB-2 8 6.4 1,775 /431

1,646 /489

1,904 /396

8 7.9 2,518 /774

2,006 /245

3,025 /356

8 9.5 2,384 /698

2,420 /823

2,349 /672

24 9.5a 4,114 /405

4,283 /316

3,950 /463

5,418 /787

5,315 /454

5,516 /1,099

5,106 /725

5,062 /116

5,146 /467

OSB-3 15 9.5a 5,200 /827

OSB-4 15 9.5a 4,848 /467

OSB-5 15 9.5a 5,177 /218

aThe dowel hole was drilled completely through the specimen bOSB -1 to 5 are oriented strand board made of Southern pine (Pinus elliottii)

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Table 1.8 Bending strength of two-pin moment-resisting dowel joints (adapted from Eckelman et al. 2002)

Estimated Ratio : Estimated Ratio : Bending Bending Strength Dowel bending estimated bending estimated

Material strength strength ratio withdrawal strength strength/test strength strength/test code Statistic 102-mm 152-mm 152/102-mm strength 102-mm. strength 152-mm. strength

---------(N-m)--------- (N) (N-m) (N-m) OSB-1 Avg. 393.2 604.6 1.54 5,253 333.7 0.85 600.6 0.99

SD 30.1 132.8 OSB-2 Avg. 281.4 500.6 1.78 4,377 278.0 0.99 500.4 1.0

SD 28.3 64.3 OSB-3 Avg. 344.1 574.9 1.67 5,431 345.0 1.0 620.9 1.08

SD 48.1 84.0

Figure 1.8 General configuration of specimens used in lateral dowel strength tests with the centre rail in: a) flat position b) edge position (adapted from Zhang et al. 2002a)

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Figure 1.9 Dimensions of the specimens used in lateral shear strength of dowel joints tested in edge and flat positions (adapted from Zhang et al. 2002a)

Figure 1.10 Methods of testing the lateral face and edge strength of dowels (adapted from Zhang et al. 2002a)

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Table 1.9 Results for lateral holding capacity of dowels: Test series 1a (adapted from Zhang et al. 2002a) Rail position Edge position Flat position Rail width 76-mm 102-mm 51-mm 102-mm

No. of dowels 2 2 1 2 Dowel spacing 25-mm 51-mm 51-mm Density Thickness

Lateral load and standard deviation per dowel (N) (kg/m3) (mm) OSB-1b 1,557 2,366 663 725 751.3 19.1

294 209 76 36 OSB-2 1,414 1,672 596 565 626.3 19.1

169 196 62 31 a All loads are in pounds per dowel bOSB -1 or 2 are oriented strand board made of mixed species

Table 1.10 Results for lateral holding capacity of dowels: Test series 2 a (adapted from Zhang et al. 2002a) Rail position Edge position Flat position Rail width 76-mm 102-mm 76-mm 51-mm

No. of dowels 2 2 2 1 Dowel spacing 38-mm 51-mm 25-mm Density Thickness

Lateral load and standard deviation per dowel (N) (kg/m3) (mm) OSB-3b 1,779 1,841 1,624 1,659 776.9 22.2

89 165 107 205 OSB-4 1,810 1,984 1,068 1,472 680.8 19.1

165 227 107 156 OSB-5 1,664 1,882 1,085 1,361 752.9 22.2

205 40 80 111 a All loads are pounds per dowel bOSB -3 to 5 are oriented strand board made of mixed species

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Figure 1.11 Configurations of the joints tested with the rail in the flat and edge positions (adapted from Zhang et al. 2002b)

Figure 1.12 Apparatus used to test joints in the flat and edge positions (adapted from Zhang et al. 2002b)

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Table 1.11 Torsional strength per joint, two multi-groove dowel, symmetrically spaced 25-mm (1 inch) from edge of rail, i.e. all rails 51-mm (2 inches) wider than dowel spacing a (adapted from Zhang et al. 2002b)

Maximum Material Rail Dowel Vertical load Torsional Shear force

Code position Spacing (Fv) per joint moment COV Per dowel Density Thickness (mm) (N) (N-m) (%) (N) (kg/m3) (mm)

First test series

OSB-1b Flat 51 230 58.5 28.2 1,268 751.3 19.1 OSB-2 Flat 51 181 45.9 15.8 992 626.3 19.1

Third test series

OSB-3 Edge 51 212 53.9 8.0 1,063 680.8 19.1 OSB-4 Edge 51 230 58.3 11.0 1,148 752.9 22.2

a n = 4 replications per cell for first and second series, and N = 10 per cell for third series. bOSB -1 to 4 are oriented strandboard made of mixed species

1.2.5.2 Joints with screws Wood screws have been used in furniture construction for about 300 years, primarily to

attach hinges to drop-leaf tables (Textbook of Eckelman 1991, Chapter VI, p. 49). They are

still widely used for fastening hardware to furniture and in replacing other fasteners such as

dowels and nails to structural-load-bearing joints. There is a growing tendency to use

screws in many of the small but highly stressed joints found in upholstered furniture

frames. For example, the highly stressed corners are often reinforced with blocks that are

glued and screwed in place. Many of the highly stressed upright braces to centre rail and

the front rail to stretcher braces are attached with screws. It is very important that these

joints be properly designed in order to safely carry the loads imposed on them in service.

Many investigations into the capacity of screws to withstand withdrawal loads involved

solid wood, particleboard, plywood, OSB and other wood composites. Johnson (1967)

investigated the screw holding capacity of plywood and particleboard with various sizes of

screws. He found out that the resistance of materials varied in proportion to the size of the

screws. The Wood Handbook (1987) contains allowable design formulae for screws used

in wood building constructions for 50 years. However, the design formulae are not

satisfactory for engineering of furniture joints. Eckelman (1978b) investigated type A

panhead sheet-metal screws widely used in furniture construction. He tested the withdrawal

strength of the screws for a wide range of hardwood used in furniture construction,

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concluding that the withdrawal strength from side grain of wood can be predicted by the

following expression:

F = 3.2 Ds (Ls-Ds)0.75 Sx (1.14)

Where:

F = screw withdrawal strength from side grain of wood (lbf);

Sx = shear strength of the wood;

Ds = screw diameter, in;

Ls = depth of penetration of the threaded portion of the screw, in.

Eckelman (1988a) also investigated the holding strength of various sizes of sheet-metal

screws in face and edge of commercially available medium-density fibreboard. He

concluded that the withdrawal resistance could be predicted by means of mathematical

expressions as given below:

F (face) = 39 (IB) 0.85 Ds 0.5 (Ls-Ds/3)1.25 (1.15)

F (edge) = 18.4 (IB) 0.85 Ds 0.5 (Ls-Ds/3)1.25 (1.16)

Where:

F = withdrawal strength on face or edge, lbf;

IB = internal bonding strength, psi.

He also demonstrated that screw withdrawal strengths were 13 percent higher when

optimum pilot holes were used compared to tests made without holes. Pilot holes not only

help to locate screws, but also facilitate their insertion in a desired direction. The

investigation found that using pilot holes of the proper diameter significantly increases the

holding strength of screws in MDF and particleboard. Rajak and Eckelman (1993)

indicated that pilot holes should be 80 to 85 percent of the root diameter of the screw, but

larger pilot holes should be used with MDF, when compared to particleboard and solid

wood, to avoid splitting. Pilot holes drilled into the edges of MDF should be approximately

equal to the root diameter of the screws and have a depth equal to the depth of embedment

of the screws (Anonymous 1980).

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Erdil (1998) tested the screw withdrawal resistance both on face and edge for OSB. Later

on, Erdil et al. (2002a) developed estimates of both face and edge screw holding strength

that could be used for the engineering design of furniture frames constructed of OSB. They

determined the effect of pilot hole size on withdrawal strength and the relationship between

withdrawal resistance, screw diameter and depth of penetration. Most importantly, they

developed predictive expressions that could be used to estimate the screw holding

resistance as a function of board properties, screw diameter and depth of penetration.

Figures 1.13 to 1.15 show specimens and test set-up used for evaluating the holding

strength of screws in plywood and OSB (Erdil et al. 2002a). The results are given in Tables

1.12 and 1.13.

Figure 1.13 Configuration of screw withdrawal test (adapted from Erdil et al. 2002a)

Figure 1.14 Screw withdrawal from edge and face (adapted from Erdil et al. 2002a)

Figure 1.15 Specimens with screw embedded to full depth (a) and with tip protruding (b) (adapted from Erdil et al. 2002a)

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Table 1.12 Face and edge withdrawal resistance (N) of screws in OSB (adapted from Erdil et al. 2002a)

Screw size Material Face-tip not protruding Face-tip protruding Code Statistica 6AB 10AB 10AB 12AB 14AB 6AB 8AB 10AB 12AB 14AB Thickness Density

(mm) (kg/m3) OSB-1 Avg. 2,082 2,335 2,402 2,620 2,771 2,455 2,580 2,811 2,544 3,376 19.1 751.3

SD 458 214 129 254 609 222 311 351 414 53 OSB-2 Avg. 1,419 1,481 1,468 1,334 1,615 1,610 1,704 1,988 1,788 1,868 19.1 626.3

SD 307 133 191 240 485 276 173 289 351 138 OSB-3 Avg. 2,660 3,234 22.2 776.9

SD 449 71 OSB-4 Avg. 2,513 3,038 22.2 680.8

SD 240 427 OSB-5 Avg. 2,518 2,891 19.1 738.5

SD 449 405 Edge-side grain Edge-end grain

OSB-1 Avg. 3,056 3,158 3,225 3,625 3,896 3,300 2,949 3,145 3,661 3,892 19.1 751.3 SD 338 160 574 142 676 200 498 302 276 236

OSB-2 Avg. 1,272 1,339 1,739 1,575 1,882 1,241 1,744 1,681 1,970 1,877 19.1 626.3 SD 289 169 129 102 342 138 294 209 298 111

OSB-3 Avg. 3,158 2,584 22.2 776.9 SD 414 329

OSB-4 Avg. 2,317 1,904 22.2 680.8 SD 1,904 329

OSB-5 Avg. 2,566 2,700 19.1 738.5 SD 209 360

a Statistic: avg. refers to average; SD refers to standard deviation.

Table 1.13 Withdrawal force versus pilot hole diameter (adapted from Erdil et al. 2002a) Pilot hole diameter (mm)

Screw gage 0 1.6 2.0 2.4 2.8 3.2 3.6 4.0 4.4 (major Withdrawal force (N)

Diameter)a Statisticb Face withdrawal – OSB-1 6AB Avg. 1,561 1,615 1,406 1,352 1,223 (3.5) SD 182 160 471 240 240 8AB Avg. 1,459 1,481 1,245 1,245 1,197 (4.2) SD 125 307 62 62 142 10AB Avg. 1,557 1,757 1,757 1,708 1,459 (4.8) SD 160 191 191 147 240 12AB Avg. 1,793 1,788 1,788 2,099 1,681 1,285 (5.5) SD 147 49 49 294 240 298 14AB Avg. 1,890 2,028 2,015 1,988 1,970 (6.1) SD 98 53 178 93 67

Edge withdrawal – OSB-1 6AB Avg. 1,303 1,481 1,134 1,330 (3.5) SD 85 227 280 120 8AB Avg. 1,655 1,668 1,539 1,370 (4.2) SD 120 53 351 116 10AB Avg. 1,686 1,721 1,686 1,410 (4.8) SD 160 214 165 200 12AB Avg. 1,597 2,019 1,655 1,784 (5.5) SD 534 160 173 302 14AB Avg. 1,984 1,699 1,699 1,970 (6.1) SD 58 165 165 67

a Major diameter refer to basic diameter (mm) of screw used in predictive expression b Statistic: avg. refers to average; SD refers to standard deviation

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Based on the results from the screw withdrawal tests, a regression analysis was carried out

and the following expression was proposed for face and edge withdrawal from OSB:

Y = a D b (L – cD)d We (1.17)

where:

Y = screw holding strength, lb;

a, b, c, d, and e = regression coefficients;

cD = tip effect, loss in strength that occurs because the tip of the screw is not in contact

with the composite when pilot holes are used;

1) For face withdrawal the proposed predictive expression is: Y = 1.99 D 0.5 (L – 2D/3) W1.78 (empirically determined from tests) (1.18)

Y = 0.87 D 0.5 (L – 2D/3) W2 (simplified) (1.19)

2) For edge withdrawal the proposed predictive expression is: Y = 0.032 D 0.547 W2.81 (empirically determined from tests) (1.20)

Y = 0.66 D 0.5 W2 (simplified) (1.21)

It can be clearly observed that the screw diameter and depth of penetration as well as the

density of the board affect the strength of such joints. Results have indicated that high

strength screw joints can be fabricated from OSB.

1.2.5.3 Staples Staples are widely used in the furniture industry. They are frequently used to hold glue

blocks in place until the adhesive dries, as well as in reinforcing joints. Moreover, the

Wood Handbook provides equations to determine the withdrawal and lateral strength of

joints made with staples intended for use in construction, but these equations are based on

static tests on nails and have not been verified for staples. But in Eurocode 5 (2004), the

equations for all metal dowel-type fasteners, such as nails, screw and staples are the same.

Staples are common in the fabrication of upholstered furniture where they are mostly used

in the attachment of fabric to the frame. More recently, staples are being used in the

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fabrication of the frame itself because they provide a rapid and convenient method of

fabricating joints.

Erdil et al. (2003a) conducted tests and developed basic strength data for staple holding

strength in both plywood and OSB (Figures 1.16 to 1.20 and Tables 1.14 to 1.17). These

could be used in the engineering design of furniture frames constructed of such materials.

Results of the tests showed that the staple holding strength from the face of plywood and

OSB was at least 50 percent higher than that from the edge. Results from the lateral

holding capacity tests of staple on edge for plywood and OSB indicated that the strength

was proportional to the number of staples (Erdil et al. 2003a). In the gusset plate stapled

moment resisting joints, results demonstrated that the size of the gusset plate and the

number of staples were the key factors in the overall strength of joints. The larger were the

dimensions of the plate and the number of the staples, the higher the strength of the joints.

Furthermore, application of glue in the gusset plates could at least double the moment

resisting strength of such joints. Zhang et al. (2001b) studied bending strength of gusset-

plate joints constructed of wood composites, as given in Table 1.18. Results showed that

the bending strength of gusset-plate joints was significantly affected by gusset-plate

thickness, width, and length. Among the plate size parameters, plate width affected joint

bending strength the most. Joint member material type and the number of staples had no

effect on bending strength.

Figure 1.16 General configuration of face (left) and edge (right) withdrawal specimens (from Erdil et al. 2003a)

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Figure 1.17 Geometric dimensions of face and edge staple withdrawal specimens (adapted from Erdil et al. 2003a)

Figure 1.18 Apparatus for evaluating face and edge withdrawal strength of staples (adapted from Erdil et al. 2003a)

Table 1.14 Withdrawal strength of staples from OSB (adapted from Erdil et al. 2003a) Withdrawal from edge Withdrawal from face

Material 1 staple 2 staples 1 staple 2 staples code DOPa Force

avg./SDb DOPa Force

avg./SDb DOPa Force

avg./SDb DOPa Force

avg./SDb Density Thickness

(mm) (N) (mm) (N) (mm) (N) (mm) (N) (kg/m3) (mm) OSB-1c 19.1 400/111 19.1 867/156 19.1 445/89 19.1 1,134/156 751.3 19.1 OSB-2 19.1 111/22 19.1 534/111 19.1 467/133 19.1 1,023/222 626.3 19.1 OSB-3 15.9 423/89 15.9 N/A 15.9 801/178 15.9 1,979/200 776.9 22.2 OSB-4 25.4 445/151 25.4 645/151 15.9 756/129 15.9 1,245/187 680.8 22.2 OSB-5 25.4 489/116 25.4 667/138 19.1 890/178 19.1 1,735/262 752.9 19.1

a DOP = nominal depth of penetration of staple shakes in the test block b SD = standard deviation c OSB -1 to 5 are oriented strandboard made of mixed softwood

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Table 1.15 Summary of grade properties on OSB panels (adapted from Forintek’s report (Wang and Knudson 2002))

(ASTM D1037-96a) Staple withdrawal Face Edge (N) (N) Mill A* 426 898 Mill B 621 914 Mill C 595 810 Mill D 564 880 Mill E 427 842 Mill F* 651 1,232 Mill G* 622 942 Mill H 741 1,073 Mill I* 935 1,023 Mill J 786 1,014 Mill K 1,089 1,044 Mill L 645 790 * OSB panels sold for furniture applications

Figure 1.19 Configuration and apparatus of staple lateral holding strength (adapted from Erdil et al. 2003a)

Table 1.16 Lateral holding strength of the staples (adapted from Erdil et al. 2003a) Lateral holding force avg./SDb DOPa(mm) 25.4 28.6 31.8 34.9 25.4 28.6 31.8 34.9 Material code

1 staple 2 staples

------------------------------------------------(N)--------------------------------------------------- OSB-1 792/98 841/111 738/93 676/107 1,317/191 1,615/125 1,499/71 1,570/102 aDOP = nominal depth of penetration of staple shakes in the test block bSD = standard deviation

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Figure 1.20 Configuration and apparatus for staple bending strength (adapted from Erdil et al. 2003a)

Table 1.17 Moment resisting strength of Douglas-fir plywood gusset and stapled joints (adapted from Erdil et al. 2003a)

Moment resisting strength (avg.)a

No. of staples Gusset dimension With adhesive Without adhesive (mm) ----------------------(N-m)----------------------- 6 102 by 102 by 4.8 425.2 (84.6)a 133.7(7.8) 10 152 by 102 by 4.8 501.5(49.4) 235.9(12.0) 12 203 by 102 by 4.8 508.5(83.8) 308.3(30.3)

a Number between brackets is the standard deviation

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Table 1.18 Bending strength of gusset-plate joints constructed of wood composites (adapted from Zhang et al. 2001b).

Material type Gusset-plate dimensions Bending strength Coefficient of variation (mm) (N-m.) (%)

6.4 by 76 by 152 630.7 13.1 6.4 by 76 by 254 759.5 18.5 6.4 by 102by 203 1,292.0 14.8 6.4 by 127 by 152 1,649.6 7.1 6.4 by 127 by 254 1,765.1 12.5 9.5 by 76 by 152 940.0 11.3 9.5 by 76by 254 1,228.9 23.7 9.5 by 102by 203 1,477.6 12.8 9.5 by 127 by 152 1,270.5 18.7

Plywood

9.5 by 127 by 254 1,882.6 8.8 6.4 by 76 by 152 710.2 10.3 6.4 by 76 by 254 688.2 17.8 6.4 by 102by 203 1,295.9 18.0 6.4 by 127 by 152 1,712.0 8.8 6.4 by 127 by 254 1,850.7 7.0 9.5 by 76 by 152 997.8 5.5 9.5 by 76by 254 1,254.9 15.8 9.5 by 102by 203 1,549.6 11.3 9.5 by 127 by 152 1,801.6 11.3

Timberstrand

9.5 by 127 by 254 2,242.5 12.4 6.4 by 76 by 152 621.8a 4.7 6.4 by 76 by 254 778.0 12.3 6.4 by 102by 203 1,265.0 10.1 6.4 by 127 by 152 1,065.4 16.6 6.4 by 127 by 254 1,777.5 5.3 9.5 by 76 by 152 902.1 8.9 9.5 by 76by 254 1,114.5 10.0 9.5 by 102by 203 1,149.5 7.2 9.5 by 127 by 152 1,410.2 9.2

ESL

9.5 by 127 by 254 1,904.4 7.4

1.2.5.4 Nails

Nails are not commonly used in furniture construction as structural load bearing fasteners

in areas of high stress; rather, they are used to hold other types of joints such as dowel

joints together until the glue dries.

Sometimes nails are used structurally and are subject to shear and/or withdrawal forces.

When the top rail on a sofa is laid in flat position, nails are often driven through it into the

top of interior uprights. In this case the nails are subjected to both shear and withdrawal

forces. Moreover, nails are often driven through side slats into the ends of the centre rail. In

such cases, nails are primarily subject to lateral shear forces. Nails are frequently used to

attach stretchers to front and back rails. In this type of construction, nails are driven

through the rails into the ends of the members, and are loaded in shear and withdrawal.

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Twelve types of panels were sampled from different OSB mills in a study carried out at

Forintek using commercial OSB panels (Wang and Knudson 2002). Panels from mill A, F,

G and I were marketed as furniture grade or sold to furniture manufacturers. The nail

withdrawal and lateral nail strength, nail pull-through resistance and planar shear-strength

are given in Table 1.19. From this Table, one can see that commercial OSB panels

currently sold for furniture applications generally have higher fastener holding capacities

than standard construction type OSB panels. There were also differences in properties

between the various OSB furniture panels.

1.2.5.5 Through bolt with dowel nuts

Through-bolts with dowel-nuts are commonly used in furniture construction, both as

primary connectors and also to reinforce weak joints. For instance bed bolts, one form of

through-bolt, have been used for many years to attach bed rails to bed posts in order to

allow transportation of bulky bed frames. Aside from their use in the construction which

must be assembled and disassembled on site, through-bolt with dowel-nut construction is

of particular interest due to its high strength and reliability (Eckelman 1989a, Eckelman

and Erdil 1998, Erdil et al. 2003b). Through-bolts with dowel-nuts are often used in chair

construction, where they are used, to reinforce the critical seat side rail to back post joints.

They are also widely used in bulky furniture where these must be shipped in a partially

Table 1.19 Summary of grade properties on OSb Panels (adapted from Forintek’s report (Wang and Knudson 2002)) (ASTM D 1037-96a) Nail withdrawal Lateral nail resistance

Nail pull-through

Planar shear- shear stress

Face Edge Para Perp N/A Para Perp --------------------------------------------------(N)-------------------------------------------------------

Mill A* 207 359 1,214 1,229 1,180 1,261 1,419 Mill B 164 199 904 1,073 1,418 814 821 Mill C 211 268 1,425 1,188 1,275 739 901 Mill D 243 266 1,148 1,132 1,384 852 829 Mill E 138 229 866 1,229 1,176 809 847 Mill F* 274 531 1,921 1,773 2,063 1,561 1,680 Mill G* 329 320 1,742 1,488 1,469 816 994 Mill H 386 401 1,620 1,808 1,688 975 911 Mill I* 427 361 1,407 1,548 1,711 1,076 1,016 Mill J 396 273 1,431 1,690 1,755 864 667 Mill K 522 418 1,597 1,712 2,311 1,081 1,212 Mill L 367 296 1,524 1,738 1,725 726 779

* Panels sold for furniture applications

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disassembled condition and where stales are used to attach the ends of legs to steel

mounting plates which are attached to the underside of table top (Eckelman 1977). These

fasteners also have significant potential value in upholstered furniture frame construction

in similar situations where strength and reliability are essential. An obvious use is the

attachment of an arm to a back post where reliability is essential.

Figures 1.21 to 1.23 demonstrated the through-bolt with dowel-nut in Erdil et al. 2003b.

The bending resistance of a number of T-shaped joints constructed with dowel nuts are

given in Table 1.20. The holding strength values of 9.5mm (3/8 inch) diameter dowel nuts

in the end of a rail are given in Table 1.21. Values are given for nuts placed 1, 1.5, and 2

inches from the end of the rail.

Figure 1.21 Through-bolt with dowel-nut (from Erdil et al. 2003b)

Figure 1.22 Dimensions of specimens for dowel-nut withdrawal test (from Erdil et al. 2003b)

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Figure 1.23 Dimensions of moment resisting through-bolt with dowel-nut specimens (adapted from Erdil et al. 2003b)

Table 1.20 Bending strength of moment resisting through- bolt with dowel nut joints (adapted from Erdil et al. 2003b)

Rail width (mm) Rail width (mm) 51 102 152

No. of nuts 1 2 3 Material

code Statistic Ultimated bending moment

(N-m) Density (kg/m3)

Thickness (mm)

OSB-1a Ave./stdev 121.5/30.1 297.2/29.6 700.6/62.0 751.3 19.1 OSB-2 Ave./stdev 76.3/14.2 268.4/33.8 546.7/82.0 626.3 19.1 OSB-3 Ave./stdev 722.1/56.2 1,037.3/105.3 776.9 22.2 OSB-4 Ave./stdev 445.8/45.4 922.1/130.7 680.8 22.2 OSB-5 Ave./stdev 523.2/43.5 795.5/137.7 738.5 19.1

a OSB -1 to 5 are oriented strand board made of mixed species

Table 1.21 Holding strength of dowel nut in relation to end distance (adapted from Erdil et al. 2003b)

Edge distance Material 25-mm. 38-mm 51-mm

code Statistic -------------------------------(N)-------------------------------- OSB-1a Ave./stdev 5,871/1,379 6,405/1,156 5,649/1,201 OSB-2 Ave./stdev 4,181/400 4,581/311 4,048/578 OSB-3 Ave./stdev 6,850/1,201 7,517/979 7,562/1,023 OSB-4 Ave./stdev 6,316/1,201 6,628/890 6,628/979 OSB-5 Ave./stdev 5,782/578 6,005/890 6,894/845

a OSB -1 to 5 are oriented strand board made of mixed species

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1.2.5.6 Toothed metal plates

One fastener used to a limited extent in upholstered furniture frame construction is the

toothed metal plate. Typical applications of this connector include the back post to side

seat rail joints in recliner type chairs and in front rail to stump (or front post) joint sofa

frames (Zhang et al. 2005). Both of these joints are highly stressed and thus require high

strength joint - which toothed metal plates can provide. Toothed metal plates also provide a

quality control advantage in that they can be inspected visually to determine if they have

been properly installed. The bending resistance of several plate and rail geometries and

material combinations are given in Tables 1.22 and 1.23. As can be seen, very high

strength values may be achieved with wider plates, particularly when used on both sides of

the joint.

1.2.5.7 Tenon-mortise joints

No literature could be found on the use of tenon and mortise joints in upholstered furniture.

With the expansion of the use of CNC machinery, it might be of interest to further explore

the broader use of such type of joints. It has been found that in certain situations, grooved

components are being used which somehow resemble half tenon and mortise joints.

1.2.5.8 T-nut joints There is very limited published literature on T-nuts joints, in spite of the fact that they are

increasingly finding application in upholstered furniture constructions, such as sofas and

chairs. Information is lacking on both static and dynamic holding strength of T-nuts. Since

such information is essential for the engineering design of furniture frames, Eckelman

(1998) carried out a study to obtain preliminary estimates of the static holding strength of

representative types of T-nuts in a wide variety of domestic wood and wood composites.

He concluded that two types of failure occur when withdrawing T-nuts. Either the nut

failed from the neck, or the material around the nut crushed and the nut pulled through.

Results of such tests have indicated that high strength joints could be constructed with

these fasteners, but that strength tends to vary greatly depending on the style and source of

the nut. Hence, specific performance information is needed for each T-nut. Based on the

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46

same study, the T-nut diameter and thickness of the parent material from which it is

manufactured significantly affect the holding strength of this fastener.

Table 1.22 Bending strengths of moment-resisting toothed metal plate connector joints (adapted from Eckelman and Erdil, 1998) Plate on one face Plate on two faces Rail width (mm) Rail width (mm) 76 102 152 76 102 102 152 152 Plate description (mm) Plate description (mm) Material 38 x 114 51 x 114 (2)1-25 x 114 38 x 114 51 x 114 76 x 114 (2)1-25 x 114 (2/1)2-25 x 114

code ----------------------------------------------(N-m)----------------------------------------------- OSB-1 210.2 436.2 529.7 329.4 606.2 1,012.5

30.3 25.1 51.0 15.9 34.5 35.3 OSB-2 187.9 363.1 523.8 318.7 506.0 878.9

11.1 31.9 87.6 14.7 7.6 120.1 OSB-3 1,183.1 1,202.3

45.2 83.6 OSB-4 1,045.3 898.4

108.5 35.0 OSB-5 934.5 965.0

70.1 44.1 (2)1 indicates that two 25mm (1 in) plates were used instead of a single plate (2/1)2 indicates that two 25mm (1 in) plates were used instead of a single plate on one side of the joint and one 25mm (1 in) plate on the other side of the joint a OSB -1 to 5 same as in article Erdil et al. (2003b)

Table 1.23 Zhang et al. (2005) evaluated the moment capacity of metal-plate-connected joints in furniture grade pine plywood.

Metal-plate length Rail width Metal-plate width 76 114 152 191

------------(mm)------------ --------------------------------------(N-m)--------------------------------- 3.5 323.5(5) 352.6 (10) 360.7 (4) 372.9 (5) 4.8 451.0 (5) 523.4 (6) 505.2 (4) 529.4(2) 83 6.1 527.5 (6) 721.4 (4) 742.5 (3) 746.4 (8) 3.5 357.4 (10) 482.2 (2) 480.8 (8) 477.5 (6) 4.8 512.0 (5) 648.2 (7) 647.9 (6) 635.7 (4) 114 6.1 608.1 (5) 884.1 (7) 878.5 (5) 928.6 (4) 3.5 567.0 (9) 691.8 (11) 675.5 (9) 746.9 (9) 4.8 672.0 (11) 850.4 (7) 873.8 (5) 884.3 (6) 152 6.1 806.3 (5) 1,110.6 (8) 1,081.9 (6) 1,062.5 (7) 3.5 731.1 (8) 877.3 (4) 956.0 (6) 1,006.9 (8) 4.8 864.9 (10) 1,120.1 (6) 1,074.0 (4) 1,142.5 (2) 191 6.1 989.9 (8) 1,500.3 (3) 1,550.5 (3) 1,536.6 (5)

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47

Erdil (1998) also tested T-nuts in upholstered furniture. From his study, two general types

of failure occurred. Either the nuts themselves failed or the wooden board below the nuts

crushed, allowing the nuts to be pulled deeply into the substrate. With OSB, the nuts were

pulled into the face of the board resulting in failure of the construction. On the other hand,

it was found that the holding strength increases linearly with the thickness of the boards.

1.2.6 Frame construction Before using stiffness matrix method in the structural analysis, Eckelman (1967) used

slope deflection methods to analyze chair frame design. Subsequently, the concepts of

elastically non-linear, semi-rigid joints based on stiffness analysis were applied in his

doctoral research (Eckelman 1968). The frame member stiffness coefficient was modified

owing to the semi-rigid joints, and an iterative approximation technique was applied to the

non-linear joint behaviour. After that, Eckelman (1970b, 1970c, 1971b) modified the

analysis to a wide range of furniture frame problems, where he incorporated these

approaches into a computer program named “CODOFF”. This program serves as the basis

for many other related program moduli in his studies.

1.2.7 Structure of sofa frames Thousands of styles for upholstered sofas are being used in the world, but generally, their

frames may be categorized into a relatively few specific types (Picado 1988). Owing to the

upholstery materials, the sofa frame may be difficult to visualize. Often only a few major

features can be identified, such as the relative positions of the arm and top rail, stump and

arm. But once the type of sofa frame is determined, it can be structurally analyzed.

According to Erdil (1998), a sofa can be structurally analyzed with respect to three

different subsystems: 1) Seat system; 2) Side frame system; 3) Back system (see

details in Chapter 3 Load distribution). A typical sofa frame construction is shown in

Figure 1.24.

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Top Rail

Front Stump

Top Arm Rail

Back Posts

Front Rail

Front Spring Rail

Stretcher

Upright

Middle Side Rail

Bottom Side Rail

Back Rail Back

SpringRail

BACK FRAME SYSTEM

SEAT FRAME SYSTEM

SIDE FRAME SYSTEMTop Rail

Front Stump

Top Arm Rail

Back Posts

Front Rail

Front Spring Rail

Stretcher

Upright

Middle Side Rail

Bottom Side Rail

Back Rail Back

SpringRail

BACK FRAME SYSTEM

SEAT FRAME SYSTEM

SIDE FRAME SYSTEM

Figure 1.24 Typical sofa frame construction (from Chen 2003).

1.2.8 Structure of other upholstered furniture frames Most of the other types of upholstered furniture frames are in fact of the sofa type but

narrower in width, with one or more seating positions. Hence, these can be modelled using

the general sofa framework described previously. One type of upholstered furniture is very

different from the sofa type, it is the reclining seat. Recliners include several of the same

subsystems presented in the sofa system. The seat, back and side subsystems can be found

too, but there are many features specific for such furniture, including the presence of the

reclining mechanism, which is a metallic device, attached to the furniture frame itself and

where load concentration occurs as well as repetitive dynamic loading. This type of

furniture has not been described in the literature.

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Chapter 2 Load Distribution on a Sofa Frame

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2.1 Introduction This chapter provides background information on how to estimate load distribution on the

joints of a full-size three-seat sofa frame. A simplified three-seat sofa frame structural

model was proposed, including only the most critical members and joints needed to resist

service loads. Structural analyses were performed on this frame using the various GSA

loading cases (i.e. light duty, medium duty and heavy duty) and boundary conditions.

Internal forces at each connection and stresses in each structural member were evaluated in

two ways. First, a simplified analysis was carried out using basic structural analysis

techniques and assuming joints rigid. Internal forces at each connection in the frame model

is determined, i.e., magnitudes and directions of axial and shear forces and bending

moments. The second method is a more rigorous analysis using Finite Element Model

(FEM). For this purpose, commercial software SAP 2000 is chosen. Results of this analysis

are reported in Chapter 7.

2.2 General configuration of loads and the construction of the sofa frame

2.2.1 Sofa frame construction The general configuration of a typical three-seat wooden sofa frame is shown in Figure

1.24. It consists of three basic structural subsystems, a) the seat frame system, b) the back

frame system, and c) the side frame system. The seat frame system includes the principal

structural members, which are: the front and back rails, the front and back spring rails, and

the stretchers. The back frame system consists of the top rail, the back posts, and the back

uprights. The side frame system’s principal members are the front stumps, the top arm

rails, the middle side rails, and the bottom side rails. Common types of joints connecting

frame members utilized in a sofa frame construction are metal fasteners (staples and

screws)-glued blocks, dowels, gusset-plates, metal-plates, mortise and tenon joints, and

metal dowel-nuts..

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2.2.2 Frame performance tests The loads on the frame were estimated in accordance with the service requirements of such

frames from GSA Specification FNAE-80-214 (see Tables 1.1 and 1.2 in Chapter 1).

These specifications were established for performance testing of upholstered furniture

frames and provide, perhaps, the best estimates of service loads, since it is known that

these specifications were based on a wide range of experimental data. Furniture

performance tests may be defined as accelerated tests that predict the ability of a piece of

furniture to fulfill its intended function. Performance test standards such as the GSA

performance test regime FNAE-80-214A are based on a stepped load model, i.e. tested

frame members and joints are subjected to cyclic stepped loads rather than a constant

cyclic load. Table 2.1 shows five test load configurations for evaluating structural

performance characteristics of upholstered furniture bare frames. These are: Top Rails-

Front to Back, Arms-Outward, Arms-Vertical, Front Rails-Vertical, and Front Spring

Rails-Inward tests. Table 2.1 also gives detailed cyclic load schedules for these tests. The

schedules include initial load, load increments, number of loads, and service acceptance

levels in terms of passed load levels and accumulative numbers of cycles. Figure 2.1 shows

the structural performance test loads of three-seat sofa frame.

Table 2.1 Cyclic load schedules of GSA performance tests for bare frame (adapted from GSA 1998)

Test Initial

load Load

increments Number of loads

Light-service acceptance

level

Medium-service acceptance

level

Heavy-service acceptance

level ---------- (N) --------- -------------------------- (N/cycle) ---------------------- Top Rails- Front to Back

334

111

3

334/25,000

445/50,000

667/100,000

Arms- Outward

222

111

1

334/50,000

667/125,000

890/175,000

Arms- Vertical

445

445

1

1,779/100,000

2,669/150,000

3,558/200,000

Front Spring Rails - Inward

445

445

3

1,334/75,000

1,779/100,000

2,669/150,000

Front Rails-Vertical

445

445

3

1,334/75,000

1,779/100,000

2,669/150,000

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TOP RAILS-FRONTTO BACK

ARMS-OUTWARD

ARMS-VERTICAL

FRONT RAILS-VERTICAL

SPRING RAILS-INWARD

TOP RAILS-FRONTTO BACK

ARMS-OUTWARD

ARMS-VERTICAL

FRONT RAILS-VERTICAL

SPRING RAILS-INWARD

Figure 2.1 Structural performance test loads of three-seat sofa frames

2.2.3 Simplified Sofa Frame Model Reduced to its basic form and function, the sofa frame (Figure 2.2) consists of the front and

back rails, the front and back spring rails, the top rail, the back posts, the front stumps, the

top arm rails, and the bottom side rails.

Top Arm Rail

72 in.

26 in.

34 in.

18 in.

Top Rail

Front Rail

Front Spring Rail

Back Spring Rail

Back Rail

Back Post

Front Stump

Side Rail

Top Arm Rail

72 in.

26 in.

34 in.

18 in.

Top Rail

Front Rail

Front Spring Rail

Back Spring Rail

Back Rail

Back Post

Front Stump

Side Rail

Figure 2.2 Simplified three-seat sofa frame structural model

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2.2.4 Simplified Analysis of Sofa Structural Joints The internal forces acting on the joints of these subsystems of the simplified sofa frame

were calculated using basic structural analysis techniques assuming rigid joints. An

analysis of each joint was made under the light level of service conditions indicated in the

GSA specification to satisfy the domestic use requirements. These requirements are based

on the cyclic performance. Since the cyclic joint strength is only equal to about half of the

static joint strength, the static strength requirement must be at least doubled (Eckelman and

Erdil 1998).

2.3 Discussion Results of the analysis are summarized in Table 2.2 Results can be evaluated under the

three structural subsystems: seat system, side system, and back system.

2.3.1 Seat System The seat system is composed of the front and back rails, front and back spring rails. Side

rails and stumps are also supporting components of the seat system. The seat system is

mainly subjected to vertical loads resulting from the sitting action, horizontal loads put

outward on arm, and out-of-plane loads owing to the spring system used as part the seat

foundation system. Generally, sinusoidal springs generate a substantial amount of out-of-

plane loads on the front and back rails. The critical joints in the seat system are the front

rail to stump (Erdil 1998).

Front rail to stump joints

The front rail to stump joints is subjected to three different loadings that can be analyzed in

detail, namely, vertical loading, outward sidethrust loading, and out of plane loading. The

joint strength values and estimated ultimate forces required for the three levels of service

conditions are given in Table 2.2.

Erdil (1998) assumed that in the case of vertical loading (Figure 2.3), the bending moment

acting on the front rail to stump joint is small and it may be neglected. Thus, the shear

strength of the joint which determines its ability to resist vertical loads is of primary

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Table 2.2 Estimated joints strengths

Joint type Loading direction Cyclic light duty load requirement

Static light duty load requirement

Vertical 2,002 N 4,003 N Horizontal 135.6 N-m 271.2 N-m

Front rail to stump

Out-of plane 1,668 N 3,336 N Vertical 1,334 N 2,669 N Horizontal 723 N 1,446 N

Back post to arm

Out-of plane 288.2 N-m 576.3 N-m Side rail to stump Horizontal 165 N-m 330 N-m

Vertical 2,002 N 4,003 N Top rail to back post Horizontal 500 N 1,001 N

concern. For example, for Front rails (Table 2.1), using light duty category, a single

vertical load is equal to 1334 N (300 lbf). As there are 3 loads acting on the front rail, the

total load becomes 4003 N (900 lbf). However, as the Front rail has two joints with stump,

each joint carries a shear force of 2002 N (450 lbf) of cyclic load. To get to the static loads,

it is necessary to double that load requirement which results in a static load of 4003 N (900

lbf).

Bending forces acting on the front rail to stump joint owing to sidethrust forces applied to

the arms (Figure 2.4) cannot be neglected. As a matter of fact, high bending forces occur in

this joint when a sidethrust load is applied to the arm or the top of the stump. This joint can

be treated as a two-pin moment resisting type of joint for such loading condition. Based on

the design of the sofa frame, it is proposed to take Arms-Outward load in Table 2.1 light

duty being equal to 334 N (75 lbf). Using a single load (Fh), the distance between this load

to the joint is 457-51 mm (18-2 in), 457 mm (18 in) is the height of arm, 51 mm (2 in) is

half of the front rail width). So the ultimate bending strength required for this joint is

estimated at 135.6 N-m (1200 lbf-in). Double that to achieve the load for static

requirement, it becomes 271.2 N-m (2400 lbf-in).

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Figure 2.3 Front rail to stump joint under vertical loading

Figure 2.4 Front rail to stump joint under horizontal sidethrust loading Front rails of sofas are also subjected to out-of-plane loads which occur due to the

attachment of sinusoidal type seat springs (Figure 2.5). As those springs are normally

attached, each imposes out-of-plane force of approximately 445 N (100 lbf) to the top of

the front and back rail. The average number of springs attached to a 1.83-m (72-in) front

rail is about 15. So total spring stress is 445 x 15 = 6,675 N (100 x 15 = 1,500 lbf), shared

by front and back spring rails, 6,675/2 = 3,337.5 N (1500/2 = 750 lbf), shared by both front

rail to stump joints and 1,669 N (375 lbf) for each joint. But as the spring forces act on the

top edge of the rail whereas the joints are located some distance below the top edge, then it

is necessary to make some minor adjustments. Therefore, the loads transferred to the end

joints should be a bit bigger than 1,669 N (375 lbf), i.e. 1,669 N (375 lbf) is the minimum

force on each front rail to stump joint, doubling that for the static load, the total loads

would be over 3,337.5 (750 lbf).

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Figure 2.5 Front rail to stump joint under out of plane loading

2.3.2 Side Rail System The side rail system can be analyzed as a two dimensional frame which generally consists

of a stump, back post, arm, and side rails. Side frames are generally subjected to vertical

forces due to sitting action on the arm, horizontal forces as a result of front to back loading

of frame, and the force which arise when a user pushes sideways on an arm. This side

forces which mainly tend to fail the front rail to stump joint as mentioned in the previous

discussion. The most critical joints in side frame systems are the back post to arm and the

side rail to stump and back post joints (Erdil 1998).

Back Post to Arm Joint Generally, the back post to arm joints must resist both vertical forces and horizontal forces

(Figure 2.6). Vertical forces occur, for example, when one or more people sit on an arm.

Consider the front rails-vertical (Table 2.1), for the light level of service, each joint should

resist an estimated load of 1,334 N (300 lbf), doubling that for static requirement to 2,669

N (600 lbf). This type of joint is basically flexible; thus, internal bending forces generated

under the action of vertical loading may be neglected.

The back post to arm joints must also resist front to back loading. Take Top rails-front to

back (Table 2.1) with a light duty load of 334 N (75 lbf), there are 3 acting loads, and two

side arms. Therefore, Fh = 334 x 3 /2 = 501 N (112.5 lbf) (Figure 2.8). As a first

approximation, the internal withdrawal force at the point of interest can be expressed as

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)lbf.(N).(

*.)hh(

Fhf h 516272320346605014660

21

1 =−

=−

= (2.1)

in which f is the internal withdrawal force (pounds), h1 is height of the back post - 660.4

mm (26 in), h2 is the distance from joint center to point of loading - 203 mm(8 in), and Fh

is the horizontal front to back load on each joint - 501 N (112.5 pounds). According to this

expression the estimated withdrawal force acting on the dowels in the arm to back post

joint is 723 N (162.5 lbf) for cyclic and 1,446 N (325 lbf) for static strength requirements.

Figure 2.7 shows the side rail system under out-of plane arm outward loading which arise

when a user pushes sideways on an arm. This side forces which mainly tend to fail the

front rail to stump joint as mentioned above. Bending forces which act on arm to back post

joint due to sidethrust forces applied to the arms cannot be neglected. As a matter of fact,

high bending forces occur in this joint when a sidethrust load is applied to the arm. This

joint can be treated as a two-pin moment resisting type of joint for such a loading

condition. Figure 2.7 shows details of the arm to backpost joint under outward sidethrust

loading condition. Based on the Table 2.1, the arm-outward for light duty is taken to be

equal to 334 N (75 lbf), with an arm length of 864 mm (34 in). The ultimate bending

moment which occurs at the backpost to arm joint should be equal to 334 x 864/1000 = 288

N-m (2550 lbf-in). For static requirement, the load at this joint could be estimated at 288 x

2 = 576 N-m (5100 lbf-in).

Figure 2.6 Side rail system under vertical loading

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Figure 2.7 The side rail system under horizontal front to back loading

Side Rails to Back Post or Stump Joints

The side rail to back post joints in a sofa frame are subjected to high in-plane bending

forces. These forces develop at the side rail to back post or side rail to stump joints when a

horizontal front to back load is applied to the top of the back post. Figure 2.8 shows the

configuration of these joints. In order to analyze these joints, the whole side system is

considered as a two dimensional frame. It may also be assumed that the arm joints in this

frame are flexible, i.e., hinged joints. Looking at Table 1.1, Top rails-front to back light

duty load of 334 N (75 lbf) with 3 loads shared by the two sides – side rail to back post

joints, the total load per joint should be equal to 334 x 3 /2 = 500 N (112.5 lbf).

Multiplying by the length of the back post – 660 mm (26 in.), the total bending moment

will be equal to 500 x 660/1000 = 330 N-m (2925 lbf-in). But as this moment is shared by

2 joints (assuming the three joints resist bending moments equally), the bending moment of

side rail to back post should be equal to 330/2 = 165 N-m (1462.5 lbf-in). Doubling that for

static loading, the proposed design moment shall be 330 N-m (2925 lbf-in).

2.3.3 Back System The back system consists of the back rail and the top rail. It is mainly subjected to

horizontal front to back shear forces, but it may also be subjected to vertical shear forces.

The top rail to back post joints are the critical joint in the back system (Erdil 1998).

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Top Rail to Back Post Joints

In the case of vertical loading, top rails are stressed both from users sitting on the rail and

from normal sitting loads transferred to the rail. If the frame supports three people sitting

on the top rail, then it should be the same analysis as the vertical load on the front rail to

the stump. The estimated ultimate lateral shear force acting on this joint is 2002 N (450 lbf)

for light duty, double for static it will be 4003 N (900 lbf).

The back post to top rail joints (Figure 2.8) are also subjected to horizontal lateral shear

forces when users lean backward in a sofa. If we take the top rail-front to back light duty

load of 334 N (75 lbf) (Table 1.1) times the number of loads (3), and assume that this total

load is shared equally by two back posts, then each joint should support 334 x 3 /2 = 501 N

(112.5 lbf). Doubling that for static loading, each joint should be able to carry 1001 N (225

lbf).

Figure 2.8 Horizontal loads on the top rail to back post joints

2.4 Summary This chapter estimated load distribution on the joints of a full-size three-seat sofa frame

model. Structural analyses were performed on this frame using the GSA loading. Internal

forces at each joint were evaluated based on basic established structural analysis

techniques. Magnitudes and directions of internal forces at each joint in the frame were

determined based on certain assumptions related to the joints. In the later Chapter, FEM

(Finite Element Method) software (SAP 2000) was used to analyze the furniture frame and

have a better idea of the stress concentration and load distribution in every member and at

every joint in the sofa frame model.

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Chapter 3 Localized density effects on fastener holding capacities in wood-based panels

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61

3.1 Localized density effects on fastener holding capacities in wood-based panels. Part 1: Static tests

3.1.1 Résumé L'objectif principal de cette étude était de caractériser l’effet de la variation de densité

locale de trois types de panneaux agglomérés à base de bois sur la tenue mécanique de

différentes attaches. Des panneaux à lamelles orientées (OSB) de trois épaisseurs

différentes, des panneaux de fibres de moyenne densité (MDF) d’une épaisseur et des

panneaux de particules (PB) d’une épaisseur ont été utilisés pour évaluer la résistance à

l’arrachement de vis et agrafes sur la face et de côté. Également, nous avons évalué l’effet

sur la résistance d’enfoncement des têtes des agrafes et vis ainsi que la résistance latérale

des vis. Ensuite, les propriétés mécaniques ont été corrélées avec les variations de densité

locales des panneaux. Les résultats d'essai ont indiqué que pour les panneaux OSB, la

variation de densité a un effet significatif sur l’arrachement des vis ainsi que sur

l’enfoncement des têtes des vis et sur les résistances latérales des vis. Cependant, les effets

étaient moins évidents pour l’arrachement et l’enfoncement des têtes des agrafes. Pour les

panneaux PB, la variation de densité a eu un effet significatif sur l’arrachement et sur

l’enfoncement des têtes des vis mais les effets étaient moins prononcés pour la résistance

latérale des vis ainsi que pour l’arrachement et l’enfoncement des têtes des agrafes. Pour

les panneaux MDF, aucune corrélation significative n'a été trouvée. Ceci peut être attribué

à une faible variation de densité de ces panneaux. Les données seront employées pour

optimiser la structure des meubles et pour fournir des recommandations à l'industrie des

panneaux concernant l'utilisation des attaches en fonction de leurs produits.

3.1.2 Abstract The main objective of this study was to characterize localized density effects on some

common fasteners’ holding capacities in wood-based panels. Oriented strand board (OSB)

of three different thicknesses, medium density fiber board (MDF), and particleboard (PB)

were tested for screws and staples withdrawal from face and edge, head pull-through, and

for screw lateral resistance. The fastener holding capacities were correlated with localized

density of the panels. Test results indicated that in the OSB panels, density variation had a

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significant effect on the screw withdrawal, head pull-through, and lateral resistances, but

the effects were less evident for the staple withdrawal and head pull-through. For PB,

density variation had a significant effect on the screw withdrawal and head pull-through

resistances, but the effects were less pronounced for screw lateral resistance, staple

withdrawal and head pull-through. For MDF, no significant correlations were found; this

could be attributed to the low density variation in these panels. The data will be used for

the optimization of furniture frames, and to provide recommendations to the panel industry

on the use of the fasteners with their products.

3.1.3 Introduction Upholstered furniture manufacturers are always looking for ways to reduce the cost of their

products through the use of new engineered materials and processes. With the development

of CNC technology, wood-based composite panels are becoming a good alternative for

solid wood. CNC technology also allows for efficient and versatile designs of frames with

fewer parts replacing redundant and bulky hardwood components (APA 1997).

Power-driven screws and staples are two of the most frequently used types of fasteners for

joining framing members in upholstered furniture due to their quick and easy installation.

A comprehensive knowledge on the performance of these fasteners in panel products is

necessary for the best use in these applications. However, the data available in technical

literature is scattered and incomplete. Performance standards for structural-use panels

(OSB and plywood) provide requirements for lateral and withdrawal capacities for nails

but not for screws or staples. Screw withdrawal capacities from face and edge of MDF and

PB have been published by Composite Panel Association (CPA 1999 and 2002). Technical

Note E830A published by APA – The Engineered Wood Association (APA 1982) provided

ultimate lateral and withdrawal loads for plywood-to-metal and plywood-to-plywood edge

connections for screws in structural applications. Based on limited number of tests, APA

(1993) issued interim recommendations for adjustment of these values for APA-

trademarked OSB.

Fastener holding capacities of different wood-based panels have been measured by several

researchers in the past (Chow et al. 1988, Williams and Nielson 1999). Table 3.1 shows

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63

screw and staple holding capacities for some panel products found in the literature. Zhang

et al. (2002c, 2002d, and 2002e) and Erdil et al. (2002 and 2003a) studied the performance

of screws and staples in joints of solid wood, plywood and OSB used in furniture.

Although it is known that fastener holding capacity is related to the specific gravity of

wood or the wood-based composites, the influence of the density distribution

Table 3.1 Screw and staple holding capacities available in literature.

Screw withdrawal (N) Staple withdrawal (N)

Reference Panel Face Edge Face Edge

Staple head pull-through

ANSI

A208.2-2002

MDF 150 16 mm 1400 1200 - - -

PB MS 16mm 900 800 - - - ANSI

A208.1-1999 PB M2

16mm 1000 900 - - -

OSB-1 11mm - - 482a (40)g - 1472a (20) Chow

(1988) OSB-2

11mm - - 402a (49) - 1419a (20)

OSB 11mm 1268b 1154d 555c 861d, e -

OSB 15mm 1330b 1173d 682c 1008d, e -

Wang and Knudson (2002) OSB

18mm 1307b 1120d 864c 968d, e -

Williams and

Nielson (1999)

OSB 18mm 1516f (5) 1109f (26) - - -

MDF 19mm 1710f (3) 1410f (2)

a Staple: gauge 16, 51-mm (2-in) long, 12.7-mm (0.5-in) crown b Screw: No. 10, 38-mm (1.5-in) sheet metal screw (ThreadFast) c Staple: 51-mm (2-in), 16 gauge, 12.7mm (0.5-in) standard crown galvanized staples d Two or three panels were glued together e The penetration of the staple: 38mm f Screw: Standard one inch No. 10 gauge, flathead, low-carbon steel wood screws g Numbers in parentheses represent: coefficient of variation (%)

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64

within the panels on their fastener holding capacity has not been well studied. In the

furniture industry, the question of non-uniform density distribution through the thickness

and in the plane of the panel is of high concern, because fasteners are often driven near or

in the edges. Wang and Knudson (2002) examined holding capacities of nails, screws and

staples by testing OSB from various mills and revealed significant variation between the

panels, which was mainly due to density variation among the mills and within the panels.

Fakopp Enterprise (2005) advertised a portable screw withdrawal force meter with a

correlation coefficient of 0.79 between the screw withdrawal force and density of solid

wood. Recently, Sackey et al. (2005) and Semple et al. (2005) found that face and edge

screw withdrawal resistances were strongly correlated with the internal bond of furniture

grade particleboard. However, the correlation with density was weak due to low density

variation in the panel.

In order to provide new markets or expand the existing market for OSB, MDF and

particleboard in upholstered furniture industry, comprehensive tests were conducted on

fasteners holding capacity of the wood-based panels. The key objectives of this study were

to: 1) develop data on the fasteners lateral, withdrawal and head pull-through capacities in

OSB, MDF and PB; and 2) investigate the effects of localized density distribution in panels

on the fastener holding capacities.

3.1.4 Materials and Methods A total of twenty full-size (1.22 by 2.44 m) panels were used with four replications of each

of the following products: 1) MDF: 16-mm thick, grade 150; 2) PB: 16-mm thick, grades

M2 and MS (two of each); 3) OSB: 11-mm (7/16 in.) thick; 4) OSB: 15-mm (19/32 in.)

thick; and 5) OSB: 18-mm (23/32 in.) thick. The OSB panels were grade O2 (CSA 1993),

made of aspen. Each of the four replications was obtained from a different panel

manufacturer.

At first, mapping of the horizontal (in-plane) density of panels was carried out to determine

in-plane density variation and to identify where fasteners should be located within the

plane of the panel. All panels were scanned using X-ray density scanning system

VSX9811. The panels were scanned with a 5-mm resolution, the data were further

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65

processed to produce a coloured contour image of the density distribution with a final

resolution of 12.5 mm, and the final images were printed out with a 25-mm square mesh.

To determine the vertical density profiles across panel thickness, twenty-four 50-mm

square specimens were cut from each panel. These specimens were selected to cover the

entire range of horizontal density distribution within the panel. The vertical (through-

thickness) density profiles were measured using an X-ray QMS Density Profiler QDP-01X,

where X-ray beam travels parallel to the plane of the panel at a speed of 0.6 mm/s and the

average in-plane density of the 50-mm specimen is assessed with a resolution of 0.6 mm

across the thickness of the specimen.

All panels were tested in bending as received, and the moisture content (MC) was

measured following testing. Sixteen 50 x 76 mm samples were randomly cut from each

panel to determine MC according to ASTM standard D4442 (ASTM 2003c) Method B. For

each type of fastener holding capacity test, ten samples of 76 x 151 mm were cut from each

panel in such a way to cover the full range of density zones identified by colors. The

number of tests carried out in each sample varied depending on the type of test. Table 3.2

provides detailed information on the type and number of tests performed. The tests were

conducted in accordance with ASTM standards D1037 (ASTM 2003a) and D1761 (ASTM

2003b).

Table 3.2 Sampling plan to evaluate the static performance of fasteners in wood based panels.

Fastener type Property

Number of specimens per panel

Panel type a

Number of tests

per panel

Rate of loading

(mm/min) Face 10 40

Parallel to long axis 10 40 Gage 10 screw (25-mm long) Withdrawal Edge Perp. to long axis 10

D 40

15

Parallel to long axis 10 60 Lateral resistance Perp. to long axis 10 A 60 6.0 Gage10 screw

(50-mm long) Head pull-through 10 ½ of B 60 1.5

Face 15 45 Parallel to long axis 10 40 Withdrawal Edge Perp. to long axis 10

C 40

2.5 Gauge 16 staple (38-mm long, 11-mm crown)

Head pull-through 10 ½ of B 40 1.5 a A, B, C, and D indicate the four panel replicates of each material type or thickness.

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For all tests, the thickness of panels as manufactured was used to represent the actual in-

service conditions of upholstered furniture frames. In accordance with ASTM D1037

guidelines for screw face withdrawal, screws were driven into the 18-mm OSB specimens

approximately 17 mm deep, whereas in all other panels, the screws were driven through the

full thickness of the panel. In staple face withdrawal specimens, staples were driven

through the full thickness, so that the staple crown was projected 13 mm above the face.

For edge withdrawal, screws and staples penetrated 17 and 25 mm into the specimen,

respectively. For screw withdrawal tests, lead holes were pre-drilled using a drilling bit of

3.2 mm in diameter. For head pull-through resistance tests, the fasteners were driven

through the specimen with the head or crown flush with the panel surface (the staples’

crowns were 45o to the panel edge). For lateral resistance tests, the screws were centered

on the width or length of the specimens and located 6.4 mm from the edge.

Analysis of variance (ANOVA) general linear model procedure was performed for

individual fastener holding capacities and individual types of panels on the correlation of

localized density and the ultimate holding capacity. The individual holding capacities were:

screw withdrawal, staple withdrawal, screw lateral, screw head pull-through and staple

head pull-through; and the individual types of panels were: 11-mm, 15-mm and 18-mm

OSB, 16-mm MDF and 16-mm PB. In order to classify the averages of fasteners holding

capacity of the panels, the Duncan’s multiple tests were performed on the averages.

3.1.5 Results and Discussion Panel Density and MC

Figure 3.1 shows typical images of horizontal density distribution of OSB, MDF and PB

panels. The different colors represent the density variation in the plane of panel, and each

color represents a density range of 50 kg/m3. OSB panels had high density variation: from

400 to 850 kg/m3. PB had less variation of density than OSB: from 550 to 800 kg/m3. MDF

had the lowest density variation: between 700 and 850 kg/m3.

Figure 3.2 shows average vertical density profiles from samples taken from all panels

tested. Considerable differences were found between the three groups of OSB panels. The

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11-mm panels had the lowest face density, while the 18-mm panels had the lowest core

density. The 11-mm and the 15-mm OSB panels had similar core density. The highest

density and the least variation in density between the face and the core were observed in

MDF. The PB samples had the biggest variations between the face and the core density.

The MCs of the OSB, MDF and PB specimens were 5.7±0.3%, 7.0±0.2%, and 6.8±0.2%,

respectively.

1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

S1 S6 S11

S16

S21

S26

S31

S36

S41

S46

800-850

750-800

700-750

650-700

600-650

550-600

500-550

450-500

400-450

DensityGradient(kg/m3)

1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

S1 S6 S11

S16

S21

S26

S31

S36

S41

S46

900-950850-900800-850750-800700-750650-700600-650550-600500-550450-500400-450

DensityGradient(kg/m3)

1

6

11

16

21

26

31

36

41

46

51

56

61

66

71

76

81

86

91

96

S1 S6 S11

S16

S21

S26

S31

S36

S41

S46

800-850750-800700-750

650-700600-650550-600500-550

450-500400-450

DensityGradient(kg/m3)

a) b) c)

Figure 3.1 Typical images of horizontal density variation in panels: a) OSB; b) MDF; and c) PB.

Figure 3.2 Vertical density profiles of OSB, MDF and PB specimens.

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Withdrawal Resistance of Screws

Table 3.3 and Figure 3.3 showed a summary of results of screw withdrawal tests.

Classified averages of screw withdrawal of each type of panels conducted by the Duncan’s

multiple tests are given in Table 3.3 and Figure 3.3. Table 3.3 only showed the

comparisons within each test for all types of panels, and Figure 3.3 gave the comparisons

between face and edge withdrawal in each type of panels. The face withdrawal resistance

was significantly higher than the edge withdrawal resistance for all panels (Figure 3.3).

This result was expected, as the edge withdrawal strength is controlled by panel core

density, which is significantly lower than the face density (Figure 3.2). Indeed, this is one

of the major concerns that have been identified by the furniture manufacturers using panel

products. There were no significant differences between edge parallel and perpendicular

withdrawal resistances for all panels tested.

For the OSB, it was found that the average face withdrawal resistance of the 18-mm OSB

was nearly 11% lower than that of the 15-mm OSB panels, suggesting that the withdrawal

resistance is not linearly proportional to the penetration depth, as observed by other

researchers for dowel joints (Eckelman 1969, Zhang et al. 2002a). In edge withdrawal, the

11-mm OSB panels showed the lowest resistance. Since the core density of these panels

was similar to the other panels, the low edge withdrawal resistance can be explained by the

smaller thickness and high probability of splitting. Some specimens exhibited splitting

during the insertion of screws prior to testing.

The face withdrawal resistance of MDF was similar to that of OSB; however, it was

stronger than OSB in edge withdrawal. Smaller differences were found between face and

edge withdrawal resistances of MDF due to a more uniform vertical density profile. For

PB, the face withdrawal strength was approximately 14%, 17%, and 8% less than that of

MDF, 15-mm and 18-mm OSB panels, respectively.

The average face withdrawal capacities of tested panels corresponded well with the

previously published data (Table 3.1). Both PB and MDF did meet the minimum

requirements of ANSI A208.1 (CPA 1999) and ANSI A208.2 (CPA 2002), respectively.

However, the edge withdrawal capacities of PB and OSB were lower than published

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values. Note that Wang and Knudson (2002) glued two or three panels together for edge

withdrawal, required by ASTMD1037 standard to reduce the chance of splitting, while our

tests were performed using a single panel thickness causing high possibility of splitting.

ANOVA statistical analysis was carried out to examine the relationship between the screw

withdrawal resistance and the localized density of the panel. Results indicated significant

relationships at 95% confidence level for the screw face and edge withdrawal from OSB

and PB panels, except for the edge withdrawal parallel to the long axis of 15-mm OSB

panel, r values were found to range from 0.47 to 0.82 (Table 3.3). There was a good

correlation between screw face withdrawal resistance and localized panel density of all

OSB specimens with r = 0.54. Poor relationship was observed for MDF due to lower

variation in the horizontal density distribution of MDF in comparison with other types of

panels.

*The comparisons were performed within each group; values with the same capital letter

are not statistically different at 5% significant level.

Figure 3.3 Average screw withdrawal resistance of OSB, MDF and PB specimens.

A A

A

A

A*

B B

B B

BB

BB

B B

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Tabl

e 3.

3 Fa

sten

er p

erfo

rman

ce w

ith lo

caliz

ed d

ensi

ty fo

r scr

ews.

Fast

ener

Pr

oper

ty

Pane

l N

omin

al

thic

knes

s (m

m)

Ave

rage

de

nsity

(k

g/m

3 ) X

Ave

rage

hol

ding

ca

paci

ty(N

) (O

bser

ved

Y)

Reg

ress

ion

equa

tion

(Pre

dict

ed Y

) r

Dif.

a

(%)

RM

SE b

11m

m

645

1087

(26.

9)c D

d y

= 2.

18x

– 32

2 0.

82*

0.3

160.

4 15

mm

67

3 14

48 (2

1.7)

A

y =

2.25

x - 6

3.7

0.47

* -0

.2

270.

3 O

SB

18m

m

588

1308

(21.

3) C

B

y =

2.13

x +

59.2

0.

52*

-0.3

23

0.9

MD

F 16

mm

78

6 13

94 (7

.4) A

B

y =

0.43

x +

1054

0.

10

0.1

101.

9 Fa

ce w

ithdr

awal

PB

16m

m

687

1206

(12.

5) C

y

= 2.

10x

- 235

0.

68*

-0.1

10

9.0

11m

m

609

712

(24.

9) D

y

= 1.

73x

- 341

0.

59*

-0.1

14

0.9

15m

m

664

953

(29.

9) B

y

= 1.

53x

- 61.

5 0.

26

-0.1

27

0.4

OSB

18

mm

58

5 94

9 (3

2.4)

B

y =

2.73

x - 6

47

0.50

* -0

.1

262.

1 M

DF

16m

m

783

1239

(6.7

) A

y =

1.17

x +

323

0.35

0

75.9

Para

llel

to

stro

ng a

xis

PB

16m

m

670

808

(10.

5) C

y

= 1.

87x

- 444

0.

80*

-0.1

50

.5

11m

m

606

801

(27.

2) C

y

= 1.

49x

- 102

0.

50*

0 18

6.7

15m

m

660

1047

(22.

4) B

y

= 2.

82x

- 817

0.

60*

0.3

185.

8 O

SB

18m

m

546

880

(30.

2) C

y

= 2.

80x

- 647

0.

51*

-0.2

22

6.2

MD

F 16

mm

78

4 11

91 (9

.8) A

y

= 0.

40x

+ 87

5 0.

10

0.2

113.

9

Scre

w

Gag

e 10

, 25

mm

lo

ng

Edge

w

ithdr

awal

Pe

rpen

dicu

lar

to

stro

ng a

xis

PB

16m

m

683

827

(11.

9) C

y

= 2.

08x

- 594

0.

69*

0 70

.0

11m

m

571

1122

(35.

3) C

y

= 3.

54x

- 899

0.

81*

0 23

3.2

15m

m

635

1842

(24.

7) B

y

= 4.

87x

- 124

7 0.

58*

-0.2

36

8.5

OSB

18

mm

58

9 22

01 (2

6.0)

A

y =

6.66

x - 1

723

0.71

* 0.

1 40

1.9

MD

F 16

mm

78

0 22

65 (7

.0) A

y

= 0.

28x

+ 20

50

0.00

-0

.1

156.

5

Para

llel

to

stro

ng a

xis

PB

16m

m

682

1154

(13.

5) C

y

= 0.

74x

+ 65

1 0.

10

-0.1

15

3.7

11m

m

568

1127

(39.

1) D

y

= 4.

10x

- 120

3 0.

77*

0.1

278.

8 15

mm

65

2 20

06 (2

7.7)

C

y =

5.13

x - 1

339

0.46

* 0

488.

3 O

SB

18m

m

591

2505

(22.

1) A

y

= 5.

81x

- 932

0.

60*

0.1

441.

7 M

DF

16m

m

790

2247

(6.7

) B

y =

-0.5

0x +

264

4 0.

00

-0.1

14

8.4

Late

ral

resi

stan

ce

Perp

endi

cula

r to

st

rong

axi

s

PB

16m

m

669

1119

(13.

2) D

y

= 2.

34x

- 447

0.

50*

0 12

6.5

11m

m

594

1491

(22.

5) C

y

= 2.

44x

+ 41

.0

0.64

* 0

254.

7 15

mm

66

0 26

77 (1

5.4)

A

y =

4.69

x - 4

23

0.73

* 0.

2 28

0.0

OSB

18

mm

59

6 24

60 (1

7.8)

B

y =

4.62

x - 2

97

0.66

* 0.

1 32

7.8

MD

F 16

mm

79

3 26

97 (7

.9) A

y

= -1

.38x

+ 3

789

0.20

0.

1 20

4.9

Scre

w

Gag

e 10

, 50

mm

lo

ng

Hea

d Pu

ll-th

roug

h

PB

16m

m

701

1587

(12.

0) C

y

= 2.

69x

- 296

0.

66*

-0.2

14

0.1

*Sig

nific

ant a

t a p

roba

bilit

y le

vel o

f 0.0

5.

Dif.

a : Diff

eren

ces b

etw

een

obse

rved

and

pre

dict

ed v

alue

s, in

per

cent

age.

RM

SE b : R

oot m

ean

squa

red

erro

r.

c Va

lues

in p

aren

thes

es a

re c

oeffi

cien

t of v

aria

tion

base

d on

all

test

spec

imen

s.

d Th

e co

mpa

riso

ns w

ere

perf

orm

ed w

ithin

eac

h te

st; va

lues

with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 5%

sign

ifica

nt le

vel.

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71

Withdrawal Resistance of Staples

Results of staple withdrawal tests are presented in Table 3.4 including classified average

staple withdrawal resistances of the panels according to the Duncan’s multiple tests, but

Table 3.4 only showed the comparisons within each test. The face withdrawal resistance

was significantly higher than the edge withdrawal for all types of panels. The MDF

specimens showed the highest withdrawal values for both face and edge.

For all tested panels, the edge withdrawal resistances of 11-mm OSB panels were

approximately half as strong as the other panels because of splitting. There were no

significant differences between edge parallel and edge perpendicular withdrawal

resistances for all tested panels. The average staple face withdrawal resistance of OSB

corresponded well with the findings of Chow et al. (1988) and Wang and Knudson (2002)

(see Table 3.1). However, the edge withdrawal values were lower than those reported by

Wang and Knudson (2002) who used longer staples and two or three panels glued together.

The relationships between localized density and face withdrawal of staples were very poor

for MDF, whereas significant correlations at 95% confidence level were found for PB and

11-mm and 18-mm OSB panels (with r values ranging from 0.41 to 0.68). The correlations

for staple edge withdrawal resistance of 18-mm OSB were also significant, while the other

panels showed no or very weak relationships (see Table 3.4). The correlation was relatively

weak between staple face withdrawal resistance and localized panel density of all OSB

specimens (r = 0.38).

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72

Tabl

e 3.

4 Fa

sten

er p

erfo

rman

ce w

ith lo

caliz

ed d

ensi

ty fo

r sta

ples

.

Fast

ener

Pr

oper

ty

Pane

l N

omin

al

thic

knes

s (m

m)

Ave

rage

de

nsity

(k

g/m

3 ) X

Ave

rage

hol

ding

ca

paci

ty(N

) (O

bser

ved

Y)

Reg

ress

ion

equa

tion

(Pre

dict

ed Y

) r

Dif.

a R

MSE

b

11m

m

608

482

(35.

0)c E d

y

= 1.

40x

- 367

0.

68*

-0.5

12

2.9

15m

m

653

820

(26.

8) C

y

= 0.

88x

+ 24

2 0.

28

0.4

208.

2 O

SB

18m

m

606

892

(27.

0) B

y

= 1.

37x

+ 59

.8

0.41

* 0.

2 21

7.3

MD

F

16m

m

786

976

(8.4

) A

y =

0.09

x +

906

0.00

-0

.1

81.0

Fa

ce w

ithdr

awal

PB

16m

m

741

630

(16.

6) D

y

= 2.

43x

- 116

9 0.

57*

-0.3

85

.1

11m

m

596

204

(40.

4) D

y

= 0.

27x

+ 43

.1

0.24

0

78.3

15

mm

65

2 47

9 (2

5.6)

C

y =

0.50

x +

152

0.22

0.

2 11

7.9

OSB

18

mm

60

1 56

4 (4

6.6)

AB

y

= 2.

98x-

1228

0.

79*

0.2

173.

4 M

DF

16

mm

78

0 62

8 (2

1.5)

A

y =

0.74

x +

52.3

0.

14

-0.2

13

0.8

Para

llel

to

stro

ng a

xis

PB

16m

m

749

513

(13.

5) C

B

y =

0.74

x - 3

8.9

0.37

* -0

.5

63.2

11

mm

59

2 27

7 (3

0.3)

D

y =

-0.0

5x +

304

0.

00

0.9

82.3

15

mm

66

2 54

8 (1

8.1)

B

y =

0.85

x - 1

1.7

0.44

* -0

.5

87.8

O

SB

18m

m

613

551

(27.

1) B

y

= 1.

04x-

83.8

0.

31

-0.5

16

4.6

MD

F

16m

m

783

612

(25.

6) A

y

= 0.

21x

+ 44

6 0.

00

0.3

153.

3

Edge

w

ithdr

awal

Pe

rpen

dicu

lar

to st

rong

axi

s

PB

16m

m

754

491

(11.

5) C

y

= 0.

21x

+ 33

5 0.

10

-0.5

55

.5

11m

m

594

882

(27.

9) C

y

= 2.

03x

- 322

0.

80*

-0.2

14

4.8

15m

m

644

1148

(30.

3) B

y

= -0

.20x

+ 1

275

0.00

0.

2 34

3.4

OSB

18

mm

57

8 10

71 (3

2.5)

B

y =

2.85

x - 5

74

0.65

* -0

.2

261.

1 M

DF

16

mm

77

1 13

87 (1

7.7)

A

y =

4.57

x - 2

140

0.36

0.

3 22

3.4

Stap

le

gaug

e 16

, 38

-mm

lo

ng,

11-m

m

crow

n

Hea

d Pu

ll-th

roug

h

PB

16m

m

700

842

(17.

5) C

y

= -0

.51x

+ 1

199

0.10

0

145.

1 *S

igni

fican

t at a

pro

babi

lity

leve

l of 0

.05.

D

if. a : D

iffer

ence

s bet

wee

n ob

serv

ed a

nd p

redi

cted

val

ues,

in p

erce

ntag

e.

RMSE

b : Roo

t mea

n sq

uare

d er

ror.

c Va

lues

in p

aren

thes

es a

re c

oeffi

cien

t of v

aria

tion

base

d on

all

test

spec

imen

s.

d Th

e co

mpa

riso

ns w

ere

perf

orm

ed w

ithin

eac

h te

st; va

lues

with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 5%

sign

ifica

nt le

vel.

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73

Lateral Resistance of Screws

Results of screw lateral resistance tests in Table 3.3 showed that the 18-mm OSB and MDF

panels both had high resistances. The screw lateral resistances of the 11-mm OSB and PB

were about half of that of the other panels. Except for the 15-mm and 18-mm OSB, there

were no significant differences between screw lateral resistances parallel and perpendicular

to the long axis of the panels.

Significant linear relationships between localized density and the lateral resistance of

screws were found for all OSB panels in both loading directions, while the relationships

were insignificant or poor for MDF and PB (see Table 3.3). The relationship between the

screw lateral resistance and localized density for all OSB panels combined which was

found significant with r = 0.54.

Screws Head Pull-Through

Screw head pull-though resistances are shown in Table 3.3. The average resistance values

of MDF and 15-mm OSB were the highest and those of PB and 11-mm OSB were the

lowest. The 15-mm OSB showed, unexpectedly, high head pull-through resistance relative

to the other OSB panels, probably caused by high density and uniform density distribution

through the thickness of the panels.

Statistical analysis indicates that the relationships between the screw head pull-through

resistance and localized density for OSB and PB panels were significant at 95% confidence

levels, with r values ranging from 0.64 and 0.73 for PB and OSB, respectively. For MDF

panels, the correlation was not found to be statistically significant due to the low variation

of the horizontal density. In Figure 3.4, the relationship between the screw head pull-

through resistance and localized density is shown for all OSB panels combined. The

relationship was found significant with r = 0.65. Aside from isolated data points, the trend

is clearly indicative of a good linear relationship. Increasing the OSB density would

certainly improve the head pull-through resistance of screws, but that would also mean

increasing the cost of the panels.

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Figure 3.4 Screw head pull-through resistance of OSB panels in relation to average localized density.

Staples Head Pull-Through

Staple head pull-through tests showed similar trends with those observed for screw (Table

3.4). The average resistance of the MDF was the highest while that of the 11-mm OSB and

PB panels were the lowest. The 18-mm OSB had slightly low head pull-through resistance

compared to the 15-mm OSB panels, likely due to lower density. Compared to the values

given by Chow et al. (1988) (see Table 3.1), the staple head pull-through resistance of OSB

showed considerably lower values, explained by the smaller crown and shorter staple used.

Also, it should be noted that in some tests, at load levels near failure, the gripping device

was not able to sustain the locking mechanism of the staple’s legs, and one leg slipped off,

while another remained locked. Consequently, the staple was pulled out of the panel by one

leg, and the overall failure load was lower than in those cases where slippage did not occur.

It might cause the poor correlation of the test data with the panel localized density.

The relationships between staple head pull-through resistance and localized density were

not statistically significant except for the 11-mm and 18-mm OSB (see Table 3.4). The

correlation computed for all OSB panels was relatively weak (r = 0.45).

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3.1.6 Conclusions and Recommendations This study focused on evaluating the holding capacity of screws and staples in OSB, MDF

and PB panels. A data base of the fasteners’ face and edge withdrawal, head pull-through,

and lateral resistance under static load was developed, and correlations between fasteners

holding capacity and the localized panel density were examined. The following

conclusions and recommendations were made:

• Overall, the structure of the panel material was the most important factor for the

fastener holding capacity, but for the same type of the panel and the same type of

fastener holding capacity, localized density was an important factor.

• Among tested panels, OSB showed the highest density variation in plane and

through thickness, which was more critical to the screw than to the staple holding

capacities. The density of MDF panels varied the least, which generally led to a

more uniform fastener holding capacity.

• Generally, fasteners driven in low density zones fail at lower load levels than those

driven in high density zones. Therefore, the panels with higher density and less

density variation are beneficial for fastener performance.

The panel industry should work closely with the fasteners’ and furniture manufacturers in

order to develop new types of connectors (e.g., T-nut) that are more suited for attaching

various panel components, taking into consideration the nature and behaviour of the panel.

Such fasteners would have to be reliable, economical and easy to install. If typical panels

with traditional fasteners (i.e., screws and staples) are to be used in the upholstered

furniture frames, then new joint designs should be developed to enhance their capacity and

reduce the likelihood of premature failures due to fasteners driven in low density zones.

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3.2 Localized density effects on fastener holding capacities in wood-based panels. Part 2: Cyclic tests

3.2.1 Résumé Pour améliorer notre compréhension de l’effet de la variation de la densité locale dans les

panneaux à base de bois sur la résistance mécanique de différents types d’attaches, nous

avons entrepris une étude approfondie incluant divers types de panneaux et attaches.

L'étude couvre des essais statiques et cycliques sur des panneaux à lamelles orientées

(OSB) de trois épaisseurs différentes, des panneaux de fibres de moyenne densité (MDF) et

des panneaux de particules (PB). La résistance à l’arrachement des vis et des agrafes sur la

face et sur la côté, la résistance latérale des vis, et la résistance d’enfoncement des têtes des

agrafes et vis ont été évaluées. Les propriétés mécaniques des attaches ont été corrélées

avec la densité locale des panneaux. Le présent article constitue la deuxième partie de cette

étude portant sur les essais cycliques, la première partie portant sur les essais statiques a

déjà été publiée dans un autre article. Similairement aux résultats des essais statiques, les

essais cycliques ont indiqué que dans le cas des panneaux OSB la variation de densité a un

effet significatif sur la résistance à l’arrachement des vis, sur l’enfoncement des têtes et sur

les résistances latérales des vis. Cependant, les effets étaient moins évidents avec la

résistance à l’arrachement et l’enfoncement des têtes des agrafes. Pour les panneaux PB, la

variation de densité a eu un effet significatif sur la résistance à l’arrachement de face et sur

la résistance à l’enfoncement des têtes des vis et des agrafes mais les effets étaient moins

prononcés pour la résistance à l’arrachement sur la côté des vis et agrafes et pour la

résistance latérale des vis. Pour les panneaux MDF, aucune corrélation significative n'a été

trouvée, ceci peut être attribué à la faible variation de densité de ces panneaux. Les

données seront employées pour optimiser la structure des meubles et pour fournir des

recommandations à l'industrie des panneaux sur l'utilisation des attaches pour leurs

produits.

3.2.2 Abstract To improve our understanding of localized density effects in wood-based panels on holding

capacities of fasteners commonly used in furniture, a comprehensive study was conducted

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77

using static and cyclic tests of withdrawal and head pull-through of screws and staples, and

lateral resistance of screws in oriented strand board (OSB), medium density fiber board

(MDF), and particleboard (PB). This article presents results of cyclic tests, and

comparisons are made with the static test results reported in Part 1. Similar to static tests,

cyclic test data indicated that density variation in OSB panels had a significant effect on

the screw withdrawal, head pull-through, and lateral resistances, but the effects were less

evident with the staple withdrawal and head pull-through. For PB, density variation had a

significant effect on the screw and staple face withdrawal and head pull-through

resistances, but the effects were less pronounced for screw and staple edge withdrawal, and

screw lateral resistances. For MDF, no significant correlations were found, likely due to the

low density variation in these panels. The data will be used to provide recommendations to

the panel industry on the use of fasteners with their products and to optimize furniture

frames.

3.2.3 Introduction To reduce the cost of framing components, upholstered furniture manufacturers are always

on the look for alternative materials that are less expensive, but as strong and reliable as the

traditional ones. With the development of CNC technology, composite panels have a good

potential to replace solid wood in upholstered furniture frames. However, the suitability

and performance of traditional fasteners used in panel products for such applications is not

well studied yet. One of the concerns is the variation and non-uniformity in the density

distribution across the thickness and in the plane of the panel, and how it could affect the

holding capacity of fasteners. Available reference values are based on static tests, while

limited information is found about the density effects on fastener holding capacities in

wood-based panels under cyclic loading conditions.

Few studies were conducted on the performance of wood or wood-based material

assemblies under cyclic or fatigue tests using different test protocols. For example,

reversed and non-reversed cyclic loading (Hayashi et al. 1980) were used to evaluate the

fatigue properties of wood butt joints with metal-plate connectors (MPC) in timber. Moura

et al. (1995) used a non-reversed cyclic load schedule (varying tension) followed by a

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sinusoidal function to examine the influence of wood density on the mechanical behavior

of MPC joints.

Upholstered furniture frames are subjected in service to a wide range of loads, which act as

repetitive events of loading and unloading. Typically, in the furniture industry, long-term

fatigue loading is carried out using a large number of non-reversed loading cycles (25,000

cycles on each load level depending on the performance acceptance level) with an average

rate of twenty cycles per minute (GSA 1998). This performance test regime is based on a

zero-to-maximum (one sided or non-reversed) cyclic stepped fatigue load method rather

than a static or constant amplitude cycling load method (Eckelman 1988b). For instance,

Zhang et al. (2006) studied bending fatigue life of MPC joints in furniture-grade pine

plywood by subjecting the joints to one-sided stepped cyclic bending loads.

This study is part of a broader research program to examine the localized density effects on

fastener holding capacities in wood-based panels. This paper presents cyclic test data and it

complements the static test results reported by Wang et al. (2007a). The key objective of

this study is to evaluate the holding capacity of screws and staples in commercial wood-

based panels under cyclic loading in comparison with the static loading. The paper also

discusses the correlation between the fastener holding capacity and the density distribution

in panels. Technical information generated in this study will be used to provide

recommendations to the panel industry on the use of fasteners with their products and to

optimize furniture frame construction.

3.2.4 Materials and Methods The specimens for cyclic tests were prepared using the same materials and mapping and

cutting techniques as described in the previous paper (Wang et al. 2007a). Table 3.5

provides detailed information on the type and number of tests performed.

ASTM D1037 and D1761 testing procedures were used to carry out the static tests at a

constant rate of loading head displacement. However, for cyclic loading, the jigs were

modified to allow for loading and unloading cycles without slack and a constant rate of

loading was applied (load-controlled test). Set-ups used for the static and cyclic screw

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lateral resistance tests are shown in Figure 3.5. Fasteners were driven in panel specimens

following the same techniques as described in Wang et al. 2007a.

Prior to cyclic testing, specimens were subjected to static monotonic loading, and results

were reported in paper Wang et al. (2007a). The ultimate reference load (Pref) for each

specific test (see Table 3.6) determined from the static tests was used to calculate the load

levels needed for the cyclic stepped loading. The cyclic loading was applied in three steps

with thirty cycles at each load level: 15%, 35% and 70% Pref, after which the specimens

were loaded to failure (Figure 3.6). Note that for the staple edge withdrawal tests, the load

levels in the first step, instead of 15%, were 30% and 25% Pref for parallel and

perpendicular orientations, respectively (see Table 3.6.2). A preload of 40 N was applied to

eliminate the slack in the system during the cycling. The load rate was adjusted to produce

15 cycles per minute, in order to finish 90 cycles in six minutes to meet average static tests.

The cyclic loading regime used in this study is referred to as a short-term fatigue to

distinguish it from a typical fatigue type of loading which is usually carried out with a large

number of loading and unloading cycles until failure occurs. Due to the long time needed

to perform a single test following the General Service Administration (GSA 1998)

procedure, it was decided to carry out the short-term cyclic test that lasts approximately six

minutes. This allowed for testing sufficient number of specimens from various panel types

and thicknesses.

Table 3.5 Sampling plan to evaluate the cyclic performance of fasteners in wood based panels.

Fastener type Property

Number of specimens per panel

Panel type a

Number of tests

per panel

Rate of loading

(cycles/min)

Face 10 20 Parallel to long axis 10 20 Gage 10 screw

(25-mm long) Withdrawal Edge Perp. to long axis 10

D 20

15

Parallel to long axis 10 20 Lateral resistance Perp. to long axis 10

A 20

15 Gage10 screw (50-mm long)

Head pull-through 10 ½ of B 20 15 Face 10 20

Parallel to long axis 10 20 Withdrawal Edge Perp. to long axis 10

20 20

15 Gauge 16

staple (38-mm long, 11-mm

crown) Head pull-through 10 ½ of B 20 15 a A, B, C, and D indicate the four panel replicates of each material type or thickness.

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Figure 3.5 A test set-up for carrying out static (left) and cyclic (right) lateral loading resistance of screws

Table 3.6 Reference load levels for cyclic loading

Table 3.6.1 Reference load levels for screw withdrawal resistance both on face and edge (N)

Panel type Face Edge (Parallel) Edge (Perpendicular)

15% 163 15% 107 15% 120 35% 380 35% 249 35% 280

OSB 11mm (7/16")

1086.7

70% 761

712.1

70% 498

800.9

70% 561 15% 217 15% 143 15% 157 35% 507 35% 334 35% 366

OSB 15mm

(19/32")

1448.2

70% 1014

953.1

70% 667

1046.5

70% 733 15% 196 15% 142 15% 132 35% 458 35% 332 35% 308

OSB 18mm

(23/32")

1307.8

70% 915

949.3

70% 665

880.3

70% 616 15% 209 15% 186 15% 179 35% 488 35% 434 35% 417 MDF

(16mm)

1394 70% 976

1239

70% 867

1191

70% 834 15% 181 15% 121 15% 124 35% 422 35% 283 35% 289 PB

(16mm)

1206 70% 844

808

70% 566

827

70% 579

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Table 3.6.2 Reference load levels for staple withdrawal resistance both on face and edge (N)

Panel type Face Edge (Parallel) Edge (Perpendicular)

15% 72 30% 61 25% 69 35% 169 35% 71 35% 97 OSB 11mm

(7/16") 482.2 70% 338

203.5 70% 142

276.6 70% 194

15% 118 15% 72 15% 82 35% 275 35% 168 35% 192 OSB 15mm

(19/32") 785.19

70% 550

479.4

70% 336

548

70% 384 15% 130 15% 85 15% 83 35% 304 35% 198 35% 193 OSB 18mm

(23/32") 869.95 70% 609

564.5 70% 395

551 70% 386

15% 146 15% 94 15% 92 35% 342 35% 220 35% 214 MDF

(16mm)

976 70% 683

628

70% 440

612

70% 428 15% 97 517 15% 78 15% 74 35% 225 35% 181 35% 172 PB

(16mm)

644 70% 451 70% 362

492

70% 344 Table 3.6.3 Reference load levels for screw lateral resistance (N)

Panel type (Parallel) (Perpendicular)

15% 168 15% 169 35% 393 35% 394 OSB 11mm (7/16") 1122.2 70% 786

1127.2 70% 789

15% 276 15% 301 35% 645 35% 703 OSB 15mm (19/32") 1841.9 70% 1289

2007.7 70% 1405

15% 330 15% 376 35% 770 35% 877 OSB 18mm (23/32") 2201 70% 1540

2505.2 70% 1755

15% 340 15% 337 35% 793 35% 786 MDF

(16mm) 2265 70% 1586

2247 70% 1573

15% 172 15% 168 35% 402 35% 392 PB

(16mm) 1148 70% 804

1119 70% 783

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Table 3.6.4 Reference load levels for screw and staple head pull-through (N)

Panel type Screw Staple

15% 224 15% 132 35% 522 35% 309 11mm (7/16") 1491.470% 1044

882.1 70% 617

15% 402 15% 172 35% 937 35% 402 15mm (19/32") 2676.970% 1874

1148.3 70% 804

15% 369 15% 161 35% 861 35% 375 18mm (23/32") 2459.970% 1722

1071 70% 750

15% 404 15% 205 35% 943 35% 479 MDF

(16mm) 2694 70% 1886

1369 70% 958

15% 238 15% 126 35% 555 35% 295 PB

(16mm) 1587 70% 1111

842 70% 589

0

200

400

600

800

1000

1200

1400

0 50 100 150 200 250 300 350 400

Time (s)

Load

(N)

30 Cycles

30 Cycles

30 Cycles

Loading to failure

Figure 3.6 An example of typical cyclic loading regime for fastener holding capacity tests of screw face withdrawal on 11-mm OSB panels.

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83

Analysis of variance (ANOVA) general linear model procedure was performed on

individual fastener holding capacities for all types of panels to examine the correlation

between localized density and the ultimate holding capacity. The following holding

capacities were analyzed: screw withdrawal, staple withdrawal, screw lateral, screw head

pull-through and staple head pull-through. The following panels were tested: 11-mm, 15-

mm and 18-mm OSB, 16-mm MDF and 16-mm PB. In order to classify the averages of

fasteners holding capacity of the panels, the Duncan’s multiple tests were performed on the

averages.

3.2.5 Results and Discussion Analysis results including comparisons between the static and cyclic loading are given in

Tables 3.7 to 3.9. An example of typical load-displacement curves of the cyclic and

corresponding static tests of screw head pull-through on 15-mm OSB panels is shown in

Figure 3.7.

Withdrawal Resistance of Screws

Table 3.7 and Figure 3.8 show a summary of test results of the withdrawal resistance of

screws from face and edge under cyclic loading. Classified averages of screw withdrawal

for each type of panels conducted with the Duncan’s multiple tests are also given in Table

3.7. But Table 3.7 only showed the comparisons within each test for all types of panels,

and Figure 3.8 gave the comparisons between face and edge withdrawal in each type of

panels. The face withdrawal strength was significantly higher than the edge withdrawal

strength with the exception of the 11-mm and 18-mm OSB panels, where the values were

not significantly different (Figure 3.8). The differences could be attributed to the

orientation of the strands and the way the testing is done for face withdrawal as strands get

usually peeled off with the repeated cycles of loading and unloading. There were no

significant differences between the edge strength in withdrawal parallel and perpendicular

to the panel long axis for all panels tested.

The average face withdrawal resistance of the 15-mm OSB was the highest and that of the

11-mm OSB was the lowest among the tested panels. MDF showed capacities similar to

Page 102: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

84

Tabl

e 3.

7 Te

st re

sults

for s

crew

per

form

ance

in c

yclic

load

ing

Fast

ener

Pr

oper

ty

Pane

l N

omin

al

thic

knes

s (m

m)

Ave

rage

de

nsity

(k

g/m

3 ) X

Ave

rage

hol

ding

ca

paci

ty (N

) (O

bser

ved

Y)

Reg

ress

ion

equa

tion

(Pre

dict

ed Y

) r

Dif.

a

(%)

RM

SE b

11m

m

586

898

(37.

4)c C

d y

= 2.

58x

- 613

0.

83*

-0.1

18

2 15

mm

61

6 14

48 (2

0.2)

A

y =

2.00

x +

218

0.53

* -0

.1

243

OSB

18

mm

58

5 12

10 (2

5.8)

B

y =

1.76

x +

179

0.47

* 0.

1 27

1 M

DF

16m

m

788

1394

(7.4

) A

y =

-0.2

7x +

160

9 0.

06

-0.2

10

1 Fa

ce w

ithdr

awal

PB

16m

m

688

1183

(9.5

) B

y =

2.66

x - 6

51

0.59

* 0.

3 89

.1

11m

m

568

813

(23.

8) B

y

= 1.

28x

+ 88

.5

0.51

* -0

.3

162

15m

m

665

1136

(16.

4) A

y

= 0.

12x

+ 10

56

0.04

0

182

OSB

18

mm

59

6 11

53 (2

3.0)

A

y =

3.08

x - 6

82

0.76

* -0

.1

167

MD

F 16

mm

78

2 11

94 (1

1.5)

A

y =

1.54

x - 1

0.9

0.24

0.

1 13

2

Para

llel t

o st

rong

axi

s

PB

16m

m

703

833

(10.

8) B

y

= 1.

58x

- 277

0.

42

-0.1

79

.1

11m

m

554

871

(18.

2) B

y

= 1.

18x

+ 21

8 0.

46*

-0.1

13

7 15

mm

67

6 11

21 (1

8.8)

A

y =

2.01

x - 2

38

0.59

* 0

165

OSB

18

mm

59

3 11

73 (2

5.7)

A

y =

2.91

x - 5

53

0.45

* 0

262

MD

F 16

mm

79

1 12

06 (9

.3) A

y

= 0.

67x

+ 67

3 0.

20

0.3

108

Scre

w

Gag

e 10

, 25

mm

lo

ng

Edge

w

ithdr

awal

Perp

endi

cula

r to

long

axi

s

PB

16m

m

683

810

(12.

5) B

y

= 0.

29x

+ 61

5 0.

09

-0.4

98

.5

11m

m

568

953

(35.

5) C

y

= 3.

17x

- 845

0.

70*

-0.3

23

8.6

15m

m

655

1829

(27.

0) B

y

= 4.

00x

– 78

8 0.

68*

-0.2

35

5 O

SB

18m

m

615

2162

(26.

2) A

y

= 6.

99x

- 213

6 0.

79*

0 34

0 M

DF

16m

m

784

2114

(9.6

) A

y =

0.89

x +

1413

0.

11

0.2

196

Para

llel t

o st

rong

axi

s

PB

16m

m

688

1037

(17.

8) C

y

= -0

.56x

+ 1

426

0.08

-0

.4

181

11m

m

583

1225

(22.

4) B

y

= 2.

35x

- 147

0.

56*

0.2

222

15m

m

645

1971

(25.

9) A

y

= 4.

31x

– 80

7 0.

57*

-0.1

40

8 O

SB

18m

m

562

2026

(24.

0) A

y

= 3.

29x

+ 17

8 0.

33

0 44

9 M

DF

16m

m

793

2162

(15.

4) A

y

= 4.

23x

– 11

92

0.34

0

305

Late

ral

resi

stan

ce

Perp

endi

cula

r to

stro

ng a

xis

PB

16m

m

675

966

(14.

8) C

y

= 1.

61x

- 123

0.

34

0.2

131

11m

m

613

1764

(25.

7) B

y

= 3.

13x

– 15

6 0.

78*

0.1

278

15m

m

675

2918

(14.

6) A

y

= 2.

42x

+ 12

83

0.43

* 0.

1 37

8 O

SB

18m

m

582

2904

(23.

4) A

y

= 6.

61x

– 94

1 0.

80*

-0.1

40

4 M

DF

16m

m

779

3008

(3.7

) A

y =

1.80

x +

1603

0.

33

0.1

101

Scre

w

Gag

e 10

, 50

mm

lo

ng

Hea

d Pu

ll-th

roug

h

PB

16m

m

685

1921

(8.3

) B

y =

3.71

x - 6

16

0.71

* -0

.2

110

* Si

gnifi

cant

at a

pro

babi

lity

leve

l of 0

.05

Dif.

a : Diff

eren

ces b

etw

een

obse

rved

and

pre

dict

ed v

alue

s, in

per

cent

age.

RM

SE b : R

oot m

ean

squa

red

erro

r.

c Va

lues

in p

aren

thes

es a

re c

oeffi

cien

t of v

aria

tion

base

d on

all

test

spec

imen

s.

d Th

e co

mpa

riso

ns w

ere

perf

orm

ed w

ithin

eac

h te

st; v

alue

s with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 5%

sign

ifica

nt le

vel.

Page 103: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

85

Tabl

e 3.

8 Te

st re

sults

for s

tapl

e pe

rfor

man

ce in

cyc

lic lo

adin

g.

Fast

ener

Pr

oper

ty

Pane

l N

omin

al

thic

knes

s (m

m)

Ave

rage

de

nsity

(k

g/m

3 ) X

Ave

rage

hol

ding

ca

paci

ty (N

) (O

bser

ved

Y)

Reg

ress

ion

equa

tion

(Pre

dict

ed Y

) r

Dif.

a R

MSE

b

11m

m

599

377

(44.

7)c D

d y

= 1.

28x

- 387

0.

82*

-0.7

94

.3

15m

m

649

752

(29.

0) B

y

= 1.

74x

- 378

0.

57*

0.1

176

OSB

18

mm

58

8 82

5 (2

1.9)

B

y =

1.65

x - 1

45

0.65

* 0

134

MD

F

16m

m

791

1029

(10.

2) A

y

= 0.

21x

+ 85

9 0.

05

0.4

102

Face

with

draw

al

PB

16m

m

762

649

(19.

8) C

y

= 1.

53x

- 516

0.

55*

-0.1

10

6 11

mm

58

0 20

9 (4

7.2)

D

y =

1.04

x –

393

0.79

* -0

.6

59.4

15

mm

65

0 38

8 (3

4.4)

C

y =

1.55

x - 6

16

0.53

* -0

.9

111

OSB

18

mm

60

5 46

1 (2

1.8)

B

y =

0.74

x +

16.2

0.

53*

-0.6

83

.6

MD

F

16m

m

776

543

(14.

7) A

y

= -1

.55x

+ 1

746

0.35

0

73.2

Para

llel t

o st

rong

axi

s

PB

16m

m

741

474

(20.

7) B

y

= -0

.68x

+ 9

79

0.20

-0

.2

94.3

11

mm

59

8 23

8 (3

6.1)

C

y =

-0.0

4x +

259

0.

002

1.2

83.9

15

mm

60

8 45

9 (2

7.9)

B

y =

1.49

x - 4

45

0.50

* -0

.4

108

OSB

18

mm

60

9 46

3 (3

5.4)

B

y =

2.03

x –

774

0.64

* 0.

2 12

4 M

DF

16

mm

77

5 60

4 (1

3.6)

A

y =

1.46

x - 5

32

0.48

* 0.

8 70

.8

Ed

ge

with

draw

al

Perp

endi

cula

r to

stro

ng a

xis

PB

16m

m

760

483

(10.

9) B

y

= 0.

59x

+ 35

0.

39

-0.1

47

.4

11m

m

566

824

(22.

6) C

y

= 1.

24x

+ 12

3 0.

49*

-0.1

15

9 15

mm

68

8 14

38 (2

8.3)

A

y =

4.20

x - 1

447

0.47

* -0

.3

351

OSB

18

mm

58

9 11

59 (1

8.1)

B

y =

1.49

x +

280

0.53

* 0.

1 17

3 M

DF

16

mm

77

8 13

46 (9

.2) A

y

= -0

.79x

+ 1

959

0.14

0.

1 12

0

Stap

le

gaug

e 16

, 38

-mm

lo

ng,

11-m

m

crow

n

Hea

d Pu

ll-th

roug

h

PB

16m

m

702

1101

(13.

1) B

y

= 1.

97x

- 282

0.

54*

0 11

8 *

Sign

ifica

nt a

t a p

roba

bilit

y le

vel o

f 0.0

5 D

if. a : D

iffer

ence

s bet

wee

n ob

serv

ed a

nd p

redi

cted

val

ues,

in p

erce

ntag

e.

RMAE

b : Roo

t mea

n sq

uare

d er

ror.

c Va

lues

in p

aren

thes

es a

re c

oeffi

cien

t of v

aria

tion

base

d on

sam

e te

st sp

ecim

ens.

d Th

e co

mpa

riso

ns w

ere

perf

orm

ed w

ithin

eac

h te

st; v

alue

s with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 5%

sign

ifica

nt le

vel.

Page 104: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

86

Tabl

e 3.

9 C

ompa

rison

s for

scre

w a

nd st

aple

per

form

ance

s in

stat

ic a

nd c

yclic

load

ings

Sc

rew

ave

rage

hol

ding

cap

acity

(N)

(Obs

erve

d Y

)

Stap

le a

vera

ge h

oldi

ng c

apac

ity (N

) (O

bser

ved

Y)

Fa

sten

er

Prop

erty

Pa

nel

Nom

inal

th

ickn

ess

(mm

) St

atic

C

yclic

St

atic

C

yclic

11m

m

1087

(26.

9) a

Ab

898

(37.

4) A

48

2 (3

5.0)

A

377

(44.

7) B

15

mm

14

48 (2

1.7)

A

1448

(20.

2) A

82

0 (2

6.8)

A

752

(29.

0) A

O

SB

18m

m

1308

(21.

3) A

12

10 (2

5.8)

A

892

(27.

0) A

82

5 (2

1.9)

A

MD

F

16m

m

1394

(7.4

) A

1394

(7.4

) A

976

(8.4

) B

1029

(10.

2) A

Fa

ce w

ithdr

awal

PB

16m

m

1206

(12.

5) A

11

83 (9

.5) A

63

0 (1

6.6)

A

649

(19.

8) A

11

mm

71

2 (2

4.9)

B

813

(23.

8) A

20

4 (4

0.4)

A

209

(47.

2) A

15

mm

95

3 (2

9.9)

B

1136

(16.

4) A

47

9 (2

5.6)

A

388

(34.

4) B

O

SB

18m

m

949

(32.

4) B

11

53 (2

3.0)

A

564

(46.

6) A

46

1 (2

1.8)

A

MD

F

16m

m

1239

(6.7

) A

1194

(11.

5) A

62

8 (2

1.5)

A

543

(14.

7) B

Para

llel t

o st

rong

axi

s

PB

16m

m

808

(10.

5) A

83

3 (1

0.8)

A

513

(13.

5) A

47

4 (2

0.7)

A

11m

m

801

(27.

2) A

87

1 (1

8.2)

A

277

(30.

3) A

23

8 (3

6.1)

A

15m

m

1047

(22.

4) A

11

21 (1

8.8)

A

548

(18.

1) A

45

9 (2

7.9)

B

OSB

18

mm

88

0 (3

0.2)

B

1173

(25.

7) A

55

1 (2

7.1)

A

463

(35.

4) A

M

DF

16m

m

1191

(9.8

) A

1206

(9.3

) A

612

(25.

6) A

60

4 (1

3.6)

A

Scre

w

Gag

e 10

, 25

mm

lo

ng

Edge

w

ithdr

awal

Pe

rpen

dicu

lar

to st

rong

axi

s

PB

16m

m

827

(11.

9) A

81

0 (1

2.5)

A

491

(11.

5) A

48

3 (1

0.9)

A

11m

m

1122

(35.

3) A

95

3 (3

5.5)

A

15m

m

1842

(24.

7) A

18

29 (2

7.0)

A

OSB

18

mm

22

01 (2

6.0)

A

2162

(26.

2) A

M

DF

16

mm

22

65 (7

.0) A

21

14 (9

.6) B

Para

llel t

o st

rong

axi

s

PB

16m

m

1154

(13.

5) A

10

37 (1

7.8)

B

11m

m

1127

(39.

1) A

12

25 (2

2.4)

A

15m

m

2006

(27.

7) A

19

71 (2

5.9)

A

OSB

18

mm

25

05 (2

2.1)

A

2026

(24.

0) B

M

DF

16

mm

22

47 (6

.7) A

21

62 (1

5.4)

A

Late

ral

resi

stan

ce

Perp

endi

cula

r to

stro

ng a

xis

PB

16m

m

1119

(13.

2) A

96

6 (1

4.8)

B

11m

m

1491

(22.

5) B

17

64 (2

5.7)

A

882

(27.

9) A

82

4 (2

2.6)

A

15m

m

2677

(15.

4) B

29

18 (1

4.6)

A

1148

(30.

3) B

14

38 (2

8.3)

A

OSB

18

mm

24

60 (1

7.8)

B

2904

(23.

4) A

10

71 (3

2.5)

A

1159

(18.

1) A

M

DF

16

mm

26

97 (7

.9) B

30

08 (3

.7) A

13

87 (1

7.7)

A

1346

(9.2

) A

Scre

w

Gag

e 10

, 50

mm

lo

ng

Hea

d Pu

ll-th

roug

h

PB

16m

m

1587

(12.

0) B

19

21 (8

.3) A

84

2 (1

7.5)

B

1101

(13.

1) A

a Va

lues

in p

aren

thes

es a

re c

oeffi

cien

t of v

aria

tion

base

d on

sam

e te

st sp

ecim

ens.

b Th

e co

mpa

riso

ns w

ere

perf

orm

ed b

etw

een

stai

c an

d cy

clic

test

s; v

alue

s with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 5%

sign

ifica

nt

leve

l.

Page 105: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

87

Figure 3.7 Example of load-displacement curves of static and cyclic tests of screw head pull-through on 15-mm OSB panels.

0

200

400

600

800

1000

1200

1400

1600

OSB 11mm OSB 15mm OSB 18mm MDF 16mm PB 16mm

Panel type

Scre

w w

ithdr

awal

str

engt

h (N

) FaceEdge PEdge Pe

* The comparisons were performed within each group; values with the same capital letter are not statistically different at 5% significant level Figure 3.8 Average cyclic withdrawal resistance of screws in OSB, MDF and PB panels.

0

300

600

900

1200

1500

1800

2100

2400

2700

15 17 19 21 23 25Deplacement (mm)

Load

(N)

CyclicStatic1Static2

Deflection (mm)

A* A

A

A

B BA

AA

BB

A

B B

A

Page 106: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

88

the 15-mm OSB. PB was similar with the 18-mm OSB. In edge withdrawal, the 11-mm

OSB and 16-mm PB panels showed the lowest resistances, which can be explained by the

low core density of PB and the smaller thickness and therefore, the high probability of

splitting of the 11-mm OSB. Some specimens exhibited splitting during the insertion of

screws prior to testing. There were no significant differences between the edge withdrawal

of 15-mm and 18-mm OSB and the 16-mm MDF.

As can be seen in Table 3.9, generally, no significant differences were found between static

and cyclic screw face withdrawal resistances for all the panels. There are some significant

between static and cyclic screw edge withdrawal for OSB panels. In fact, for screw edge

withdrawal resistance in both parallel and perpendicular to the strong axis of the panel, the

cyclic edge withdrawal was higher than that of the static edge withdrawal for all OSB

panels. This could be related to the densification of the wood strands due to the repeated

cycles of loading and unloading. Or this cyclic load used in the tests which had not

produced fatigue damage. More research is needed in this area with an increased number of

cycles to determine if the effect persists.

The ultimate fastener holding capacity has been used as an indicator in this study.

However, other parameters associated with the load-displacement relationship could be

established to identify the difference between the static and cyclic behavior of fasteners, for

example, the initial stiffness, the slip or fastener movement in the panel specimen at a

certain load level or at ultimate load.

ANOVA was carried out to verify if a relationship exists between the screw face and edge

withdrawal resistances and the localized density of the panel. Results indicated that for the

cyclic face withdrawal in all OSB and PB panels, the relationship was significant at 95%

confidence level; r-values were found to range from 0.47 to 0.83 (Table 3.7). However,

poor relationship was observed for MDF. This could be attributed to the uniformity in the

MDF localized density as less variation is usually found in the horizontal density

distribution of MDF in comparison to OSB or PB panels. For edge withdrawal of screws

under cyclic load, the relationship was found to be significant for all OSB panel specimens

perpendicular to the long axis of the panel, while for the parallel direction, the relationship

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89

was only significant for 11-mm and 18-mm OSB (Table 3.7). However, relationships were

poor for both MDF and PB panels. There was a relatively good correlation between screw

face withdrawal resistance and localized panel density of all OSB specimens (r = 0.59).

Withdrawal Resistance of Staples

Table 3.8 presents the results of cyclic staple withdrawal tests including classified average

values according to the Duncan’s multiple test. But Table 3.8 only showed the comparisons

within each test for all types of panels. Face withdrawal resistance was significantly higher

than the edge withdrawal for all types of panels. For both face and edge withdrawal, MDF

specimens showed the highest resistance, while 11-mm OSB demonstrated the lowest for

all panel types. The edge withdrawal resistance of 11-mm OSB was less than half that of

the other panels which can be explained by the splitting associated with stapling due to the

small thickness. In fact the split was visible in some specimens before the test. There were

no significant differences between the edge withdrawal resistances parallel and

perpendicular to the long side of the panel for all tested materials except MDF.

From Table 3.9, generally, lower withdrawal resistances were observed following cyclic

loading in comparison to static loading for OSB panels. It could be explained by OSB

might have more gap between the chips and less wood contact. Therefore, it could be

concluded that staple face and edge withdrawal resistance in OSB is more sensitive to

cyclic loading than in other panel products tested.

Examining interactions between the localized density and the face withdrawal of the

staples under the cyclic load, it was evident that the relationships are significant for OSB

and PB panels, but not for MDF, at 95% confidence level as can be seen in Table 3.8. The

r-values ranged from 0.55 to 0.82. For staple edge withdrawal resistance parallel to the

long panel axis, the relationships were significant for OSB panels but not for MDF and PB.

However, for perpendicular direction, the correlation was only significant for the 15-mm

and 18-mm OSB and MDF panels. PB specimens did not exhibit any significant

relationship between the two parameters (Table 3.8). The correlation was good between

staple face withdrawal resistance and localized panel density of all OSB specimens (r =

0.61).

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90

Lateral Resistance of Screws

Test results in Table 3.7 indicate that the 18-mm OSB and MDF panels demonstrated the

highest resistances among the tested panels. The resistances of the 11-mm OSB and PB

were the lowest. Except for the 11-mm OSB, there were no significant differences between

screw lateral resistances in the direction parallel and perpendicular to the long axis of the

panels.

As showed in Table 3.9, some cyclic lateral resistances of screws appeared to be lower

than those determined from static tests; the rests were not significantly different.

Significant linear relationships between localized density and the lateral resistance of

screws were found for OSB panels in both loading directions, except for the 18-mm OSB

panels with screws loaded perpendicular to the long axis of the panel. However, the

relationships were found insignificant for MDF and PB (see Table 3.7). The relationship

between the screw lateral resistance and localized density of OSB panels combined was

found to be significant (r = 0.51).

Screw Head Pull-Through

Screw head pull-though resistance values are shown in Table 3.7. The average resistance

value of MDF panels was the highest and that of the 11-mm OSB was the lowest. The 15-

mm OSB exhibited similar resistance to the 18-mm OSB and the 16-mm MDF panels,

probably due to high density and uniform density distribution through the thickness of the

panels.

The average cyclic screw head pull-through resistance was higher than the static resistance

for all tested panels (Table 3.9). One possible explanation is that this cyclic load used in the

tests which had not produced fatigue damage. Another explanation could be the repeated

cycles of loading and unloading lead to a densification of the wood fiber underneath the

screw head, which does not occur in static test. In practice, such densification is only

possible if the head pull-through resistance of screws does not exceed the withdrawal

resistance of the screw shank from the main member. Otherwise, the screws will withdraw

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completely from the other component before the full head pull-through resistance is

developed.

Statistical analysis indicates that the relationships between the screw head pull-through

resistance and localized density for OSB and PB panels were significant at 95% confidence

levels, with r-values ranging from 0.43 to 0.80 for OSB and PB, respectively. For MDF

panels, the correlation could not be proven statistically significant due to the low variation

of the horizontal density. The relationship between the screw head pull-through resistance

and localized density for OSB panels combined was relatively weak (r = 0.48).

Staple Head Pull-Through

Staple head pull-though resistances are presented in Table 3.8. The average resistance of

the 15-mm OSB was the highest while that of the 11-mm OSB was the lowest. The 18-mm

OSB showed a lower resistance than the 15-mm OSB panels, likely due to lower density.

The average resistance of MDF panels was in the same order as that of 15-mm OSB

panels, likely due to the high face and core density of the panels.

It should be noted that in some tests, at load levels near failure, the gripping device was not

able to sustain the locking mechanism of the staple’s legs, and one leg slipped off, while

the other remained locked. Consequently, the staple was pulled out of the panel by one leg,

and the overall failure load was lower than in those cases where the slippage did not occur.

The slippage was observed more often during static tests. This phenomenon might have

caused the poor correlation of the test data with the localized density of the panel.

Examining the cyclic staple head pull-through resistance of the 15-mm OSB and PB

specimens, it was evident that the resistance under cyclic loading was higher than that of

the static one. No significant differences were observed for the other panels. One could

assume that the potential increase in the staple head pull-through could be attributed to the

localized densification of the wood fibers underneath the staple crown that occurred due to

repetitive loading and unloading. We could not find any explanation as to why such

phenomenon was associated with the 15-mm thick OSB and PB but not other OSB or MDF

panels.

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92

The relationship between staple head pull-through resistance and localized density was

statistically significant except for the MDF (see Table 3.8). The small r-value (0.47 to 0.54)

associated with the relationship might be attributed to the small number of samples tested.

The relationship between staple head pull-through resistance and localized density showed

a good correlation for OSB panels combined, and it was found significant with r-value =

0.64 (Figure 3.9). Aside from isolated data points, the trend is clearly indicative of a good

linear relationship. Increasing the OSB density would certainly improve the staple head

pull-through resistance, but that would probably mean increasing the cost of the panels.

y = 2.85x - 622R2 = 0.403

r = 0.64

400

800

1200

1600

2000

2400

400 450 500 550 600 650 700 750 800

Averaged localized density (kg/m3)

Cyc

lic s

tapl

e he

ad p

ull-t

hrou

gh

resi

stan

ce (

N)

Figure 3.9 Cyclic head pull-through resistance of staples in OSB panels in relation to average localized density.

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93

3.2.6 Conclusions and Recommendations Generally, cyclic tests of fastener holding capacities in wood-based panels showed similar

results to the corresponding static tests. For the cyclic loading regimes used in this study

(90 cycles at different load levels), no significant differences were observed between static

and cyclic behavior in terms of ultimate fasteners holding capacity with few exceptions.

Localized densification of wood fibers could be attributed to increasing fasteners capacities

for certain panels and fasteners combinations following repeated events of loading and

unloading. Lower values of cyclic capacity for other combinations could be associated with

the fatigue effect. In order to better understand the fatigue response, different loading

regimes with increased number of loading cycles are needed. Further analysis of the load-

deformation relationships including initial stiffness and deformation at a certain load level

can be used to better characterize the cyclic behavior of the fasteners.

Increasing panel density would improve the fastener holding capacity. However, reducing

the variation in localized density by producing panels with more consistent and uniform

density distribution for use in the upholstered furniture industry could be more effective

and possibly more economical for improving the fastener holding design values of the

panels.

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Chapter 4 Gusset-plate joints

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95

4.1 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1: Static load

4.1.1 Résumé Afin d’obtenir une rapidité et une la facilité d’installation, des agrafeuses électriques sont

généralement employées pour assembler les différents constituants structuraux des meubles

rembourrés. Pour introduire avec succès les panneaux à lamelles orientées (OSB) comme

élément de structure dans l’industrie du meuble rembourré, il est nécessaire d’acquérir des

connaissances concernant la résistance mécanique en flexion de joints de type goussets

agrafés construits avec de l'OSB. Dans cette étude, la résistance mécanique statique en

flexion de joints en forme de T abouté avec deux goussets a été évaluée expérimentalement

et analytiquement pour des goussets de différentes longueurs (4, 6, 8, 10 et 12-po) (102,

152, 203, 254 et 305-mm) attachés avec des agrafes de 1.0 pouce (25-mm) et 1.5 pouce

(38-mm), avec et sans adhésif. La résistance mécanique en flexion du joint a augmenté

proportionnellement avec la longueur du gousset jusqu'à ce que la force du gousset excède

celle du joint principal. La prévision analytique de la résistance mécanique en flexion des

joints agrafés a été satisfaisante. L'application d’un adhésif sur la surface de connexion a

changé les modes de rupture des joints et a augmenté leur résistance mécanique en flexion.

4.1.2 Abstract Power-driven staples are commonly used to join framing members in upholstered furniture

construction due to their quick and easy installation. To successfully introduce oriented

strandboard (OSB) into upholstered furniture as frame stock, moment capacity data for

stapled gusset-plate joints constructed of OSB is needed. In this study, the static moment

capacity of T-shaped, end-to-side joints with two gusset-plates was determined

experimentally and analytically for gusset-plates of different lengths (4, 6, 8, 10 and 12-in)

(102, 152, 203, 254 and 305-mm) attached with 1.0-in (25-mm) and 1.5-in (38-mm) long

staples with and without adhesive. The moment capacity of the joint increased in

proportion with the length of the gusset-plate until the strength of the gusset exceeded that

of the main joint member. Analytical prediction of the moment capacity of an unglued

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96

stapled joint was found satisfactory. Application of glue to the connection surface changed

the failure modes of the joints and increased their moment resistance capacity.

4.1.3 Introduction Today, seventy-five percent of homes built in North America utilize OSB panels for floor,

wall, and roof sheathing (SBA 2004). OSB producers continue to supply the market with

large quantities of panels. However, OSB consumption by the housing industry has

matured and offers limited growth potential; therefore, the OSB manufacturers should seek

new markets with the furniture industry being a candidate. In today’s competition with

foreign manufacturers, the furniture industry needs innovative products more than ever. In

general, OSB panels cost less than plywood or solid wood; therefore, the use of OSB in

upholstered furniture frames can reduce the cost of production and allow for more profits.

Modification of a product or designing a new one requires reliable information about the

performance of materials and joints which are going to replace traditional ones in order to

maintain the quality and to meet the consumer’s expectations. In order to encourage the

furniture industry to consider OSB as a new material for their products, technical

information on the performance of OSB as a framing member must be made available to

the industry.

Due to their quick and easy installation, power-driven staples are the most commonly used

fasteners to join framing members and to attach fabric to the frame in upholstered

furniture. Generally, it is believed that staples have limited holding strength in withdrawal.

When staples are used to attach two members by gusset-plates, the joint may develop

considerable strength, as the staples resist shear load rather than withdrawal (Zhang and

Maupin 2004). Therefore, the gusset-plate joints could be used for critical joints, such as

back bottom rail - back post and bottom side rail - back post joints in upholstered furniture

frame as shown in Figure 4.1, since these joints are highly stressed and difficult to

reinforce.

Limited information is available about the moment capacities of gusset-plate joints

constructed of wood composites. Eckelman (1971c) and Zhang et al. (2001b) studied the

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97

performance of T-shaped, end-to-side joints with glued-on plywood gusset-plates of

different configurations. Eckelman (1971c), using Douglas-fir plywood as joint members,

showed that the strength of the joints was limited by the properties of gusset-plate

materials, specifically, by rolling shear strength and in-plane shear strength. Zhang et al.

(2001b) expanded on Eckelman’s research by using southern yellow pine plywood, aspen

Timberstrand, and aspen Engineered Strand Lumber (ESL) as joint members and gusset-

plates made of southern yellow pine plywood attached with glue and staples. It was

reported that the material of the joint member and the number of staples did not influence

the joint strength, since all failures occurred in gusset-plates. Performance of OSB as a

frame member or a gusset-plate in a T-shaped joint has not been studied.

In North America, design values for stapled connections are based on empirical data, and

not on mechanics-based models. In this paper, the European Yield Model (EYM) equations

from Eurocode 5 (2004) and geometry considerations are used for analysis of the

connection capacity. The equations used in the EYM are based upon a theory first

developed by Johansen (1949). The equations predict the ultimate strength of a dowel-type

joint due to either a bearing failure of the joint members or the simultaneous development

of a bearing failure of the joint members and plastic hinge formation in the fastener. In

deriving Johansen's ultimate load equations it is assumed that both the fastener and the

timber are ideal rigid-plastic materials. The mode of failure and the ultimate shear strength

for a single fastener are determined by the thickness and the embedding strength of the

main and side members and by the fastener diameter and yield moment.

Side rail to back post joint

28 in.

72 in.

Side rail

Side rail

Top rail

Back

pos

t

34 in. Front rail

Back rail

Back rail to back post joint

Bac

k po

st

Figure 4.1 Schematic of a three-seat sofa frame (Critical joints—Side rail to back post joint & Back rail to back post joint).

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98

The primary objective of this research was to develop basic technical data on static

moment capacities of stapled and glued-stapled, T-shaped, end-to-side gusset-plate joints

constructed of OSB. The specific objectives were to 1) understand how gusset-plate length,

number and size of staples affect the moment capacity of T-shaped joints, 2) compare

moment capacities of gusset-plate joints with and without glue application, and 3) verify

analytical equations of the EYM for prediction of load capacity of stapled gusset-plate

joints. The data will be further used for fatigue testing of joints and for optimization of

upholstered furniture frame design.

4.1.4 Materials and Methods The T-shaped, end-to-side stapled gusset-plate joint specimens comprised two principal

members, a post and a rail, joined by two gusset-plates symmetrically attached on both

sides of the joint as shown in Figure 4.2. The joints were constructed of OSB produced by

Norbord (Canada). The principal members were 23/32-in. (18-mm) thick, 6-in. (152-mm)

wide, 16-in. (406-mm) long, and the gussets were 7/16-in. (11-mm) thick, 6-in. (152-mm)

wide and five different lengths: 4, 6, 8, 10 and 12-in. (102, 152, 203, 254 and 305-mm).

The width of the principal members was taken based on recommendations by Chen (2003).

The number of staples per side and their length varied with the length of the gusset plate as

is shown in Table 4.1. Figure 4.2 shows the staple placement pattern for glued joints, and

Figure 4.3 shows the placement of staples in gusset-plates of unglued joints. The staples,

commonly used in furniture production, were SENCO N17 16-gage galvanized chisel-end-

point type with a crown width of 7/16-in. (11-mm) and leg lengths of 1.0 and 1.5-in. (25

and 38-mm) with leg cross-section of 0.062 x 0.055-in. (1.57 x 1.40-mm). The staples were

coated with Sencote coating, a nitro-cellulose based plastic. The staples were power-driven

flush into specimens with a pressure of 55 psi (380 kPa). Five series of tests were

conducted with the glued-on gusset-plates. A PVA adhesive with solid content of 47%,

typically used in furniture manufacturing, was supplied by ADHESIFS ADHPRO INC.

To prepare the components, 4 by 8-ft (1.22 by 2.44-m) panels were cut into 6-in. (152-mm)

strips along the 8-ft (2.44-m) direction, then cut to length, and randomized. Static tests on

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99

the glued joints were conducted at least 48 hours after the application of glue to allow for

curing. Density, moisture content, internal bond strength and flat and edgewise bending

properties of OSB were determined using the matching specimens. The mechanical

properties were evaluated in accordance with ASTM D 1037 (ASTM 2005a).

355P

-

-

152

406

51

406

20

3030

20 20 20

12.7 D.15

2Rail

Post

* All dimensions in mm.

Figure 4.2 Configuration of a typical staple-glued gusset-plate joint.

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100

Tabl

e 4.

1 D

escr

iptio

n of

the

spec

imen

s, lo

ad c

apac

ities

, and

failu

re m

odes

of g

usse

t-pla

te jo

ints

con

stru

cted

of O

SB.

G

usse

t-pl

ate

leng

th

Stap

le

leng

th

Num

ber

of

stap

les

Num

ber

of

spec

imen

s

Pred

icte

d ul

timat

e lo

ad

Mea

n ul

timat

e lo

ad

CO

V

Ref

eren

ce

resi

stan

ce a

Dif.

b M

ode

of fa

ilure

c Jo

int

conf

igur

atio

n (in

) (in

)

(K

ip)

(Kip

) (%

) (K

ip)

(%)

a

4 1.

5 20

10

0.

694

0.67

Ad

4.8

0.64

6 -7

W

40%

, W+S

10%

, SO

50%

b 6

1.5

20

10

0.72

9 0.

85 B

7.

6 0.

825

13

W 3

0%, W

+S 1

0%,

W+S

O 2

0%, W

+GR

10%

, G

R+S

O 2

0%, G

R 1

0%

c 8

1.5

20

10

0.85

7 1.

01 C

5.

3 0.

973

14

W 4

0%, W

+GR

20%

, W

+GR

+S 2

0%, S

O 2

0%

d 10

1.

5 20

10

0.

937

1.02

C

5.3

0.98

0 5

W 6

0%, W

+GR

10%

, GR

10%

, M

R 1

0%, S

O 1

0%

e 12

1.

5 20

10

1.

032

0.98

C

6.3

0.94

7 -8

W

70%

, W+G

R 2

0%, M

R 1

0%

f 10

1.

0 32

10

0.

786

0.87

B

7.8

0.84

1 7

W 7

0%, W

+GR

20%

, W+S

10%

g 10

1.

0 32

10

0.

756

0.87

B

7.0

0.84

2 11

W

70%

, W+G

R 1

0%, W

+S 2

0%h

10

1.0

36

10

0.81

1 0.

97 C

9.

4 0.

942

16

W 5

0%, W

+GR

30%

, W+S

20%

Ung

lued

i 8

1.0

40

10

0.79

9 0.

92 B

, C

8.4

0.89

5 12

W

10%

, W+G

R 1

0%,

W+S

O 2

0%, W

+S 4

0%,

GR

+S 1

0%, G

R 1

0%

4 1.

0 8

10

0.

68 A

7.

0 0.

661

S

100%

6

1.0

8 10

0.92

B, C

6.

9 0.

890

M

R 1

0%, G

R+S

30%

, S 6

0%

8 1.

0 8

10

1.

15 D

8.

7 1.

116

M

R 3

0%, G

R+S

60%

, S 1

0%

10

1.0

8 10

1.27

E

11.6

1.

250

M

R 4

0%, G

R 6

0%

Glu

ed

12

1.0

8 10

1.24

D, E

11

.8

1.21

6

GR

100

%

a Ref

eren

ce re

sist

ance

com

pute

d us

ing

expe

rim

enta

l dat

a an

d AS

TM D

5457

pro

cedu

re (K

R = 1

). b D

iffer

ence

bet

wee

n pr

edic

ted

peak

load

and

refe

renc

e re

sist

ance

. c W

= st

aple

with

draw

al; S

= in

-pla

ne sh

ear f

ailu

re o

f OSB

; SO

= S

hear

-out

of O

SB; M

R =

mem

ber r

uptu

re; G

R =

gus

set-p

late

rupt

ure.

d Va

lues

with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t the

95%

sign

ifica

nce

leve

l.

1in

= 2

5.4

mm

; 1K

ip =

100

0 lbf =

4.4

48 k

N.

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101

1717

1751

262526 252525152

313031 3030152

2018

1820

76

314531 45152

2120

2020

102

21

314531 45152

2625

2525

127

26

314531 45152

3130

3030

152

31

(

a)

(b)

(c

)

(d

)

(e)

313031 30152

1818

1818

127

1918

18

30

313031 30152

2221

2121

127

2121

30

313031 30

152

2221

2121

127

2121

30

313031 30152

1717

1717

102

1717

30

(f

)

(g

)

(h)

(i)

* Al

l dim

ensi

ons i

n m

m.

Figu

re 4

.3 P

lace

men

t of s

tapl

es in

gus

set-p

late

s of u

nglu

ed jo

ints

(Con

figur

atio

ns a

-i).

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102

In order to conform to durability performance test standards such as the General Service

Administration (GSA) test regimen FNAE-80-214A (GSA 1998), strength design of

upholstered furniture frame requires information about the performance of each joint in a

sofa frame. According to the GSA, the bending moment acting on the back rail to back post

joint is considered very high. For a 72-in. (1.83-m) long three-seat sofa of medium-duty

category, three concentrated vertical loads of 300 lbf (1334N) are applied to the back-rail

with a total of 900 lbf (4003 N) (Table 4.2). If the back-rail has two rigid joints with back

posts, each joint carries a bending moment of 300×72/8+300×12×(72-12)/72=5700 lbf-in

(644 N-m) in fatigue test (Figure 4.4). To estimate the static load capacity, the load is

doubled resulting in a static moment capacity of 11400 lbf-in (1288 N-m). To comply with

the GSA requirements, the target static load on the joint with a 14-in. (356-mm) long arm

used in the tests is approximately 11400/14 = 814 lbf (3621 N).

All specimens were tested using a Tinius-Olsen universal testing machine. The post of the

joint was bolted to the test fixture with 2/3-in. (17-mm) aluminium spacers so that the

gusset-plates could deform freely during the test. Vertical upward load was applied to the

rail at a rate of 0.2 in./min (5.1mm/min) (Zhang et al. 2001b), and the load at failure was

recorded using a load cell with the accuracy of 0.2%.

Table 4.2 Performance-acceptance levels of upholstered furniture referencing to GSA (1998).

Cyclic Vertical Load

Test

Initial Loads

Load Increments

Number of Loads

Light-service

Acceptance Level

Medium-service

Acceptance Level

Heavy-service

Acceptance Level

(lbf) (lbf) (lbf) (lbf) (lbf)

On Front Rail 100 100 3 300 400 600

On Back Rail 100 100 3 200 300 500 1.000 lbf = 4.448 N

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103

28 in.

72 in.

Side rail

Side rail

Top rail Back post

300 lbf.300 lbf. 300 lbf.

Back rail

Back rail to back post joint

Back rail to back post joint

Front rail

24 in.24 in.12 in. 12 in.Bac

k po

st

Figure 4.4 GSA load applied on the back rail of a three-seat sofa frame (back rail to back post joint).

Predicted Ultimate Load

To predict the load capacity of the moment resisting connection, the analysis of a single

dowel-type fastener (staple) was combined with the analysis of its performance in the joint

of a given geometry. To ensure the design performance of the joint, the location of the

fasteners with respect to the end and the edge of the members should conform to the

assumptions of Eurocode 5 (EYM 2004). However, the design is not always controlled by

the load-carrying capacity of the single fastener. It depends on the configuration of the

connection that may induce supplementary moment couple and shear stresses in the joint

due to eccentricity.

(1) Analysis of a single staple:

To estimate the load capacity of a single staple, R, the following properties were assumed:

embedding strength of OSB = 9,120 psi (63 MPa), tensile strength of the staple = 87,020

psi (600 MPa) from Eurocode 5 (EYM 2004), and the cross-section of the staple leg 0.062

x 0.055 in. (1.57 x 1.40 mm). Calculations for staples using EYM equations (see page 110)

showed that in the joint of a given configuration, staples yield in bending at two plastic-

hinge points per shear plane, with limited localized crushing of OSB near the shear planes

in the side members. The characteristic resistance values were estimated at 190 lbf (860 N)

and 150 lbf (670 N) for the 1.5-in. and 1.0-in. staples, respectively.

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104

(2) Performance of the staple in the moment resisting connection.

To derive the design equations, the mechanical behaviour of the moment resisting

connection is examined. To counteract the applied moment, each fastener is loaded at a

different angle depending on the layout of the joint. The assumption is made that the

eccentric load P can be replaced by an equivalent force and an eccentric moment of

magnitude M=P×e acting at the centroid C of the fastener group as shown in Figure 4.5.

The eccentricity e is a function of the geometry of the joint. For a symmetric fastener

pattern, the centroid is found at the geometrical center of the group and the maximum

resultant shear force in the most-stressed fastener is determined for the fastener located

furthermost from the centroid using the following procedure.

For any fastener with coordinates (xi, yi) at a radial distance ri from the centroid of a group

of n fasteners under the load P, the resultant force Ri can be presented by its components

Rxi and Ryi, as shown in Figure 4.6. For the most-stressed fastener at the point with

coordinates (xa, ya), the resultant force is calculated from:

222yaxaa RRR += (4.1)

where:

= 2)(

i

axa r

yMR

(4.2)

∑+= 2

)(

i

aya r

xMnPR

(4.3)

222 ∑∑∑ += iii yxr

(4.4)

The connection design is adequate if Ra is less than the ultimate shear strength R of a single

fastener. Equations (1) to (4) can be used to estimate the load-carrying capacity P of the

moment resisting joint when R is known.

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105

e

P

c

Figure 4.5 Schematic of a moment-resisting connection.

P

rA

ri

x

y

MC

i

A

Rxi

RyiRi

Figure 4.6 Forces in fasteners of a moment-resisting connection.

4.1.5 Results and discussion Mechanical and physical properties of OSB

Table 4.3 shows the mechanical and physical properties of OSB panels used in the tests.

For each property shown in the Table, between 22 and 44 specimens were tested.

ra

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106

Table 4.3 Average values (COV%) of physical and mechanical properties of joint members and gusset-plates.

MOE (GPa) MOR (MPa) Materials Density

(kg/m3)

Moisture content

(%)

Internal Bond (MPa) Flatwise Edgewise Flatwise Edgewise

Joint member: 23/32 in. (18mm)

OSB

594 (6.8)

6.8 (7.7)

0.426 (18.2)

6.33 (8.2)

4.74 (5.4)

32.2 (12.1)

22.4 (11.7)

Gusset-plate:

7/16 in. (11mm)

OSB

590 (6.8)

6.2 (7.0)

0.417 (17.5)

6.66 (15.7)

5.18 (9.1)

37.1 (16.7)

23.1 (16.4)

Failure Modes

In the tested samples, six failure modes were observed: staple withdrawal, OSB shear-out,

in-plane shear failure of OSB rail member, in-plane shear failure of OSB gusset-plate

gusset-plate rupture and rail member rupture as shown in Figure 4.7 and Table 4.1. In the

joints with intermediate gusset-plates (6, 8 and 10-in) (152, 203 and 254-mm), a mixture of

failure modes was observed. Note, however, that in unglued stapled joints shear-out was

the dominant failure mode in short (4-in) (102-mm) gusset-plates whereas staple

withdrawal was most often observed in the joints with long (12-in) (305-mm) gusset-

plates. Differences in performance of the short and long gusset plates became more

obvious in the glued joints. All 4-in (102-mm) gusset-plates failed in shear in plane of the

panel (Figure 4.7f), while all 12-in (305-mm) gusset-plates failed in gusset plate rupture

(Figure 4.7c). These results indicate that the 4-in (102-mm) gusset-plate was not

adequately sized for the optimum capacity and the 12-in (305-mm) gusset-plate was

oversized. The discussion of load capacities presented below confirms this conclusion.

Load capacity

Mean values and coefficients of variation (COV) of ultimate load capacity of the tested

joints are summarized in Table 4.1. Statistical comparisons of results were performed using

ANOVA general linear model and the Tukey’s multiple comparison tests.

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107

(a) OSB shear-out (b) Staple withdrawal

(c) Gusset-plate rupture (d) Member rupture

(e) in-plane shear of rail member (f) Shear in plane of gusset-plate

Figure 4.7 Typical failure modes of gusset-plate joints.

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108

In unglued joints with twenty 1.5-in (38-mm) long staples, an increase of gusset-plate

length from 4 to 6-in (102 to 152-mm) and from 6 to 8-in (152 to 203-mm) significantly

increased the peak load by 27% and 19%, respectively. Further increase of gusset-plate

length did not increase the load capacity of the joints as can be seen in Figure 4.8.

Therefore, for this particular joint geometry, the 8-in (203-mm) gusset-plate presented the

optimum design. Note that to achieve similar load levels, about twice as many 1.0-in (25-

mm) long staples were needed (Figures 4.3h and 4.3i). Comparison of configurations f and

g (Figures 4.3f and 4.3g) shows that changing positions of staples in gusset-plates did not

influence the ultimate load significantly.

0

200

400

600

800

1000

1200

1400

0 2 4 6 8 10 12 14

Gusset-plate length (in.)

Ref

eren

ce re

sist

ance

(lbf

.)

Glued joints (experimental)

Stapled unglued joints (experimental)

Stapled unglued joints (predicted)

Figure 4.8 Experimental reference resistance vs. predicted peak loads of stapled gusset-plate joint assemblies with/without glue.

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109

Based on the experimental data, the reference resistance values were calculated as the

lower 5-th percentile with a 75% confidence using the procedure described in ASTM

D5457 (ASTM 2005b)., assuming two-parameter Weibull distribution and a reliability

normalisation factor KR = 1. Table 4.1 and Figure 4.8 show a comparison between the

experimental reference resistance values and the predicted ultimate loads of stapled joints

calculated using the EYM equations and the connection geometry. The experimental values

for stapled joints were 5 to 16% higher than the predicted loads with two exceptions. The

loads carried by 4-in (102-mm) and 12-in (305-mm) gusset-plates were 7% to 8% less than

predicted. This can be explained by the analysis of the failure modes observed during the

tests. The 4-in (102-mm) gusset-plates were inadequately short, and the densely placed

staples often caused shear-out failure in the post before the fasteners developed their full

capacity (Figure 4.7a). On the other hand, the 12-in (305-mm) gusset-plates were

excessively large for this joint; most staples did not reach their shear capacity and failed in

withdrawal due to lateral instability of the rail. These results warrant caution when

applying the principles of the EYM to the joint design where the sizes of the members and

placement of fasteners may not be adequate to develop plastic hinges as assumed in the

theory.

In spite of the satisfactory prediction of stapled gusset-plate joints static strength , the use

of so many staples to construct the joint is not desirable for furniture makers. The use of

glue to attach gusset-plates is much more efficient and requires the minimum number of

staples to fabricate a joint of the same size with the same or higher load capacity.

Experimental results showed that the load capacity of glued joints increased in proportion

with the size of the gusset-plates up to the length of 10 in (254-mm) (Figure 4.8). Further

increase in length of the gusset-plate did not lead to any significant improvement due to the

fact that the strength of the glue bond exceeded the strength of the gusset-plate material

(see Figure 4.7c). In comparison with unglued joints with 20 staples, the mean ultimate

load capacities of joints with 6, 8, 10 and 12-in (152, 203, 254 and 305-mm) gusset-plates

were increased by 8%, 14%, 25% and 27%, respectively.

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110

4.1.6 Conclusion Effects of gusset-plate length, number and length of staples, placement of staples, and glue

application on the static load capacity of T-shape OSB gusset-plate joints were

investigated. Application of glue was the most important factor affecting the performance

of the joints, which allowed for strength increase up to 27%. An increase in length of

gusset-plate from 4 to 8-in (102 to 203-mm) boosted peak load for both glued and unglued

joints, but further increase of gusset-plate length did not enhance the strength of the joints.

Twice as many 1.0-in (25-mm) long staples had to be used to achieve similar load levels

with 1.5-in (38-mm) long staples for unglued gusset-plate joints. Changing positions of the

staples in gusset-plates did not affect the strength of the joints of tested configurations.

Failure modes depended on the size of the gusset-plates. Predicted and experimental

reference resistance values for stapled joints were in satisfactory agreement; however, there

is a limit to the application of the yield theory when the geometry of the joint prevents the

development of the full shear capacity. It is advisable to verify extreme cases by tests.

4.1.7 APPENDIX Formulas for characteristic strength of staples:

( ) ( )

( ) ( )

⎪⎪⎪⎪⎪⎪⎪⎪

⎪⎪⎪⎪⎪⎪⎪⎪

++

+⎥⎥⎦

⎢⎢⎣

⎡−

+++

+

+⎥⎥⎦

⎢⎢⎣

⎡−

+++

+

+⎥⎥

⎢⎢

⎟⎟⎠

⎞⎜⎜⎝

⎛+−⎟⎟

⎞⎜⎜⎝

⎛+

⎥⎥⎦

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+++

+

=

42

1215.1

4214

1221

05.1

424

122

05.1

4112

1

.min

,,1,,

,22,1,

,22,1,

,21,1,

,1,1,

,

1

2

2

1

232

1

2

1

221,1,

2,2,

1,1,

,

RkaxkhRky

Rkax

kh

Rkykh

Rkax

kh

Rkykh

Rkaxkh

kh

kh

Rkv

FdfM

Fdtf

Mdtf

Fdtf

Mdtf

Ftt

tt

tt

ttdtf

dtfdtf

F

ββ

βββ

βββ

βββ

βββ

βββββ

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111

where: RkvF , = characteristic load-carrying capacity per shear plane per fastener, N;

it = panel thickness or penetration depth, with i = 1 or 2, mm;

kihf ,, = 1.07.065 itd − , characteristic embedment strength in ith member, N/mm2;

d = 48.140.157.1 =× , fastener diameter, mm;

RkyM , = 6.245.0 dfu , characteristic fastener yield moment, Nmm; where uf = 600, tensile strength of the wire, N/mm2;

β =kh

kh

ff

,1,

,2, , ratio between the embedment strength of the members;

RkaxF , = penkax dtf , , characteristic axial withdrawal capacity of the fastener, N;

where 26, 1020 kkaxf ρ−×= , characteristic pointside withdrawal strength, N/mm2;

kρ = 500, characteristic panel density, kg/m3; Notes:

1) 1.5-in. long staples were considered in single shear, because pent = 9 mm = 6d is not sufficient to develop the second shear plane.

2) For 1-in. long staples, pent = 14.3 mm ≤ 14 d , therefore a factor of 69.07.20/3.1414/ ==dt pen was applied.

The Figures A1 and A2 show 1.5-in (38-mm) and 1-in (25-mm) long staples in the panels:

t1=11.1mm

t2=18.3mm

OSB 11.1mm

OSB 18.3mm

OSB 11.1mm t3 = 8.6mm

t1=11.1mm

t2=14.3mm

OSB 11.1mm

OSB 18.3mm

OSB 11.1mm

(A1) (A2)

Figure A-- Schematic of 1.5-in (38-mm) (A1) and 1-in (25-mm) (A2) long staples penetration in the panels.

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112

4.2 Moment capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 2: Fatigue load

4.2.1 Résumé Pour obtenir le rapport entre la résistance mécanique en flexion statique et la fatigue, la

performance à la fatigue de joints en forme de T aboutés avec deux goussets construit en

panneaux à lamelles orientés (OSB), a été étudiée. Au total, 108 joints agrafés et agrafés-

collés avec des goussets des différentes longueurs (6, 8 et 10 po) (152, 203 et 254-mm) ont

été soumis à des charges échelonnées de flexion cyclique sur un seul côté. Les résultats

d'essai ont montré que les assemblages avec des goussets d'OSB parviennent à la rupture

en moins de 25 000 cycles lorsqu’un niveau de chargement échelonné a excédé 63

pourcent de leur résistance en flexion statique. Le ratio de dépassement pour le test statique

à la fatigue était en moyenne de 2.1 avec un coefficient de variation de 12 pour cent. Dans

les joints agrafés, les ratios les plus élevés étaient associés à l’arrachement d'agrafe comme

mode de rupture dominant. Dans les joints agrafé-collé, les ratios bas étaient associés au

cisaillement dans le plan et les ratios élevés, avec la rupture des panneaux OSB.

4.2.2 Abstract In order to obtain the ratios of static-to-fatigue moment capacity, the fatigue performance

of T-shaped, end-to-side gusset-plate joints made of oriented strandboard (OSB) was

investigated. A total of 108 stapled and glued-stapled joints with gusset-plates of different

lengths (6, 8 and 10 in) (152, 203 and 254-mm) were subjected to one-side cyclic stepped

bending loads. Test results showed that assemblies with OSB gusset-plates would fail

within 25,000 cycles when a stepped load level exceeded 63 percent of their static moment

capacity. The passing static-to-fatigue ratio averaged 2.1 with the coefficient of variation of

12 percent. In the stapled joints, the higher ratios were associated with the staple

withdrawal as dominating failure mode. In the glued-stapled joints lower ratios were

associated with in-plane shear and the higher ratios – with the rupture of the OSB panels.

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113

4.2.3 Introduction The furniture manufacturing, including upholstered furniture, is a dynamic industry with

many opportunities to diversify their products using various materials and designs. The use

of panel products, such as plywood and oriented strand board (OSB), to substitute solid

hardwood in upholstered furniture frames, is gaining popularity. Gusset-plates are used to

join back rail to back post and side rail to back post and other highly stressed joints, which

are difficult to reinforce by other means (Zhang et al. 2001b). For OSB to access the

upholstered furniture industry, technical data on the performance of connections made with

OSB must be provided to ensure that it is well-suited for such application. This is the

second paper in a series that deals with this topic (Wang et al. 2007b), which will focus on

the fatigue performance of joints made with OSB framing members and gusset-plates

assembled with staples with and without glue.

In engineering, the term of fatigue is defined as the progressive damage that occurs in

materials subjected to cyclic loading (USDA 1999). By contrast to common belief, fatigue

is the main cause of failure in wooden furniture; therefore, special attention must be paid to

the fatigue resistance of a wood frame (Eckelman and Zhang 1995), which is controlled, in

principle, by the fatigue life of its critical joints. The furniture performance test standards

such as GSA test regimen FNAE-80-214A (GSA 1998), requires information on the joint

fatigue performance, particularly fatigue failure load and fatigue life, i.e. the number of

load cycles survived until failure. The standard performance test regime is based on a zero-

to-maximum non-reversed cyclic stepped fatigue load method rather than static or constant

amplitude cycling load method (Eckelman 1988b).

Multi-cycle fatigue tests are expensive as they require specialized equipment and

considerable testing time in comparison with static tests. Therefore, it would be useful to

correlate the static and fatigue performance to characterize various types of joints in the

future. Several studies were focused on correlating the static and fatigue moment resistance

of wood joints with various fasteners. Zhang et al. (2003) investigated the fatigue life of T-

shaped, end-to-side assemblies using two-pin dowel joints by subjecting them to one-side

constant and stepped cyclic bending loading. A mathematical representation was developed

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114

to correlate the applied moment to the number of cycles to failure. Zhang et al. (2006)

studied the bending fatigue life of metal-plate-connected joints in furniture grade pine

plywood subjected to one-side cyclic stepped bending loads. They reported that there was a

strong relationship between the static moment capacity and the load level causing failure in

a fatigue test. The passing fatigue moment level was 46% of the static moment capacity.

No information has been found in literature on the fatigue resistance of gusset-plate joints

made of OSB. The main objective of this study was to evaluate the fatigue resistance of

OSB gusset-plate joints and determine the ratio of the static moment capacities to their

fatigue moment capacities for design purposes. The second objective was to gather the

information on the failure modes of such assemblies under stepped fatigue loads.

4.2.4 Materials and Methods Each test specimen consisted of post and rail made of structural 23/32-in (18-mm) OSB

joined with a pair of 7/16-in (11-mm) OSB gusset-plates symmetrically attached on both

sides of the joint with staples with or without glue. Basic material properties, fabrication

procedures, and configuration details of the joints tested statically were reported in Wang

et al. (2007b). For fatigue tests, the panel materials from the same batch were used and the

joints of the same configurations were constructed using the same procedures with the

exception of the length of the rail and the gusset-plates. The rail length was increased from

16-in (406-mm) to 23-in (584-mm) to accommodate the capacity of the pneumatic

cylinders used in the test setup. The gusset-plates used in fatigue tests were 6, 8 and 10-in

(152, 203 and 254-mm) long, because the static tests (Wang et al. 2007b) showed that

shorter and longer gusset-plates were not efficient in these joints. Columns 1 through 7 of

Tables 4.4 and 4.5 provide the information on the tested configurations including the

number of replicates and the average static moment capacity as reported by Wang et al.

(2007b).

Joint assemblies were subjected to two loading schedules, representing 1) the backrest

frame and 2) seat load foundation test for a 72-in (1.83-m) long three-seat sofa frame

without middle upright on the back (Figure 4.9). To determine the loads for the first

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115

Tabl

e 4.

4 Te

st sp

ecim

en c

onfig

urat

ions

and

resu

lts fo

r GSA

bac

kres

t fra

me

sche

dule

.

Fatig

ue

Rat

io o

f st

atic

/fatig

ue

Gusset-plate

length

Staple length

Number of staple

Number of specimens

Stat

ic

peak

lo

ad

(Ave

.)

Stat

ic

mom

ent

(Ave

.) Pa

ssed

m

omen

t Fa

iled

mom

ent

Cum

ulat

ive

No.

of

cycl

es to

failu

re

Pass

ed

Faile

d M

ode

of fa

ilure

a

Type of joint

(in)

(Kip

) (K

ip-in

)

1

2 3

4 5

6 7

8 9

10

11

12

13

6 1.

5 20

9

0.86

(8

.1)

12.1

6.

77

(8)b

7.82

(7

) 10

0,00

0+19

,479

Ac

(10)

1.

78

1.54

WR

+GR

2/9

W

R+G

R+S

3/9

, W

R+S

3/9

, W

R 1

/9

8 1.

5 20

9

1.01

(5

.3)

14.1

6.

42

(5)

7.47

(5)

100,

000+

14,1

45 A

(8

) 2.

20

1.89

W

R 5

/9,

WR

+GR

+S 4

/9

Stapled

10

1.5

20

9 1.

04

(4.7

) 14

.5

7.23

(5

) 8.

28

(4)

125,

000+

7,89

7 B

(5

) 2.

00

1.75

W

R 4

/9,

WR

+GR

3/9

, W

R+G

R+S

2/9

6 1

8 9

0.92

(6

.9)

12.9

7.

82

(10)

8.

87

(9)

150,

000+

237

C

(10)

1.

65

1.45

M

R 5

/9, S

4/9

8 1

8 9

1.15

(8

.7)

16.1

9.

10

(12)

10

.2

(10)

15

0,00

0+23

,864

D

(14)

1.

77

1.59

M

R 4

/9,

GR

+S 4

/9,

S 1/

9

Glued

10

1 8

9 1.

28

(11.

2)

17.9

8.

98

(8)

10.0

(8)

150,

000+

23,1

93 D

(9

) 1.

99

1.78

M

R 6

/9, G

R 3

/9

a Mod

e of

failu

re: W

R =

stap

le w

ithdr

awal

and

rupt

ure;

S =

in-p

lane

shea

r fai

lure

of O

SB; M

R =

mem

ber r

uptu

re; G

R =

gus

set-p

late

ru

ptur

e.

b Valu

es in

par

enth

eses

are

the

coef

ficie

nt o

f var

iatio

n (%

).

c Valu

es w

ith th

e sa

me

capi

tal l

ette

r are

not

stat

istic

ally

diff

eren

t at t

he 9

5% si

gnifi

canc

e le

vel.

1in

= 2

5.4

mm

; 1K

ip =

100

0 lbf =

4.4

48 k

N; 1

Kip

-in=

113

N-m

.

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116

Tabl

e 4.

5 Te

st sp

ecim

en c

onfig

urat

ions

and

resu

lts fo

r GSA

seat

load

foun

datio

n sc

hedu

le.

Fatig

ue

Rat

io o

f st

atic

/fatig

ue

Gusset-plate length

Staple length

Number of staple

Number of specimens

Stat

ic

peak

lo

ad

(Ave

.)

Stat

ic

mom

ent

(Ave

.) Pa

ssed

m

omen

t Fa

iled

mom

ent

Cum

ulat

ive

No.

of

cycl

es to

failu

re

Pass

ed

Faile

d

Mod

e of

failu

rea

Type of joint

(in)

(Kip

) (K

ip-in

)

1

2 3

4 5

6 7

8 9

10

11

12

13

6 1.

5 20

9

0.86

(8

.1)

12.1

6.

00

(0)b

9.00

(0

) 50

,000

+402

Ac

(1)

2.01

1.

34

W 6

/9,

W+G

R 2

/9,

W+S

1/9

8 1.

5 20

9

1.01

(5

.3)

14.1

6.

00

(0)

9.00

(0

) 50

,000

+365

A

(0)

2.36

1.

57

W 6

/9, W

+S 3

/9

Stapled

10

1.5

20

9 1.

04

(4.7

) 14

.5

6.00

(0

) 9.

00

(0)

50,0

00+2

,624

C

(2)

2.42

1.

61

W 9

/9

6 1

8 9

0.92

(6

.9)

12.9

6.

00

(0)

9.00

(0

) 50

,000

+1,6

04 B

(4

) 2.

15

1.43

G

R+S

5/9

, S 4

/9

8 1

8 9

1.15

(8

.7)

16.1

7.

33

(22)

1.

03

(15)

50

,000

+21,

577

D

(8)

2.19

1.

56

MR

4/9

, G

R+S

4/9

, S

1/9

Glued

10

1 8

9 1.

28

(11.

2)

17.9

8.

00

(19)

1.

10

(14)

50

,000

+22,

467

D

(11)

2.

24

1.63

M

R 6

/9, G

R 2

/9,

GR

+S 1

/9

a Mod

e of

failu

re: W

= st

aple

with

draw

al; S

= sh

ear i

n pl

ane

of O

SB; M

R =

mem

ber r

uptu

re; G

R =

gus

set-p

late

rupt

ure.

b Va

lues

in p

aren

thes

es a

re th

e co

effic

ient

of v

aria

tion

(%).

c Valu

es w

ith th

e sa

me

capi

tal l

ette

r are

not

stat

istic

ally

diff

eren

t at t

he 9

5% si

gnifi

canc

e le

vel.

1in

= 2

5.4

mm

; 1K

ip =

100

0 lbf =

4.4

48 k

N; 1

Kip

-in =

113

N-m

.

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Side rail to back post joint

Side rail to back post joint

100 lbf.100 lbf.

28 in.

72 in.

Side rail

Side rail

100 lbf.

Top rail Back post

Bac

k po

st

34 in. Front rail

Back rail

(a)

28 in.

72 in.

Side rail

Side rail

Top rail Back post

100 lbf.100 lbf. 100 lbf.

Back rail

Back rail to back post joint

Back rail to back post joint

Front rail

24 in.24 in.12 in. 12 in.Back

pos

t

(b)

Figure 4.9 Schematic of a three-seat sofa frame: a) side rail to back post joint; b) back rail to back post joint.

schedule (Table 4.6), it was assumed that three equidistant point loads shown in Figure

4.9(a) were applied horizontally at the top back rail connected to the top ends of two back

posts. The magnitude of these loads at each load step is shown in column 1 (Table 4.6).

These forces deliver loads acting on each of two back posts with the magnitude equal half

of the total load as is shown in column 2 (Table 4.6). Assuming that the height of the back

post in real sofa is 28-in (711-mm), the loads produce moment couples shown in column 3

(Table 4.6). To create the same moments during the tests with the arm of 21-in (533-mm),

the forces shown in column 4 (Table 4.6) were applied to the rail. Similarly, for the second

schedule (Table 4.7), three equidistant point loads applied vertically to the bottom back rail

were assumed as shown in Figure 4.9 (b) and column 1 (Table 4.7). Therefore, the end post

was subjected to a moment couple shown in column 2 (Table 4.7), under the load shown in

column 3 applied at the 20-in (508-mm) arm.

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Table 4.6 Cyclic stepped load schedule using GSA backrest frame testing schedule.

Backrest frame test

(moment arm = 28 in) Joint test (moment arm = 21 in)

Rail loads Reaction forces

Applied moments Loads

(lbf) (lbf) (Kip-in) (lbf)

Cumulative cycles

3 x 75 112.5 3.15 150 25,000 3 x 100 150 4.20 200 50,000 3 x 125 187.5 5.25 250 75,000 3 x 150 225 6.30 300 100,000

Extended test 3 x 175 262.5 7.35 350 125,000 3 x 200 300 8.40 400 150,000 3 x 225 337.5 9.45 450 175,000 3 x 250 375 10.50 500 200,000

1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.

Table 4.7 Cyclic stepped load schedule for testing using GSA seat load foundation testing schedule.

Joint test (moment arm = 20 in) Seat load foundation

test loads

Applied moments Loads

(lbf) (Kip-in) (lbf) Cumulative

cycles 3 x 100 3.00 150 25,000 3 x 200 6.00 300 50,000 3 x 300 9.00 450 75,000 3 x 400 12.00 600 100,000 3 x 500 15.00 750 125,000

1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.

The fatigue tests were conducted using pneumatic cylinders built-in a specially designed

supporting frame illustrated in Figure 4.10, which allowed testing nine specimens

simultaneously. In both backrest frame and seat load foundation tests, 25,000 load cycles

were applied at a rate of 20 cycles/min at each load level according to the schedules shown

in Tables 4.6 and 4.7, respectively (GSA 1998). After 25,000 cycles, the load was

increased to the next level and load cycling continued. Limit switches were installed on

each cylinder to stop the test of a specimen which suffered a major damage. When backrest

frame joint assemblies passed all levels in the main load schedule the tests continued on to

the extended load schedule shown in Table 4.6 until all the specimens failed. The highest

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119

load level sustained by a specimen for 25,000 cycles without failure was used to calculate

the “passed” moment. The number of cycles sustained by the specimen at the next load

level was included into the cumulative number of cycles and the load level at failure was

used to calculate the “failed” moment. Failure modes were determined for each specimen.

4.2.5 Results and Discussion Test results of backrest frame and seat foundation joints are summarized in Tables 4.4 and

4.5, respectively. Columns 8 to 10 show the average values and coefficients of variation of

the passed and failed moments and the cumulative number of cycles to failure. ANOVA

general linear model procedure was performed for different sizes of gusset-plates with or

without glue applications on the fatigue passed load, fatigue failed load, fatigue passed

moment, fatigue failed moment, and fatigue cumulative No. of cycles to failure. Tukey’s

multiple tests were also performed for the classification of the average fatigue cumulative

No. of cycles to failure (Column 10). The average values of passed and failed moments and

Figure 4.10 Setup for the fatigue test of gusset-plate connected joint assemblies.

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120

the corresponding average static moment capacities (column 7) were used to calculate,

respectively, the passed and failed static-to-fatigue moment capacity ratios shown in

columns 11 and 12. Higher static-to-fatigue ratios indicate a larger gap between the fatigue

moment capacity of the joint and its capacity determined in static tests; i.e., for a given

fatigue resistance the joint would be required a higher static strength. The last column in

Tables 4.4 and 4.5 lists all observed failure modes and their relative frequency within the

group.

As was expected from the static tests, the glued-stapled joints (Table 4.4) showed

significantly higher failure loads and fatigue life in comparison with the unglued stapled

joints. Unglued stapled joints with 6-in (152-mm) and 8-in (203-mm) gusset-plates

demonstrated no significant difference of fatigue failure loads. Therefore, the static-to-

fatigue ratio of the joints with 6-in (152-mm) gusset-plates appeared to be lower

considering their lower static strength. The stapled joints with 10-in (254-mm) gusset-

plates demonstrated statistically higher fatigue resistance and, accordingly, higher fatigue

life; however, their static-to-fatigue ratios were similar to those with 8-in (203-mm) gusset-

plates. Analysis of the failure modes suggests contribution of OSB panel failures generally

associated with the lower static-to-fatigue ratios, while the higher ratios were associated

with withdrawal of staples.

Similar correlations were found for the glued-stapled joints. The joints with 6-in. gusset-

plates with statistically lower fatigue capacity and fatigue life demonstrated lower static-to-

fatigue capacity ratios; whereas the joints with larger gusset-plates (8 and 10-in) (203 and

254-mm) showed no significant difference of fatigue performance with higher static-to-

fatigue ratios for the 10-in (254-mm) plates. Analysis of failure modes shows that

approximately half of the glued joints with 6-in (152-mm) and 8-in (203-mm) gusset-plates

failed from in-plane shear, while all glued joints with 10-in (254-mm) plates failed in

rupture of one of the joint members, indicating that in the latter case the strength of the

glued area exceeded the strength of the joint members.

It can be noted in Table 4.5 that due to larger load increments in the seat load foundation

test schedule, there were fewer differences observed between pass-fail loads of joints with

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121

different gusset-plates, i.e., the load schedule was less sensitive to the differences in the

joint configurations. Therefore, in spite of a slightly longer fatigue life, the static-to-fatigue

ratios of the joints with larger gusset-plates turned out to be higher for both unglued and

glued joint assemblies because of their higher static resistance.

Static to fatigue moment capacity ratio

The ratio of the static to failed fatigue moment varied from 1.34 to 1.89 for stapled joints

and from 1.43 to 1.78 for the glued-stapled joints. The corresponding ratio for the passed

fatigue moment varied from 1.78 to 2.42 and from 1.65 to 2.24 for the stapled and glued-

stapled joints, respectively, with the lower values obtained for the joints with smaller

gusset-plates. The average ratio of static moment to fatigue failed moment for 12 tested

groups subjected to two different schedules was 1.60 with a coefficient of variation (COV)

of 10 percent. In other words, the average OSB gusset-plate joint failed under a load level

of 63 percent of its static moment capacity after being subjected to a series of cyclic

stepped loads. Respectively, the average ratio of static to fatigue passed moment was 2.06

with a COV of 12 percent.

Previously, the average static to fatigue passed moment capacity ratio of 2.2 with a COV of

13 percent was reported for two-pin dowel joints (Zhang et al. 2003) and 2.5 with a COV

of 11 percent for metal-plate connected joints in furniture grade pine plywood (Zhang et al.

2006). Comparison with these studies shows that the average ratio of static to fatigue

moment capacity of upholstered furniture frame joints varies from one fastening system to

another. Based on this information, it is suggested that to pass the fatigue test, an average

ratio of 2.2 for wooden dowels, 2.5 for the metal-plate connectors, and 2.1 for OSB gusset-

plates could be used for upholstered furniture design.

4.2.6 Conclusions Cyclic load fatigue tests on stapled and glued-stapled OSB joints with gusset-plates of

three different sizes were performed and compared with their static moment resistance to

determine the influence of the gusset-plate size, material and fastening system on the static-

to-fatigue moment capacity ratio and on failure modes of the joints. Results showed that

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122

despite differences in failure modes, both stapled and glued-stapled joints had similar

static-to-fatigue moment capacity ratios. In the stapled joints, the higher ratios were

associated with the staple withdrawal as the dominating failure mode. In the glued-stapled

joints lower ratios were associated with in-plane shear, and the higher ratios – with the

rupture of the OSB panels. Statistical analysis and comparison with previous studies

showed that the average value of 2.1 can be used as the passing static-to-fatigue ratio for

design of upholstered furniture frames with OSB gusset-plate joints. In other words, it is

advised to design gusset-plate joints so that they will not be loaded to more than 48 percent

of their static moment capacity.

4.2.7 Practicality Information obtained in this study of joint assemblies subjected to cyclic stepped loads

provides designers with technical data assisting in rational and optimum designs of

upholstered furniture frames to meet certain desired performance requirements.

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Chapter 5 Metal-plate connected joints

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124

5.1 Static bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames

5.1.1 Résumé Des connecteurs de plaque métallique sont généralement utilisés pour relier les joints

critiques dans les structures des meubles rembourrés à cause de leur résistance mécanique

élevée, leur assemblage rapide et le raccordement facile des membres d’épaisseur

uniforme. Pour faciliter l’introduction de panneaux à lamelles orientés (OSB) dans les

structures de meubles rembourrés, des données de base pour les connecteurs métalliques

construits avec de l’OSB sont nécessaires. Dans cette étude, la résistance statique en

flexion de joints en forme de T avec des plaques métalliques a été déterminée

expérimentalement pour différentes configurations. La résistance des joints avec une paire

de plaques métalliques a augmenté proportionnellement avec la largeur de la plaque

métallique et cela jusqu'à 6-po (152-mm). Lorsque les plaques métalliques étaient égales à

la largeur de la pièce d'OSB, la quantité et la concentration de dents ont affaibli

l’assemblage. Les joints avec deux paires de plaques métalliques étaient environ 50% plus

forts que ceux avec une seule paire pour une même couverture. Les mêmes observations

ont été trouvées pour la rigidité.

5.1.2 Abstract Metal-plate connectors are commonly used to connect critical joints in upholstered

furniture frames due to their high load resistance, rapid assembly, and easy connection of

members with uniform thickness. To successfully introduce oriented strand board (OSB)

into furniture frames, basic data for metal-plate connected joints constructed of OSB is

needed. In this study, the static moment capacity of T-shaped joints with metal-plates was

determined experimentally for different configurations. The moment capacity of the joint

with one pair of metal-plates increased in proportion with the width of the metal-plate up to

6-in (152-mm). When the metal-plate was equal the full width of the OSB member, too

many teeth cut into it, making the assembly weaker. Metal-plated joints with two pairs of

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125

plates were about 50% stronger than those with a single pair of metal-plates covering the

same area. The same trends were found for the stiffness of metal-plated joints.

5.1.3 Introduction Metal plate connectors (MPC), commonly called “truss plates”, are widely used for joining

wood members, and especially in trussed rafters and joists. Introduced by A. Carroll

Sanford in 1952, MPC changed the wood construction industry. Prefabricated wooden roof

and floor trusses, most of which use MPC, are used in 80% of light commercial and

residential construction in the United States and Canada. The MPC are typically fabricated

from rolled metal sheets of 20, 18 or 16-gauge steel. The sheet metal is cut into a variety of

sizes. The size of MPC depends on the geometry of the joint intended to be held in

equilibrium. Requiring little time for joint fabrication and enhancing the strength and

stiffness of trusses of almost any shape, MPC reduces fabrication cost and time, and

develops a degree of efficiency and architectural flexibility which was not possible before.

The furniture industry is a relatively new area for the MPC. Although originally designed

for use in construction applications, MPC has gained popularity as a connector for critical

joints such as front post-front rail and side rail-back post joint in upholstered furniture

frame construction (Zhang et al. 2005). As a connector in upholstered furniture, MPC

provides high load resistance, rapid joint assembly and easy connection of members with

uniform thickness.

The furniture industry continues to use more and more wood-based panels, but limited

information is available on the moment capacities of metal-plate connected joints

constructed of wood composites. The moment capacities of metal-plated and gusset-plated

joints constructed of plywood and OSB have been addressed by a few researchers. Tables

5.1 and 5.2 show the moment capacities of metal-plated and gusset-plated joints for

plywood and OSB found in the literature. Eckelman (1980) studied the performance of T-

shaped, end to side-grain joints constructed of red oak, yellow-poplar, soft maple, and

Douglas-fir with 18- and 20-gage metal plates of various shapes. Zhang et al. (2005, 2006)

expanded Eckelman’s research by using furniture grade 3/4-in (19-mm) thick 7-ply

southern yellow pine plywood as material. They reported that metal-plate and rail widths

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126

affected the moment capacity of MPC plywood joints significantly. Generally, there is very

little research on connections in OSB furniture frames. Wang et al. (2007b, 2007c)

evaluated the feasibility of using OSB as a material for gusset-plated joints in upholstered

furniture. The results showed that the moment capacity of the joint increased in proportion

to the length of the gusset-plate until the strength of the gusset exceeded that of the main

member; application of glue changed the failure modes of the joints and increased their

strength significantly. The performance of OSB as a frame member in a T-shaped metal-

plated joint has not been studied before.

The primary objective of this research was to develop basic data on the static bending

resistance of T-shaped, metal-plate connected joints constructed of OSB. The specific

objectives were 1) to understand how metal-plate width, number and configurations affect

moment resistance of T-shaped joints; 2) to determine the stiffness of metal-plate joints

constructed of OSB; 3) to understand the behavior of the joints through their failure modes;

and 4) to determine an optimum configuration for the bending capacity of metal-plated

joints. The data will be further used for fatigue testing of the joints and for optimization of

upholstered furniture frame designs.

Table 5.1 Moment capacities of metal-plated joints constructed of plywood available in literature (Zhang et al. 2005).

Rail width Metal-plate length Metal-plate width Moment capacity b Panel

(in) (in) (in) (kip-in)

1.6 6.12 (11) 2.4 7.53 (7) 4.5 3.2 9.83 (8) 1.6 5.98 (9) 2.4 7.73 (5)

Plywooda

6.0

6.0 3.2 9.57 (6)

a Furniture grade 3/4-in (19-mm) thick seven-ply southern yellow pine plywood. b Mean value (COV%) 1in = 25.4 mm; 1kip-in = 113 N-m.

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127

Table 5.2 Moment capacities of gusset-plate joints constructed of OSB available in literature (Wang et al. 2007b).

Rail width

Gusset-plate width

Gusset-plate

length

Staple length

Number of

staples

Mean ultimate

load COV Moment

capacityJoint configuration Panel

(in) (in) (in) (in) (in) (kip) (%) (kip-in) a 4.0 1.5 20 0.67 Ab 4.8 9.38 b 6.0 1.5 20 0.85 B 7.6 11.9 f 10.0 1.0 32 0.87 B 7.8 12.2

Unglued

g 10.0 1.0 32 0.87 B 7.0 12.2 4.0 1.0 8 0.68 A 7.0 9.52 Glued

OSB a 6.0 6.0

6.0 1.0 8 0.92 B 6.9 12.9 a 23/32-in (18-mm) thick OSB produced by Norbord (Canada). b Values with the same letter are not statistically different at the 95% significance level. 1in = 25.4 mm; 1kip = 1000 lbf = 4.448 kN; 1kip-in = 113 N-m.

5.1.4 Materials and Methods The T-shaped, end-to-side, metal-plate joint specimens were comprised of two principal

members, a post and a rail, joined by one or two pairs of metal-plates symmetrically

attached on both sides of the joint, i.e., an equal number of teeth were pressed into both the

rail and post, as shown in Figure 5.1. For the configurations with two pairs of metal-plates

on each side (series G1 and G3), a distance of 0.5-in (12.7-mm) was left between edges of

the rails and that of the plates. The two structural members were positioned in such a way

that the long side center of the post was perfectly aligned with the short side center of the

rail. The joints were constructed of OSB conforming to CSA 0325 (CSA 2003) produced

by Norbord (Canada). The OSB members were 23/32-in (18-mm) thick, 6-in (152-mm)

wide, 16-in (406-mm) long; and the metal-plates were 2x6-in (51x152-mm) or 4x6-in

(102x152-mm), SK-20 manufactured and provided by Jager Building Systems Inc. For

configurations involving metal-plates of 1.0-in or 3.0-in (25-mm or 76-mm) wide, the

metal-plates were cut from either the 2x6-in (51x152-mm) or 4x6-in (102x152-mm) plates.

Care was taken during cutting to ensure symmetric plates with the same number of teeth

were produced.

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128

Figure 5.1 An example of metal-plated joint with two LVDTs’ points A and B.

To prepare the OSB components, 4 by 8-ft (1.22 by 2.44-m) OSB panels were cut into 6-in

(152-mm) strips along the 8-ft (2.44-m) direction, then crosscut into 16-in (406-mm) long

blanks and randomized. The metal-plates were installed with a hydraulic press, using a

pressure of 70 psi (483 kPa). To ensure rail end and post side tight contact, two staples

were used to pre-align the joint. To hold metal-plates and members in alignment, the two

opposite corners of each metal-plate were hammered into the two members. Metal-plates

were pressed one at a time to full uniform contact between plate and OSB. Six series of

tests were conducted with metal-plates. The configuration of the T-shaped, end-to-side

MPC joint specimens for this study are shown in Figure 5.2. Density, moisture content,

internal bond strength and flat and edgewise bending properties of the OSB were

determined before testing the assemblies. The mechanical properties were evaluated in

accordance with ASTM D1037 (ASTM 2005a).

In order to conform to durability performance test standards such as GSA test regimen

FNAE-80-214A (GSA 1998), design strength of upholstered furniture frames requires

information about the performance of each joint in a typical sofa frame. According to the

GSA, the bending moment acting on the back rail to back post joint is considered very

high. For a 72-in (1.83-m) long three-seat sofa of light-duty category, three concentrated

A

B

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129

vertical loads of 200 lbf (890 N) are applied to the back-rail with a total of 600 lbf (2669

N) (Table 5.3). If the back-rail has two rigid joints with back posts, each joint carries a

bending moment of 200×72/8+200×12×(72-12)/72=3800 lbf-in (429.4 N-m) in fatigue test.

To estimate the static load capacity, the load is doubled resulting in a static moment

capacity of 7600 lbf-in (858.8 N-m) With a 14-in (356-mm) long arm used in the tests, the

target static load on the joint is approximately 7600/14 = 543 lbf (2415 N).

All specimens were tested using a Tinius-Olsen universal testing machine. The post of the

joint was bolted to the test fixture with 0.67-in (17-mm) aluminium spacers so that the

metal-plates could deform freely during the test. Vertical upward load was applied to the

rail at a rate of 0.2 in/min (5 mm/min) (Zhang et al. 2005), and the load at failure was

recorded using a load cell with accuracy of 0.2%. As can be seen in Figure 5.1, joint

slippages at top and bottom between two points (A and B) were measured using two linear

variable differential transducers (LVDTs).

Calculation of the rotational stiffness of the joint

As shown in Figure 5.3, the two points of LVDTs were originally located at A and B at a

distance of 8.78 in (223 mm) from each other, which remained constant. During the test,

the LVDT at point A contracted the distance AA’ = a; the LVDT at point B retracted the

distance CB’ = b. Therefore, angle of rotation, α, of the arm can be expressed from:

xb

xatg

−==

223α (5.1)

It can be derived as a function of displacements a and b as follows:

223batg +=α (5.2)

Moment-rotation curves (as shown in Figure 5.4) were used to calculate the rotational

stiffness of the joints as a slope between 10-lbf (44.5-N) and 40% of ultimate load

(Gebremedhin et al. 1992).

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Configuration G1: Configuration G2:

1 in

1 in

3 in16 in

6 in 16 in

6 in

2 in16 in

6 in 16 in

6 in

(a) (b) Configuration G3: Configuration G4:

2 in

2 in

1 in16 in

6 in 16 in

6 in

3 in16 in

6 in 16 in

6 in

(c) (d) Configuration G5: Configuration G6:

4 in16 in

6 in 16 in

6 in

6 in16 in

6 in 16 in

6 in

(e) (f)

* 1 in = 25.4 mm

Figure 5.2 Configurations of metal-plated joints.

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Table 5.3 Acceptance performance level of upholstered furniture in accordance with GSA (1998).

Test Initial Loads

Load Increments

Number of

Loads

Light-service

Acceptance Level

Medium-service

Acceptance Level

Heavy-service

Acceptance Level

(lbf) (lbf) (lbf) (lbf) (lbf) Cyclic Vertical Load Test on -- Front Rail 100 100

3

300

400 600

-- Back Rail 100 100

3

200

300 500 1.000 lbf = 4.448 N

Figure 5.3 Measurement of the angle of rotation, α.

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0

1

2

3

4

5

6

7

8

9

10

0 0.005 0.01 0.015 0.02 0.025 0.03

Angle of rotation (rad.)

Mom

ent (

Kip

-in.)

G1-1G1-2G1-3G1-4G1-5G1-7G1-8G1-9G1-10

Figure 5.4 Typical moment-rotation curves of metal-plated joints.

5.1.5 Results and Discussion Physical and mechanical properties of OSB

Table 5.4 shows the physical and mechanical properties of OSB panels used in the tested

specimens.

Failure Modes

In tested assemblies, five types of failure modes were observed (Figure 5.5 and Table 5.5):

metal-plate yield in tension, metal-plate tooth pull-out, OSB crushing on the top corner of

rail member, in-plane shear of OSB, and OSB member rupture. In the test assemblies with

two pairs of metal-plates (G1-2 by 1x6-in (25x152-mm) and G3-2 by 2x6-in (51x152-

mm)), mixed failure modes were observed. However, metal-plate yielding in tension

(Figure 5.5a) was the dominant failure mode in narrower metal-plates (G1-2 by 1x6-in

(25x152-mm), G2-1 by 2x6-in (51x152-mm), and G4-1 by 3x6-in (76x152-mm)). Metal-

plate tooth pull-out (Figure 5.5b) was most often observed in the joints with wider metal-

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plates (G5-1 by 4x6-in (102x152-mm), and G3-2 by 2x6-in (51x152-mm)). In test

assemblies with the widest metal-plate (G6-1 by 6x6-in (152x152-mm)), OSB member

rupture on the tension side (Figure 5.5e) was evident, since too many teeth cut into the

OSB, weakening the member. The discussion of bending strength presented below

confirms this conclusion.

Table 5.4 Physical & mechanical properties of OSB.

Property Mean (COV%) Modulus of elasticity flatwise MOE, GPa 6.33 (8.2) Modulus of elasticity edgewise MOE, GPa 4.74 (5.4) Modulus of rupture flatwise MOR, MPa 32.2 (12.1) Modulus of rupture edgewise MOR, MPa 22.4 (11.7) Density, kg/m3 594 (6.8) Moisture content, % 6.8 (7.7) Internal bond, MPa 0.426 (18.2)

Table 5.5 Ultimate load capacity and failure modes of metal-plated joints constructed of OSB.

Metal-plate size

Pair of metal-plates

Number of

specimens

Mean ultimate

load COV Moment

capacity Mode of failure a Joint configuration

(in) (lbf) (%) (kip-in)

G1 1x6 2 10 575 Cb 7.7 8.05 50% PY,

20% PY+TP, 10% TP, 20% CR

G2 2x6 1 10 384 D 9.1 5.38 100% PY

G3 2x6 2 10 798 A 8.3 11.2 50% TP,

30% TP+S, 10% CR, 10% MR

G4 3x6 1 10 542 C 6.0 7.59 90% PY, 10% TP G5 4x6 1 10 697 B 5.8 9.76 100% TP G6 6x6 1 10 780 A 9.3 10.9 90% MR, 10% TP

a PY = Metal-plate yield in tension; TP = Metal-plate tooth pull-out; CR = OSB crushed on the top corner of rail member; S =In-plane shear of OSB; MR = OSB member rupture. b Values with the same letter are not statistically different at the 95% significance level. 1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.

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(a) Metal-plate yield in tension (b) Metal-plate tooth pull-out

(c) OSB crushed on the top of rail (d) Shear in plane of OSB

(e) OSB member rupture

Figure 5.5 Typical failure modes of metal-plated joints.

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Load and moment capacity

Mean values and coefficients of variation (COV) of ultimate load capacity of OSB metal-

plated assemblies are summarized in Table 5.5. Statistical comparisons of results were

performed using an ANOVA general linear model and Tukey’s multiple comparison tests.

In joints with one pair of metal-plates, an increase of metal-plate width from 2 to 3-in (51

to 76-mm), 3 to 4-in (76 to 102-mm), and 4 to 6-in (102 to 152-mm) significantly increased

the mean ultimate load by 41%, 29% and 12%, respectively. In assemblies with two pairs

of metal-plate joints, significant differences were found. The mean ultimate load of two

pairs of 2 by 6-in (51 by 152-mm) metal-plates (G3) was 39% higher than assemblies with

two pairs of 1 by 6-in (25 by 152-mm) metal-plates (G1). Assemblies made with two pairs

of 1 by 6-in (25 by 152-mm) (G1) were, on average, 50% stronger than those made with

one pair of 2 by 6-in (51 by 152-mm) (G2) and 6% stronger than those with one pair of 3

by 6-in (76 by 152-mm) (G4) metal-plates. The mean ultimate load of assemblies with two

pairs of 2 by 6-in (51 by 152-mm) (G3) was 14% higher than that of assemblies with one

pair of 4 by 6-in (102 to 152-mm) (G5) and no significant difference than that of

assemblies with one pair of 6 by 6-in (152 by 152-mm) plates (G6). This again can be

explained by the fact that there were too many teeth cutting into the OSB members which

made it weaker. The assembly with two pairs of 2 by 6-in (51 by 152-mm) (G3) metal-

plates had the highest bending strength of all configurations as can be seen in Table 5.5 and

Figure 5.6. Therefore, it can be concluded that for this particular joint geometry and size,

the two pairs of 2 by 6-in (51 by 152-mm) (G3) metal-plates were the optimum design.

Comparisons were made for the moment capacities of tested assemblies (Table 5.5) with

the previously published data (Wang et al. 2007b) on plywood assemblies with metal-

plates and OSB with gusset-plates (Tables 5.1 and 5.2). The moment capacity (5.38 kip-in

(608 N-m)) of the OSB joint with one pair of 2 by 6-in (51 by 152-mm) (G2) plates was

lower than that of the plywood joint with one pair of 1.6 by 6-in (41 by 152-mm) plates

(5.98 kip-in (676 N-m)) from Table 5.1. The moment capacity (7.59 kip-in (858 N-m)) of

the OSB joint with one pair of 3 by 6-in (76 by 152-mm) (G4) plates was also lower than

that of a plywood joint with one pair of 2.4 by 6-in (61 by 152-mm) plates (7.73 kip-in

(873 N-m)) from Table 5.1. In OSB assemblies with two pairs of 1 by 6-in (25 by 152-mm)

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0

100

200

300

400

500

600

700

800

900

G2 G4 G5 G6 G1 G3

Metal-plate configuration

Mea

n ul

timat

e lo

ad (l

bf.)

Figure 5.6 Experimental mean ultimate loads of metal-plated joints.

(G1) plates, the moment capacity (8.05 kip-in (910 N-m)) was somewhat higher than that

of the plywood joint with one pair of 2.4 by 6-in (61 by 152-mm) plates (7.73 kip-in (873

N-m)) from Table 5.1. However, the moment capacity of the OSB joints with two pairs of

2 by 6-in (51 by 152-mm) (G3) metal plates (11.2 kip-in (1,266 N-m)) was quite similar to

those with one pair of 6 by 6-in (152 by 152-mm) stapled gusset-plate unglued joint of

OSB (11.9 kip-in (1,345 N-m)) from Table 5.2, and higher than one pair of 4 by 6-in (102

to 152-mm) gusset-plate in both glued and unglued joints (9.52 and 9.38 kip-in (1,076 and

1,060 N-m), respectively).

Rotational stiffness of metal-plate joints

Moment-rotation curves in Figure 5.4 demonstrate a nonlinear relationship, but the lower

half portion of the curves can reasonably be characterized as linear. Therefore, in this

study, the slope of the curve between 10-lbf (44.5-N) to 40% of ultimate load was used to

calculate the rotational stiffness of joints. Generally, the stiffness value of the joints with

one pair of metal-plates was much lower than that of the joints with two pairs of metal-

plates, as shown in Figure 5.7. Assemblies with two pairs of 1 by 6-in (25 by 152-mm)

(G1) metal-plates were even stiffer than those with one pair of 6 by 6-in (152 by 152-mm)

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(G6) metal-plates. Among the joints with one pair of metal plates, the 1 by 4x6-in

(102x152-mm) (G5) was much stiffer than 1 by 3x6-in (76x152-mm) (G4), as shown in

Table 5.6 and Figure 5.7.

Table 5.6 Stiffness of six configurations of metal-plate joints.

Metal-plate size Rotational stiffness COV Joint

configuration (in)

Number of metal-plates (kip-in/rad) (%)

G1 1x6 2 1677 A a 29

G2 2x6 1 252 D 31

G3 2x6 2 1852 A 35

G4 3x6 1 558 C 34

G5 4x6 1 1295 B 10

G6 6x6 1 1391 B 8 a Values with the same letter are not statistically different at the 95% significance level. 1in = 25.4 mm; 1kip-in = 113 N-m.

0

400

800

1200

1600

2000

G2 G4 G5 G6 G1 G3

Metal-plate configurations

Stiff

ness

(Kip

-in./r

ad)

Figure 5.7 Rotational stiffness of metal-plated joints.

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5.1.6 Conclusion The effect of metal-plate width and number of metal-plates on the static bending resistance

of T-shaped OSB metal-plated joints was investigated. For the same width of metal-plates,

the use of two pairs of metal-plates was the most critical factor affecting the performance

of the joints, allowing for strength increase up to 50% in comparison with one pair of

metal-plates. An increase in the width of metal-plates from 2 to 4-in (51 to 102-mm)

boosted the mean ultimate load considerably for both one and two pairs of metal-plated

joints. In assemblies with one pair of 6 by 6-in (152 by 152-mm) metal-plates, the mean

ultimate load was slightly lower than that of assemblies with two pairs of 2 by 6-in (51 by

152-mm) This can be explained by the weakening of the OSB section due to the large

number of teeth cutting through the member. The stiffness values for the joints with one

pair of metal-plates were lower than those for joints with two pairs of metal-plates. The

failure modes observed depended on the size and configuration of the metal-plates. Among

the tested configurations, the joint with two pairs of 2 by 6-in (51 by 152-mm) plates was

the strongest and showed the highest stiffness.

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5.2 Fatigue bending resistance of metal-plate connected joints constructed of oriented strandboard for upholstered furniture frames

5.2.1 Résumé Cette étude a permis d’évaluer la performance à la fatigue de joints en forme de T en

panneaux à lamelles orientés (OSB) connectés avec deux plaques métalliques. Cette étude

a permis d’obtenir les ratios de résistance en flexion statique versus fatigue. Au total, 80

joints avec des plaques en métal de différentes configurations ont été soumis à des charges

échelonnées de flexion cyclique sur un seul côté. Les résultats d'essai ont prouvé que ces

assemblages atteignent la rupture après moins de 25.000 cycles lorsqu’un niveau de

chargement échelonné excède 63 pour cent de leur résistance statique de flexion. Les ratios

de dépassement de statique versus fatigue étaient en moyenne de 2,5 avec un coefficient de

variation de 22 pour cent. Dans tous les joints de plaques métallique, le mode de rupture

dominant était la rupture de la plaque métallique, le reste était du cisaillement en

arrachement de l’OSB.

5.2.2 Abstract This study evaluated the fatigue performance of T-shaped, end-to-side, metal-plate

connected joints made of oriented strandboard (OSB) to obtain the static-to-fatigue

moment capacity ratios. A total of 80 joints with metal plates of different configurations

were subjected to one-side cyclic stepped bending loads. Test results showed that

assemblies with OSB metal-plates would fail within 25,000 cycles when a stepped load

level exceeded 63 percent of their static moment capacity. The passing static-to-fatigue

ratios averaged 2.5 with a coefficient of variation of 22 percent. In all metal-plated joints,

the dominating failure mode was metal-plate yield; the rest was shear-out of OSB.

5.2.3 Introduction Upholstered furniture generally refers to seating furniture, such as sofas, chairs, and stools,

which are padded for comfort and covered with fabric or leather. The framework of

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upholstered furniture is usually made of wood or wood based products. The growth of the

industry is influenced by the rate of new home construction and the number of existing

homes being remodelled.

High quality products, made possible by the availability of technical information on the

materials and joints connecting the various components, are important to the upholstered

furniture industry. Such information will help the industry to develop and produce well-

designed and durable furniture. Wood and wood based products are used widely in

furniture production and are rapidly gaining popularity. Oriented strand board (OSB) is one

of these wood based panels which has experienced high growth and is expected to continue

on this trend. For OSB to access the upholstered furniture market, technical data on the

performance of connections made with OSB must be provided to ensure that it is well-

designed and well-suited for such applications.

The behaviour of joints under load is a function of the fasteners and materials that are used

to construct the joints. Different types of connections are used to make joints in the

upholstered furniture. A connector or a fastener is a mechanical device (e.g., staple, screw,

nail, bolt, etc.) or a mechanical assembly (e.g., shear plate, nailed or toothed metal plate,

etc.), or an adhesive used to hold together two or more pieces of wood or wood based

products.

Metal-plate connectors (MPC) are made of sheet steel with punched teeth. The teeth are

integral metal projections of the plate formed perpendicular to the plate during the

stamping process. When pressed into the fibre of wood, these teeth can transmit lateral

loads.

In engineering, the term fatigue is defined as the progressive damage that occurs in

materials subjected to cyclic loading (USDA 1999) and it has been much less studied in the

past than the static loading. In daily use, upholstered furniture is exposed to repeated loads,

which may cause fatigue failure. The response of the furniture or more specifically of the

joints to repeated loads determines the quality of the joints and subsequently of the

furniture. In order to support the use of OSB in the furniture, relevant technical information

is needed. This paper is focused on the fatigue performance of joints made with OSB

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framing members and metal-plates, and it is one of a series of publications dealing with

introduction of OSB in upholstered furniture frames (Wang et al. 2007a, 2007b, 2007c, and

2007d).

Multi-cycle fatigue tests are expensive as they require specialized equipment and

considerable testing time in comparison with static tests. Therefore, it would be useful to

correlate static and fatigue performance to characterize various types of joints. Several

previous studies have focused on correlating the static and fatigue moment resistance of

wood joints with various fasteners. Zhang et al. (2003) investigated the fatigue life of T-

shaped, end-to-side assemblies using two-pin dowel joints by subjecting them to one-sided

constant and stepped cyclic bending loading. A mathematical representation was developed

to correlate the applied moment to the number of cycles to failure. Zhang et al. (2006)

studied the bending fatigue life of metal-plate-connected joints in furniture grade pine

plywood subjected to one-sided cyclic stepped bending loads. They reported that there was

a strong relationship between static moment capacity and the load level causing failure in a

fatigue test. The passing fatigue moment level achieved just prior to failure was 46% of the

static moment capacity. Wang et al. (2007c) evaluated the moment capacity of OSB

gusset-plate joints for upholstered furniture under fatigue load. Test results showed that

assemblies with OSB gusset-plates would fail within 25,000 cycles when a stepped load

level exceeded 63 percent of their static moment capacity. The passing static-to-fatigue

capacity ratio averaged 2.1 with a coefficient of variation of 12 percent.

The literature review has shown that no technical information is available on the fatigue

performance of metal-plate connected joints constructed of OSB. The main objective of

this study was to evaluate the fatigue resistance of OSB metal-plate connected joints and

determine the ratio of the static to their fatigue moment capacities for design purposes. The

second objective was to gather the information on the failure modes of such assemblies

under stepped fatigue loads.

5.2.4 Materials and Methods Each test specimen consisted of a post and a rail made of structural 23/32-in (18-mm) OSB

joined with one pair or two pairs of metal-plates symmetrically attached on both sides of

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the joint. Basic material properties, fabrication procedures, and configuration details of the

joints tested statically are reported in a previous paper by the authors (Wang et al. 2007d).

For fatigue tests, the panel materials from the same batch were used and joints of the same

configurations were constructed using the same procedures with the exception of the length

of the rail. The rail length was increased from 16 in (406 mm) to 23 in (584 mm) to

accommodate the load capacity of the pneumatic cylinders used in the test setup. The

metal-plated series used in fatigue tests were G1, G5, G3 and G4. Series G2 and G6 were

not tested in fatigue because static tests showed that G2 and G6 metal-plates were not

efficient (Wang et al. 2007d). The configuration of the T-shaped, end-to-side MPC joint

specimens for this study are shown in Figure 5.8. Table 5.7 provides the information on the

tested configurations and the number of replicates.

Joints were subjected to two loading schedules from GSA test regimen FNAE-80-214A

(GSA 1998), representing 1) the backrest frame, and 2) seat load foundation test for a 72-in

(1.83-m) long three-seat sofa frame without middle upright on the back (Figure 5.9). To

determine the loads for the first schedule (Table 5.8), it was assumed that three equidistant

point loads shown in Figure 5.9(a) were applied horizontally at the top back rail connected

to the top ends of two back posts. The magnitude of these loads at each load step is shown

in column 1 of Table 5.8. These forces deliver loads acting on each of the two back posts

with a magnitude equal to one half of the total load as is shown in column 2 of Table 5.8.

Assuming that the height of the back post in a real sofa is 28-in (711-mm), the loads

produce moment couples shown in column 3 of Table 5.8. To produce the same moment

magnitude during the tests with a moment arm of 21-in (533-mm), test loads were

calculated and applied to the rail (as given in column 4 of Table 5.8). Similarly, for the

second schedule (Table 5.9), three equidistant point loads applied vertically to the bottom

back rail were assumed as shown in Figure 5.9(b) and column 1 of Table 5.9. Therefore,

the end post was subjected to a moment couple shown in column 2 of Table 5.9, which

produced a test load values as given in column 3 of Table 5.9 applied at a 20-in (508-mm)

arm.

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Configuration G1:

1 in

1 in

3 in16 in

6 in 16 in

6 in

(a) Configuration G3: Configuration G4:

2 in

2 in

1 in16 in

6 in 16 in

6 in

3 in16 in

6 in 16 in

6 in

(b) (c) Configuration G5:

4 in16 in

6 in 16 in

6 in

(d)

* 1in = 25.4 mm

Figure 5.8 Configurations of metal-plated joints for fatigue tests.

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Table 5.7 Test specimen configurations.

Metal-plate dimensions Pair of metal-plates Number of replicates (in)

G1 1x6 2 10 G5 4x6 1 10 G3 2x6 2 10 G4 3x6 1 10

Note: 1 in = 25.4 mm

Side rail to back post joint

Side rail to back post joint

100 lbf.100 lbf.

28 in.

72 in.

Side rail

Side rail

100 lbf.

Top rail Back post

Bac

k po

st

34 in. Front rail

Back rail

(a)

28 in.

72 in.

Side rail

Side rail

Top rail Back post

100 lbf.100 lbf. 100 lbf.

Back rail

Back rail to back post joint

Back rail to back post joint

Front rail

24 in.24 in.12 in. 12 in.Bac

k po

st

(b)

Figure 5.9 Schematic of a three-seat sofa frame. a) side rail to back post joint; b) back rail to back post joint.

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Table 5.8 Cyclic stepped load levels using GSA backrest frame testing schedule.

Backrest frame test

(moment arm = 28 in) Joint test (moment arm = 21 in)

Rail loads Reaction forces

Applied moments Test loads

(lbf) (lbf) (kip-in) (lbf)

Cumulative No. of cycles

3 x 75 113 3.15 150 25,000 3 x 100 150 4.20 200 50,000 3 x 125 188 5.25 250 75,000 3 x 150 225 6.30 300 100,000

Extended test 3 x 175 263 7.35 350 125,000 3 x 200 300 8.40 400 150,000 3 x 225 338 9.45 450 175,000 3 x 250 375 10.5 500 200,000

Note: 1in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.

The fatigue tests were conducted using specially designed testing bench made of pneumatic

cylinders attached to a supporting frame as illustrated in Figure 5.10, which allowed testing

of ten specimens simultaneously. In both backrest frame and seat load foundation tests,

25,000 load cycles were applied at a rate of 20 cycles/min at each load level according to

the schedules shown in Tables 5.8 and 5.9, respectively. After 25,000 cycles, the load was

increased to the next level and load cycling continued. Limit switches were installed on

each cylinder to stop testing of individual specimens which suffered major damage. When

backrest frame joints passed all levels in the main load schedule the tests continued on to

the extended load schedule shown in Table 5.8 until all the specimens failed. The highest

load level sustained by a specimen after 25,000 load cycles without failure was used to

calculate the “passed” moment. The number of cycles sustained by the specimen at the

next load level was included into the cumulative number of cycles and the load level at

failure was used to calculate the “failed” moment. Failure modes were determined for each

specimen.

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Table 5.9 Cyclic stepped load levels using GSA seat load foundation testing schedule.

Joint test (moment arm = 20 in) Seat load foundation test

loads Applied moments

Test loads (lbf) (kip-in) (lbf)

Cumulative No. of cycles

3 x 100 3.00 150 25,000 3 x 200 6.00 300 50,000 3 x 300 9.00 450 75,000 3 x 400 12.0 600 100,000 3 x 500 15.0 750 125,000

Note: 1 in = 25.4 mm; 1lbf = 4.448 N; 1kip-in = 113 N-m.

Figure 5.10 Setup for fatigue test of metal-plate connected joints.

5.2.5 Results and Discussion Test results of backrest frame and seat foundation joints are summarized in Tables 5.10 and

5.11. Columns 4 to 6 of both tables show the average values and coefficients of variation of

the passed and failed moments and the cumulative number of cycles to failure. ANOVA

general linear model procedure was performed for different configurations of metal-plates

on the fatigue passed load, fatigue failed load, fatigue passed moment, fatigue failed

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moment, and fatigue cumulative number of cycles to failure. Tukey’s multiple tests were

also performed for the classification of the average fatigue cumulative number of cycles to

failure (Column 6). The average values of passed and failed moments and the

corresponding average static moment capacities (column 3) were used to calculate,

respectively, the passed and failed static-to-fatigue moment capacity ratios shown in

columns 7 and 8. Higher static-to-fatigue ratios indicate a larger gap between the fatigue

moment capacity of the joint and its capacity determined in static tests. The last column in

Tables 5.10 and 5.11 lists the observed failure modes and their relative frequency of

occurrence within the test group.

As was expected from the static tests, the series with two pairs of metal-plate joints (Table

5.10) showed significantly higher failure loads and fatigue life in comparison with those

where one pair of the same or similar width of metal-plate joints were used. The joints with

two pairs of 1 by 6-in (25 by 152-mm) plates (G1) demonstrated no significant difference

of fatigue failure loads of joints with one pair of 4 by 6-in (102 by 152-mm) plates (G5).

Joints with two pairs of 2 by 6-in (51 by 152-mm) plates (G3) demonstrated statistically

highest fatigue resistance and, accordingly, higher fatigue life; however, their static-to-

fatigue ratio was similar to that of joints with two pairs of 1 by 6-in (25 by 152-mm) plates

(G1). Analysis of the failure modes indicated that mixed metal-plate yield with shear-out

of OSB failure modes were generally associated with the higher fatigue life joints, while

the joints with lower fatigue life mostly associated with metal-plate yield.

Similar correlations are shown in Table 5.11. The joints with two pairs of plates showed

significantly higher failure loads and fatigue life in comparison with the joints with one

pair of plates of the same or similar width. The joints with two pairs of 2 by 6-in (51 by

152-mm) plates (G3) demonstrated the highest fatigue resistance. However, their static-to-

fatigue ratio was the lowest due to the high static moment capacity. Analysis of failure

modes showed that all specimens in series G4 with the lowest fatigue life failed due to

metal-plate yield, while the higher fatigue life series (G1, G5 and G3) failed in a mixed

metal-plate yield and shear-out-of-OSB failure modes.

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148

Tabl

e 5.

10 T

est r

esul

ts u

sing

GSA

bac

kres

t fra

me

sche

dule

.

Fa

tigue

R

atio

St

atic

pe

ak

load

(A

ve.)

Stat

ic

mom

ent

(Ave

.) Pa

ssed

m

omen

t Fa

iled

mom

ent

Cum

ulat

ive

No.

of

cycl

es to

failu

re

Stat

ic/

pass

ed

Stat

ic/

faile

d

M

ode

of fa

ilure

a

(lbf)

(k

ip-in

)

G1

575

(7.7

) b

8.04

4.

20

(0)

5.25

(0)

50,0

00+7

,801

(7) B

c 1.

92

1.53

20

% M

-P Y

, 80%

M-P

Y +

SP

G5

697

(5

.8)

9.76

4.

52

(11)

5.

57

(9)

50,0

00+1

5,00

6 (1

7) B

2.

16

1.75

10

0% M

-P Y

+ S

P

G3

798

(8.3

) 11

.2

5.67

(1

0)

6.72

(8)

75,0

00+1

6,96

7 (1

4) A

1.

97

1.66

30

% M

-P Y

, 70%

M-P

Y +

SP

G4

542

(6.0

) 7.

58

2.52

(5

2)

3.99

(11)

25

,000

+4,6

74 (2

4) C

3.

01

1.90

90

% M

-P Y

, 10%

M-P

Y +

SP

a Mod

e of

failu

re: M

-P Y

= M

etal

-pla

te y

ield

; SP

= S

hear

- out

of O

SB.

b Valu

es in

par

enth

eses

are

the

coef

ficie

nt o

f var

iatio

n (%

).

c Valu

es w

ith th

e sa

me

lette

r are

not

stat

istic

ally

diff

eren

t at t

he 9

5% si

gnifi

canc

e le

vel.

1lbf

= 4

.448

N; 1

kip-

in =

113

N-m

.

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149

Tabl

e 5.

11 T

est r

esul

ts u

sing

GSA

seat

load

foun

datio

n sc

hedu

le.

Fa

tigue

R

atio

St

atic

pe

ak

load

(A

ve.)

Stat

ic

mom

ent

(Ave

.) Pa

ssed

m

omen

t Fa

iled

mom

ent

Cum

ulat

ive

No.

of

cycl

es to

failu

re

Stat

ic/

pass

ed

Stat

ic/

faile

d

M

ode

of fa

ilure

a

(lbf)

(k

ip-in

)

G1

575

(7.7

) b

8.04

3.

00

(0)

6.00

(0)

25,0

00+2

,182

(3) C

c 2.

68

1.34

40

% M

-P Y

, 60%

M-P

Y +

SP

G5

697

(5

.8)

9.76

3.

00

(0)

6.00

(0)

25,0

00+1

2,62

9 (1

0) B

3.

25

1.63

30

% M

-P Y

, 70%

M-P

Y +

SP

G3

798

(8.3

) 11

.2

6.00

(0

) 9.

00

(0)

50,0

00+1

,618

(3) A

1.

86

1.24

10

% M

-P Y

, 10%

SP,

80

% M

-P Y

+ S

P

G4

542

(6.0

) 7.

58

2.70

(3

5)

5.70

(1

7)

25,0

00+1

92 (9

) D

2.81

1.

33

100%

M-P

Y

a Mod

e of

failu

re: M

-P Y

= M

etal

-pla

te y

ield

; SP

= S

hear

-out

of O

SB.

b Valu

es in

par

enth

eses

are

the

coef

ficie

nt o

f var

iatio

n (%

).

c Valu

es w

ith th

e sa

me

lette

r are

not

stat

istic

ally

diff

eren

t at t

he 9

5% si

gnifi

canc

e le

vel.

1lbf

= 4

.448

N; 1

kip-

in =

113

N-m

.

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Static to fatigue moment capacity ratio

The ratio of static to failed fatigue moment varied from 1.24 to 1.66 for joints with two

pairs of plates and from 1.33 to 1.90 for joints with one pair of plates. The corresponding

ratio for the passed fatigue moment varied from 1.86 to 2.68 and from 2.16 to 3.25 for the

joints with two pairs and one pair of plates, respectively. The overall average ratio of static

moment to fatigue failed moment for all eight test series subjected to two different loading

schedules was 1.59 with a coefficient of variation (COV) of 20 percent. In other words, the

average OSB metal-plated joint failed under a load level of 63 percent of its static moment

capacity after being subjected to a series of cyclic stepped loads. The results are similar to

those obtained with OSB gusset-plate (Wang et al. 2007c). Under stepped loads with a

maximum magnitude of 63 percent of static moment capacity, the fatigue moment

resistance of metal-plated connected joints was mostly governed by failure in the OSB

material, rather than metal tooth rupture.

The average ratio of static to fatigue passed moment was 2.5 with a COV of 22 percent.

Previously, an average static to fatigue passed moment capacity ratio of 2.2 with a COV of

13 percent was reported for two-pin dowel joints (Zhang et al. 2003), 2.5 with a COV of 11

percent for metal-plated connected joints in furniture grade pine plywood (Zhang et al.

2006), and 2.1 with a COV of 12 percent for OSB gusset-plated joints (Wang et al. 2007c).

Comparison with these studies shows that the average ratio of static to fatigue moment

capacity of upholstered furniture frame joints varies from one fastening system to another.

However, based on this information and for simplification purposes, it could be suggested

that an approximate ratio of 2.5 for the metal-plate connectors with plywood or OSB could

be adopted for upholstered furniture designs.

5.2.6 Conclusions Cyclic load fatigue tests on OSB joints with metal-plates of four configurations were

performed and compared with their static moment resistance to determine the influence of

the metal-plate configuration, material and fastening system on the static-to-fatigue

moment capacity ratio and on failure modes of the joints. Results showed that despite

differences in failure modes, joints with either one pair or two pairs of metal connector

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151

plates had similar static-to-fatigue moment capacity ratios. In joints with two pairs of

plates, a mixture of metal-plate yield and shear-out of OSB was the dominant failure mode.

In joints with one pair of plates, lower fatigue life was associated with essentially metal-

plate yield. Statistical analysis and comparison with previous studies showed that a static-

to-fatigue ratio of 2.5 can be adopted as the passing ratio for design of upholstered

furniture frames. In other words, it is advised to design metal-plated joints so that they will

not be loaded to more than 40 percent of their static moment capacity.

5.2.7 Practicality Information obtained in this study of joint assemblies subjected to cyclic stepped loads

provides designers with technical data that can be used to develop rational and optimum

designs of upholstered furniture frames to meet desired performance requirements.

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Chapter 6 Out-of-plane static bending resistance of gusset-plate and metal-plate joints constructed of

oriented strand board for upholstered furniture frames

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153

6.1 Résumé Les connecteurs avec goussets et avec plaques métalliques sont généralement utilisés pour

les joints critiques dans les structures des meubles rembourrés à cause de leur résistance

mécanique élevée. Pour introduire avec succès des panneaux à lamelles orientés (OSB)

dans les structures des meubles rembourrés, nous avons évalué des joint de type gousset en

OSB ainsi que des joints de type plaques métallique. Dans cette étude, la résistance statique

en flexion en dehors du plan des joints en forme de T avec des goussets et des plaques

métallique a été déterminée expérimentalement pour différentes configurations. La

comparaison avec les résistances en flexion dans le plan a été faite également. La

résistance en flexion dans le plan était beaucoup plus grande que la résistance en flexion en

dehors du plan pour les joints métal-plaqué et gousset-plaqué. Le joint avec deux paires de

2 par 6-po (51 par 152-mm)de plaque métallique est la configuration optimum qui a montré

la charge unitaire maximale la plus élevée parmi tous les joints à plaque métallique

examinés. Pour les joints à gousset, une augmentation de longueur de gousset-plat de 4 à

8-po (102 à 203-mm) a résulté en une charge maximale amplifiée pour les joints collé et

sans colle, mais un accroissement ultérieur de la longueur du gousset-plat, ne résulta pas en

une augmentation significative de la peformance, on peut en conclure que pour cette

géométrie, le gousset-plat 8-po (203-mm) présente la conception optimum. Les joints de

plaque métallique et de gousset d’OSB sans colle ont montré les valeurs semblables de

rigidité, mais les joints de gousset collés ont eu une rigidité beaucoup plus grande que les

joints gousset sans colle. Les joints gousset ont présenté environ 80% de résistance

supplémentaires en flexion hors du plan par rapport à la moyenne que des joints avec

plaque métallique.

6.2 Abstract Gusset-plate and metal-plate connectors are commonly used to connect critical joints in

upholstered furniture frames due to their high load resistance. To successfully introduce

oriented strand board (OSB) into furniture frames, basic data on the performance of gusset-

plate and metal-plate joints constructed of OSB is needed. In this study, out-of-plane static

moment capacity of T-shaped joints with gusset-plates and metal-plates were determined

experimentally for different configurations and comparison with in-plane moment

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154

capacities were made. In-plane moment capacities were found to be 4 to 6 times higher

than out-of-plane moment capacities for both metal-plate and gusset-plate joints. Joints

with two pairs of 2 by 6-in (51 by 152-mm) metal-plates, which showed the highest

ultimate unit load, appeared to be the optimum configuration among all the metal-plate

joint configurations tested. For gusset-plate joints, an increase in length of gusset-plate

from 4 to 8-in (102 to 203-mm), boosted the peak load for both glued and unglued joints,

but a further increase of the length did not result in any significant increase in the peak

load. It can be concluded that for this particular joint geometry, the 8-in (203-mm) gusset-

plate presented the optimum design. Metal-plate and unglued gusset-plate joints

demonstrated similar stiffness values; however, glued gusset-plate joints had much higher

stiffness than unglued gusset-plate joints. On average, gusset-plate joints exhibited about

80% higher out-of-plane static moment capacity than metal-plate joints.

6.3 Introduction The wood-based panel industry has experienced increasing growth since its inception and it

is predicted to increase its production capacity further by economizing the utilization of

raw materials. OSB capacity in Canada increased from 3.21 to 10.30 million m3 during last

decade (1994 to 2004) and it is expected to reach 13.13 million m3 by 2008 (RISI 2004).

To date, OSB has captured about 75 percent of the residential construction market as a

sheathing material. But there is a limit for OSB volumes that can be supplied to

construction applications because the demand varies with the price of structural panels. As

a result, OSB manufactures are looking for new markets for their product in order to

maintain their increasing production capacity. The upholstered furniture sector is one

market where there is a potential for expansion (APA 1997, Tabarasi 2002). The recent

development in the Computer Numeric Control (CNC) technology and machinery

encourages upholstered furniture producers to think of alternative ways of minimizing the

cost of raw material and speeding up the production process. However, such new markets

require technical information about the performance of the wood-based panels and joints in

terms of design and manufacturing processes for upholstered furniture to suit their end-use

applications.

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155

Metal plate connectors (MPC) have been used in light-frame constructions in North

America since 1950s. The MPC requires little time for joint fabrication and enhances the

strength and stiffness of trusses of almost any shape. However, the use of MPC in the

furniture industry is relatively new, especially in frames made with OSB. MPC and gusset-

plates provide high load resistance, rapid joint assembly and easy connection of members.

They are already used for critical joints such as front post-front rail and side rail-back post

joint in upholstered furniture frame construction (Zhang et al. 2001b and 2005).

Some information is available on the in-plane moment capacities of metal-plate and gusset-

plate joints constructed of plywood and OSB. Eckelman (1971c) and Zhang et al. (2001b)

studied the performance of T-shaped, end-to-side joints with glued-on plywood gusset-

plates of different configurations. Eckelman (1980) studied the performance of T-shaped,

end to side-grain joints constructed of red oak, yellow-poplar, soft maple, and Douglas-fir

with 18- and 20-gauge metal plates of various shapes. Zhang et al. (2005) expanded

Eckelman’s research by using furniture grade 3/4-in (19-mm) thick 7-ply southern yellow

pine plywood as material. They reported that metal-plate and rail widths affected the

moment capacity of MPC plywood joints significantly. Generally, there is limited research

on connections in OSB furniture frames. Wang et al. (2007b, 2007c, 2007d, and 2007e)

evaluated the feasibility of using OSB as a material for gusset-plate and metal-plate joints

in upholstered furniture. The results show that the in-plane moment capacity of the joint

increased in proportion to the length of the gusset-plate until the capacity of the gusset

plate exceeded that of the main member. Application of glue, generally, altered the failure

modes of the joints and increased significantly their strength.

Although, proper designs of frames will attempt to avoid out-of-plane loading, certain

upholstered furniture designs with panels will require that joints be subjected to out-of-

plane loads. For example loads acting on the sofa seat springs apply out-of-plane bending

to the front rail. Tables 6.1 and 6.2 show in-plane moment capacities of metal-plate and

gusset-plate joints for OSB determined previously by Wang et al. 2007d and 2007b.

The primary objective of this research was to develop basic data on the out-of-plane static

bending resistance of T-shaped, gusset-plate and metal-plate joints constructed of OSB.

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156

The specific objectives were 1) to understand how plate configurations affect out-of-plane

moment resistance of T-shape joints; 2) to determine the stiffness of joints constructed of

OSB; 3) to understand the behavior of joints based on their failure modes; and 4) to

determine an optimum configuration for the bending capacity of metal-plate and gusset-

plate joints. The data will further be used for the optimization of upholstered furniture

frame designs.

6.4 Materials and Methods Each test specimen consisted of a post and a rail (T-shaped) made of structural 23/32-in

(18-mm) OSB joined with one pair of gusset-plates or one pair or two pairs of metal-plates

symmetrically attached on both sides of the joint. Basic material properties, fabrication

procedures, and configuration details of the joints tested statically were reported in a

previous paper by the authors (Wang et al. 2007b, 2007d). For this study, panel materials

from the same batch were used and joints of the same configurations were constructed

using the same procedures. The configurations of the T-shaped, end-to-side gusset-plate

and MPC joint specimens for this study are shown in Figures 6.1 to 6.3. Tables 6.3 and 6.4

provide the information on the tested configurations and the number of replicates. Density,

moisture content, internal bond, flat and edgewise bending properties of the OSB were

determined before testing the assemblies. The mechanical properties were evaluated in

accordance with ASTM D 1037 standard (ASTM 2005a).

In order to conform to durability performance test standards such as the GSA test regime

FNAE-80-214A (GSA 1998), structural design of upholstered furniture frames requires

information on the performance of each joint in a typical sofa frame. According to the

GSA, for a 72-in (1.83-m) long three-seat sofa of light-duty category, three concentrated

vertical loads of 300 lbf (1,334 N) are applied to the front-rail for a total of 900 lbf (4,003

N) (Table 6.5). Fifteen springs are installed along the sofa to carry the entire load with 5

springs per seat to carry the horizontal loads distributed as shown in Table 6.6. If the front-

rail is assumed to have two rigid joints with front posts, each joint will carry an out-of-

plane bending moment of 61×4+76×8+81×12/2=1338 lbf-in (151 N-m) in fatigue test, as

shown in Figure 6.4. To estimate the static load capacity, the load is doubled resulting in a

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157

static moment capacity of 2676 lbf-in (302 N-m). With a 14-in. (356-mm) long arm used in

the tests, the target static load on the joint is approximately 2676/14 = 191 lbf (850 N).

All specimens were tested using a Tinius-Olsen universal testing machine. The post

member of the specimen was clamped to the test fixture. Vertical upward load was applied

to the rail at a rate of 0.2 in./min (5 mm/min) (Zhang et al. 2001b), and the load at failure

was recorded using a load cell with an accuracy of 0.2%. As shown in Figure 6.5, the

displacement of the joint was measured using a Linear Variable Differential Transducer

(LVDT) at the bottom point A located at a distance of 6.5 in (165 mm) from the juncture of

the post and rail. As can be seen in Figure 6.6, during the test, the LVDT at point A

retracted the distance AA’ = a; Therefore, the angle of rotation, α, of the arm can be

expressed as a function of displacement a:

165atg =α (6.1)

Moment-rotation graphs (Figure 6.7) were used to calculate the rotational stiffness of the

joints expressed as the slope of the straight line between 10-lbf (44.5-N) and 40% of

ultimate load (Gebremedhin et al. 1992).

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158

Tabl

e 6.

1 In

-pla

ne m

omen

t cap

aciti

es o

f met

al-p

late

d jo

ints

con

stru

cted

of O

SB a

vaila

ble

in li

tera

ture

(Wan

g et

al.

2007

d).

M

etal

-pl

ate

size

Pair

of

met

al-

plat

es

Num

ber

of

spec

imen

s

Mea

n ul

timat

e lo

ad

CO

VM

omen

t ca

paci

ty

Stiff

ness

C

OV

M

ode

of fa

ilure

a Jo

int

conf

igur

atio

n (in

)

(lb

f)

(%)

(kip

-in)

(kip

-in/ra

d)

(%)

G1

1x6

2 10

57

5 C

b 7.

7 8.

05

1677

Ab

29

50%

PY

, 20

% P

Y+T

P,

10%

TP,

20%

CR

G

2 2x

6 1

10

384

D

9.1

5.38

25

2 D

31

10

0% P

Y

G3

2x6

2 10

79

8 A

8.

3 11

.2

1852

A

35

50%

TP,

30

% T

P+S,

10

% C

R, 1

0% M

R

G4

3x6

1 10

54

2 C

6.

0 7.

59

558

C

34

90%

PY

, 10%

TP

G5

4x6

1 10

69

7 B

5.

8 9.

76

1295

B

10

100%

TP

G6

6x6

1 10

78

0 A

9.

3 10

.9

1391

B

8 90

% M

R, 1

0% T

P a P

Y =

Met

al-p

late

yie

ld in

tens

ion;

TP

= M

etal

-pla

te to

oth

pull-

out;

CR

= O

SB c

rush

ed o

n th

e to

p co

rner

of r

ail m

embe

r; S

=In

-pl

ane

shea

r of O

SB; M

R =

OSB

mem

ber r

uptu

re.

b Va

lues

with

the

sam

e le

tter a

re n

ot st

atis

tical

ly d

iffer

ent a

t the

95%

sign

ifica

nce

leve

l.

1in

= 2

5.4

mm

; 1 lb

f = 4

.448

kN

; 1ki

p-in

= 1

13 N

-m.

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159

Tabl

e 6.

2 In

-pla

ne m

omen

t cap

aciti

es o

f gus

set-p

late

join

ts c

onst

ruct

ed o

f OSB

ava

ilabl

e in

lite

ratu

re (W

ang

et a

l. 20

07b)

.

G

usse

t-pl

ate

leng

th

Stap

le

leng

th

Num

ber

of

stap

les

Num

ber

of

spec

imen

s

Pred

icte

d ul

timat

e lo

ad

Mea

n ul

timat

e lo

ad

CO

V

Ref

eren

ce

resi

stan

ce a

Dif.

b M

ode

of fa

ilure

c Jo

int

conf

igur

atio

n (in

) (in

)

(k

ip)

(kip

) (%

) (k

ip)

(%)

a

4 1.

5 20

10

0.

694

0.67

Ad

4.8

0.64

6 -7

W

40%

, W+S

10%

, SO

50%

b 6

1.5

20

10

0.72

9 0.

85 B

7.

6 0.

825

13

W 3

0%, W

+S 1

0%,

W+S

O 2

0%, W

+GR

10%

, G

R+S

O 2

0%, G

R 1

0%

c 8

1.5

20

10

0.85

7 1.

01 C

5.

3 0.

973

14

W 4

0%, W

+GR

20%

, W

+GR

+S 2

0%, S

O 2

0%

d 10

1.

5 20

10

0.

937

1.02

C

5.3

0.98

0 5

W 6

0%, W

+GR

10%

, GR

10%

, M

R 1

0%, S

O 1

0%

e 12

1.

5 20

10

1.

032

0.98

C

6.3

0.94

7 -8

W

70%

, W+G

R 2

0%, M

R 1

0%

f 10

1.

0 32

10

0.

786

0.87

B

7.8

0.84

1 7

W 7

0%, W

+GR

20%

, W+S

10%

g 10

1.

0 32

10

0.

756

0.87

B

7.0

0.84

2 11

W

70%

, W+G

R 1

0%, W

+S 2

0%h

10

1.0

36

10

0.81

1 0.

97 C

9.

4 0.

942

16

W 5

0%, W

+GR

30%

, W+S

20%

Ung

lued

i 8

1.0

40

10

0.79

9 0.

92 B

, C

8.4

0.89

5 12

W

10%

, W+G

R 1

0%,

W+S

O 2

0%, W

+S 4

0%,

GR

+S 1

0%, G

R 1

0%

4 1.

0 8

10

0.

68 A

7.

0 0.

661

S

100%

6

1.0

8 10

0.92

B, C

6.

9 0.

890

M

R 1

0%, G

R+S

30%

, S 6

0%

8 1.

0 8

10

1.

15 D

8.

7 1.

116

M

R 3

0%, G

R+S

60%

, S 1

0%

10

1.0

8 10

1.27

E

11.6

1.

250

M

R 4

0%, G

R 6

0%

Glu

ed

12

1.0

8 10

1.24

D, E

11

.8

1.21

6

GR

100

%

a Ref

eren

ce re

sist

ance

com

pute

d us

ing

expe

rim

enta

l dat

a an

d AS

TM D

5457

pro

cedu

re (K

R = 1

). b D

iffer

ence

bet

wee

n pr

edic

ted

peak

load

and

refe

renc

e re

sist

ance

. c W

= st

aple

with

draw

al; S

= in

-pla

ne sh

ear f

ailu

re o

f OSB

; SO

= S

hear

-out

of O

SB; M

R =

mem

ber r

uptu

re; G

R =

gus

set-p

late

rupt

ure.

d Va

lues

with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 95%

sign

ifica

nce

leve

l.

1in

= 2

5.4

mm

; 1ki

p =

100

0 lbf =

4.4

48 k

N.

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160

Configuration G1: Configuration G2:

1 in

1 in

3 in16 in

6 in 16 in

6 in

2 in16 in

6 in 16 in

6 in

(a) (b) Configuration G3: Configuration G4:

2 in

2 in

1 in16 in

6 in 16 in

6 in

3 in16 in

6 in 16 in

6 in

(c) (d) Configuration G5: Configuration G6:

4 in16 in

6 in 16 in

6 in

6 in16 in

6 in 16 in

6 in

(e) (f) * 1in = 25.4 mm

Figure 6.1 Configurations of metal-plate joints for out-of-plane moment tests.

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161

355P

-

-

15240

651

406

20

3030

20 20 20

12.7 D.

152Rail

Post

* All dimensions are in mm.

Figure 6.2 Configuration of a typical staple-glued gusset-plate joint for out-of-plane moment tests.

Page 180: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

162

1717

1751

262526 252525152

313031 3030152

2018

1820

76

314531 45152

2120

2020

102

21

314531 45152

2625

2525

127

26

314531 45152

3130

3030

152

31

(

a)

(b)

(c

)

(d

)

(e)

313031 30152

1818

1818

127

1918

18

30

313031 30152

2221

2121

127

2121

30

313031 30

152

2221

2121

127

2121

30

313031 30152

1717

1717

102

1717

30

(f

)

(g

)

(h)

(i)

* Al

l dim

ensi

ons a

re in

mm

. Fi

gure

6.3

Pla

cem

ent o

f sta

ples

in g

usse

t-pla

tes o

f ung

lued

join

ts (C

onfig

urat

ions

a-i)

for o

ut-o

f-pl

ane

mom

ent t

ests

.

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163

Tabl

e 6.

3 O

ut-o

f-pl

ane

mom

ent c

apac

ities

and

stiff

ness

of m

etal

-pla

te jo

ints

con

stru

cted

of O

SB.

M

etal

-pl

ate

size

Pair

of

met

al-

plat

es

Num

ber

of

spec

imen

s

Mea

n ul

timat

e lo

ad

CO

VM

omen

t ca

paci

ty

Stiff

ness

C

OV

M

ode

of fa

ilure

a Jo

int

conf

igur

atio

n (in

)

(lb

f)

(%)

(kip

-in)

(lbf-

in/ra

d)

(%)

G1

1x6

2 5

113.

3 B

b 12

.6

1.59

19

584

C

5.7

PY+T

P+M

B 2

0%,

TP+M

B 2

0%,

MB

40%

, G

2 2x

6 1

5 99

.0 C

12

.0

1.39

15

688

D

5.4

100%

TP

G3

2x6

2 5

132.

9 A

3.

7 1.

86

2425

8 A

7.

3 10

0% T

P+S

G4

3x6

1 5

101.

0 C

13

.0

1.41

18

330

C

2.8

100%

TP+

S G

5 4x

6 1

5 12

2.4

A, B

5.

6 1.

71

2212

2 B

4.

5 10

0% T

P+S

G6

6x6

1 5

133.

9 A

5.

4 1.

87

2497

6 A

8.

1 10

0% T

P+S

a PY

= M

etal

-pla

te y

ield

in te

nsio

n; T

P =

Met

al-p

late

toot

h pu

ll-ou

t; M

B =

Met

al-p

late

ben

d; S

=In

-pla

ne sh

ear o

f OSB

mem

ber.

b Va

lues

with

the

sam

e le

tter i

ndex

are

not

stat

istic

ally

diff

eren

t at 9

5% si

gnifi

canc

e le

vel.

1i

n =

25.

4 m

m; 1

lbf =

4.4

48 N

; 1ki

p-in

= 1

13 N

-m; 1

lbf-i

n =

113

N-m

m.

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164

Tabl

e 6.

4 O

ut-o

f-pl

ane

mom

ent c

apac

ities

and

stiff

ness

of g

usse

t-pla

te jo

ints

con

stru

cted

of O

SB.

G

usse

t-pl

ate

leng

th

Stap

le

leng

th

Num

ber

of

stap

les

Num

ber

of

spec

imen

s

Mea

n ul

timat

e lo

ad

CO

V

Mea

n ul

timat

e m

omen

t

St

iffne

ss

C

OV

Mod

e of

failu

re a

Join

t co

nfig

urat

ion

(in)

(in)

(lbf)

(%

) (lb

f-in

) (lb

f-in

/rad)

(%

)

a 4

1.5

20

5 11

2.8

Gb

15.4

15

79

1557

1 H

5.

8 G

W+S

100

%

b 6

1.5

20

5 16

1.3

E, F

6.

1 22

58

1998

6 G

12

.8

GW

+S 1

00%

c 8

1.5

20

5 20

0.7

B, C

5.

3 28

10

2229

7 F

4.7

GW

+S 8

0%,

GR

+S 2

0%

d 10

1.

5 20

5

203.

1 A

, B

7.4

2844

26

065

E 9.

9

GR

20%

, M

R 2

0%,

GW

+S 2

0%,

S 40

%

e 12

1.

5 20

5

208.

7 A

, B

15.0

29

21

2692

0 E

4.8

S 80

%,

S+G

R 2

0%

f 10

1.

0 32

5

183.

3 C

, D

13.8

25

67

2715

6 E

7.1

S 60

%, M

R 4

0%

g 10

1.

0 32

5

221.

8 A

5.

1 31

05

2728

4 E

5.8

S 40

%, M

R 6

0%

h 10

1.

0 36

5

198.

8 B

, C, D

6.

3 27

84

2588

1 E

5.2

S 80

%, M

R 2

0%

Ung

lued

i 8

1.0

40

5 18

0.1

D, E

10

.5

2521

21

894

F, G

6.

0 S

20%

, GR

20%

, M

R60

%

4 1.

0 8

5 11

7.6

G

8.4

1646

22

588

F 3.

3 S

100%

6

1.0

8 5

160.

2 F

5.7

2243

30

864

D

4.8

S 10

0%

8 1.

0 8

5 19

4.8

B, C

, D

3.9

2727

40

449

C

3.1

S 80

%, M

R 2

0%

10

1.0

8 5

209.

9 A

, B

4.6

2939

46

888

B

5.8

S 10

0%

Glu

ed

12

1.0

8 5

221

A

10.7

30

94

5022

4 A

4.

1 S

100%

a G

W =

Gus

set-p

late

stap

le w

ithdr

awal

; S =

In-p

lane

shea

r fai

lure

of O

SB m

embe

r; M

R =

mem

ber r

uptu

re; G

R =

gus

set-p

late

ru

ptur

e.

b Va

lues

with

the

sam

e ca

pita

l let

ter a

re n

ot st

atis

tical

ly d

iffer

ent a

t 95%

sign

ifica

nce

leve

l.

1in

= 2

5.4

mm

; 1lb

f = 4

.448

N; 1

lbf-i

n =

113

N-m

m.

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165

Table 6.5 Acceptance performance level of upholstered furniture in accordance with GSA (1998).

Test Initial Loads

Load Increments

Number of Loads

Light-service

Acceptance Level

Medium-service

Acceptance Level

Heavy-service

Acceptance Level

(lbf) (lbf) (lbf) (lbf) (lbf)

Cyclic Vertical Load Test on -- Front Rail 100 100

3

300

400 600

-- Back Rail 100 100

3

200

300 500 1.000 lbf = 4.448 N. Table 6.6 Distributed loads applied on each springs per seat of sofa (from Tackett and Zhang 2007).

Load distribution Spring 1 Spring 2 Spring 3 Spring 4 Spring 5

(lbf)

Horizontal 61 76 81 76 61

Vertical 30 60 65 60 30

1.000 lbf = 4.448 N.

61 lbf

61 lbf

76 lbf

76 lbf

81 lbf

12 in.

8 in.

4 in.

Figure 6.4 Schematic of the out-of-plane bending carried by the front rail.

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166

Figure 6.5 An example of out-of-plane bending test joint with a LVDT point A.

Figure 6.6 Measurement of the angle of rotation, α.

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167

0

500

1000

1500

2000

2500

3000

3500

0 0,05 0,1 0,15 0,2 0,25

Angle of rotation (rad.)

Out

-of-p

lane

mom

ent (

lbf-i

n.)

C8-1C8-2C8-3C8-4C8-5

(a)

0

500

1000

1500

2000

2500

0 0,05 0,1 0,15 0,2 0,25

Angle of rotation (rad.)

Out

-of-p

lane

mom

ent (

lbf-i

n.)

G3-1G3-2G3-3G3-4G3-5

(b)

Figure 6.7 Typical out-of-plane moment-rotation curves: (a) gusset-plate, and (b) metal-plate joints.

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168

6.5 Results and Discussion Table 6.7 shows the physical and mechanical properties of OSB panels from which the test

specimens were fabricated.

Failure Modes

In tested assemblies, seven types of failure modes were observed as shown in Figure 6.8

and Tables 6.3 and 6.4. For metal-plate joints, assemblies with two pairs of narrow metal-

plates (G1-2 by 1x6-in (25x152-mm)) experienced mixed failure modes, including metal-

plate yield in tension (Figure 6.8d), metal-plate tooth pull-out (Figure 6.8c), and metal-

plate bend (Figure 6.8e). Metal-plate tooth pull-out was the dominant failure mode in the

narrowest metal-plate joints (G2-1 by 2x6-in (51x152-mm)). Metal-plate tooth pull-out

mixed with in-plane shear of OSB member (Figure 6.8a or 6.8b) were more common in the

joints with wider metal-plates (G3-2 by 2x6-in (51x152-mm), G4-1 by 3x6-in (76x152-

mm), G5-1 by 4x6-in (102x152-mm), and G6-1 by 6x6-in (152x152-mm)). For gusset-

plate joints, in-plane shear failure of OSB member was evident for all configurations,

especially for joints with glue. For joints without glue, gusset-plate staple withdrawal

(Figure 6.8h) controlled the smaller gussets (4, 6 and 8-in long) (102, 152 and 203-mm

long). When gusset length increased to 10-in (254-mm) and 12 in (305-mm), mixed failure

modes were observed which included: gusset-plate rupture (Figure 6.8g), OSB member

rupture (Figure 6.8f), gusset-plate staple withdrawal plus in-plane shear failure of OSB

member. The in-plane shear of OSB was the most dominant failure mode of the large

gusset plates. In configurations with 10-in (254-mm) long gusset-plates without glue, the

OSB member rupture was the most frequently observed. The discussion of load and

moment capacity presented below confirms this observation.

Out-of-plane load and moment capacity

Mean values and coefficients of variation (COV) of out-of-plane ultimate load and moment

capacities of metal-plate and gusset-plate OSB joints are summarized in Tables 6.3 and 6.4,

respectively. Statistical comparisons of results were performed using an ANOVA general

linear model and the Tukey’s multiple comparison tests.

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169

In joints with one pair of metal-plates, an increase of metal-plate width from 2 to 3-in (51

to 76-mm), showed no significant difference in ultimate load (99 vs. 101 lbf) (440 vs. 449

N), whereas an increase from 3 to 4-in (76 to 102-mm), and from 4 to 6-in (102 to 152-

mm) significantly increased the mean ultimate load by 21% and 9%, respectively. In

assemblies with two pairs of metal-plates, significant differences were found. For example,

the mean ultimate load of two pairs of 2 by 6-in (51 by 152-mm) metal-plates (G3) was

17% higher than that of assemblies with two pairs of 1 by 6-in (25 by 152-mm) metal-

plates (G1). Assemblies made of two pairs of 1 by 6-in (25 by 152-mm) (G1) were, on

average, 14% stronger than those made with one pair of 2 by 6-in (51 by 152-mm) (G2)

and 12% stronger than those with one pair of 3 by 6-in (76 by 152-mm) (G4) metal-plates.

The mean ultimate load of assemblies with two pairs of 2 by 6-in (51 by 152-mm) (G3)

was 9% higher than that of assemblies with one pair of 4 by 6-in (102 by 152-mm) (G5),

and similar to that of assemblies with one pair of 6 by 6-in (152 by 152-mm) plates (G6).

The assembly with two pairs of 2 by-6 in (51 by 152-mm) (G3) metal-plates had the

second highest ultimate load among all configurations, but no significant differences were

found between this series and the one with the highest ultimate load (i.e., one pair of 6 by

6-in (152 by 152-mm) plates (G6)), as can be seen in Table 6.3 and Figure 6.9. Therefore,

for the ultimate unit load (Load/Area), the joint with two pairs of 2 by 6-in (51 by 152-mm)

(G3) metal-plates was almost 50% more efficient than one pair of 6 by 6-in (152 by 152-

mm) plates (G6) (5.5 vs. 3.7 lbf/in2) (37.9 vs. 25.5 KPa). It can be concluded that for this

particular joint geometry and size, the two pairs of 2 by 6-in (51 by 152-mm) (G3) metal-

plates was the optimum design configuration. Comparisons were made for the out-of-plane

moment capacities of tested assemblies (Table 6.3) with the previously obtained data of in-

plane moment capacities on assemblies with similar metal-plates configurations (Tables

6.1). The in-plane moment capacities were, on average 4.3 times higher than the out-of-

plane capacities, varying from 2.9 times (G2) to 5.0 times (G3), but both have exhibited

similar trends in terms of the tested configurations.

For unglued gusset-plate joints with twenty 1.5-in (38-mm) long staples, an increase of

gusset-plate length from 4 to 6 in (102 by 152-mm) and from 6 to 8 in (152 by 203-mm)

significantly increased the peak load by 43% and 24%, respectively. Further increase of

gusset-plate length did not increase the load capacity of the joints as can be seen in Table

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170

6.4 and Figure 6.9. Therefore, for this particular joint geometry, the 8-in (203-mm) gusset-

plate presented the optimum design. Comparison of configurations f and g (Figures 6.3f

and 6.3g) shows that changing positions of staples in gusset-plates did influence the

ultimate load significantly (21% difference).

The load capacity of glued joints increased in proportion with the size of the gusset-plates

up to a length of 10 in (254-mm) (Figure 6.9). Further increase in length of the gusset-plate

did not result in any significant improvement due to the fact that the strength of the glue

bond exceeded the strength of the OSB material. For the same size of gusset-plate joints (4,

6, 8, 10 and 12-in) (102, 152, 203, 254 and 305-mm), either glued or unglued (with 20

staples), the mean ultimate load capacities of joints were not significantly different. In

comparison with in-plane moment capacities on assemblies with similar gusset-plates

configurations (Table 6.2), the in-plane capacities were, on average 3.9 times higher than

out-of-plane capacities varying from 2.9 times (configuration g) to 4.9 times (configuration

a).

Rotational stiffness

Moment-rotation curves in Figure 6.7 demonstrate a nonlinear relationship, but the lower

section of the curves can reasonably be assumed linear. In this study, the slope of the

straight section of the curve between 15-lbf (67-N) to 40% of ultimate load was used to

calculate the rotational stiffness of joints.

Generally, for metal-plate joints, similar tendency was observed for stiffness and ultimate

load. The stiffness of the joints with one pair of 6 by 6-in (152 by 152-mm) (G6) and two

pairs of 2 by 6-in (51 by 152-mm) (G3) metal-plates were the highest as shown in Table

6.3 and Figure 6.10. Assemblies with two pairs of 1 by 6-in (25 by 152-mm) (G1) metal-

plates were stiffer than those with one pair of 3 by 6-in (76 by 152-mm) (G4) metal-plates.

Among the joints with metal plates, the stiffness of one pair of 2 by 6-in (51 by 152-mm)

(G2) was the lowest.

The gusset-plate joints with glue were much stiffer than the joints without glue (see Table

6.4 and Figure 6.10). Different configurations with 10-in (254-mm) unglued gusset-plates

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171

demonstrated no significant difference in stiffness. The stiffness values of metal-plate

joints and unglued gusset-plate joints were similar.

Table 6.7 Physical and mechanical properties of OSB.

Property Mean (COV%) Modulus of elasticity flatwise MOE, GPa 6.33 (8.2) Modulus of elasticity edgewise MOE, GPa 4.74 (5.4) Modulus of rupture flatwise MOR, MPa 32.2 (12.1) Modulus of rupture edgewise MOR, MPa 22.4 (11.7) Density, kg/m3 594 (6.8) Moisture content, % 6.8 (7.7) Internal bond, MPa 0.426 (18.2)

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172

(a) In-plane shear of OSB (front) (b) In-plane shear of OSB (back)

(c) Metal-plate tooth pull-out (d) Metal-plate yield in tension

(e) Metal-plate bend (f) OSB member rupture

(g) Gusset-plate rupture (h) Gusset-plate staple withdrawal

Figure 6.8 Typical failure modes of test joints.

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0

50

100

150

200

250

a b c d e f g h i 4 6 8 10 12 G1 G2 G3 G4 G5 G6

Gusset-plate and metal-plate configurations

Ulti

mat

e ou

t-of-p

lane

load

(lbf

)

Figure 6.9 Experimental mean ultimate out-of-plane loads of gusset-plated and metal-plated joints.

0

9000

18000

27000

36000

45000

54000

a b c d e f g h i 4 6 8 10 12 G1 G2 G3 G4 G5 G6

Gusset-plate and metal-plate configurations

Stiff

ness

(lbf

-in./r

ad)

Figure 6.10 Stiffness of all configurations of gusset-plated and metal-plated joints.

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6.6 Conclusion Effects of metal-plate width, number of metal-plates, gusset-plate length, placement of

staples, and glue application on the out-of plane static bending resistance of T-shape OSB

metal-plate and gusset-plate joints were investigated. Comparison with in-plane moment

capacities of identical configurations were also made. The out-of-plane moment capacities

of both types of joints were, on average, 4 times lower than the in-plane capacities.

For the same width of metal-plates, two pairs were 14% stronger than one pair. An increase

in the width of metal-plates from 2 to 4-in (51 to 102-mm) boosted the joint load capacity

for assemblies with one pair or two pairs of metal-plate joints by 19% and 15%,

respectively. Among metal-plate joints, assemblies with two pairs of 2 by 6-in (51 by 152-

mm) plates (G3) showed the highest ultimate unit load. The stiffness values for the joints

with metal-plates demonstrated similar tendency with the values of the ultimate load.

Similar stiffness values were observed for metal-plate joints and unglued gusset-plate

joints.

For joints with gusset-plates, application of glue was the most important factor affecting

the stiffness of the joints, which allowed for a stiffness increase up to 87%, with little

increase in the mean ultimate load. Configurations with the same length of gusset-plate

showed similar mean ultimate load for both glued and unglued joints. An increase in length

of gusset-plate from 4 to 8-in (102 to 203-mm) increased load capacity for both glued and

unglued joints. However, a further increase in gusset-plate length did not enhance the

strength of the joints. Changing positions of staples in gusset-plates did affect the strength

of the joints of tested configurations.

Joints with gusset-plates resisted higher out-of-plane moment than metal-plate joints (max.

220 lbf. vs. 134 lbf) (979 N vs. 596 N). It can be concluded that metal-plate joints are not

as effective in resisting out-of-plane moment when compared to gusset-plate joints.

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Chapter 7 Finite element model of sofa frames made of OSB

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7.1 Introduction In order to use a new material in the assembly of a sofa frame, it is useful to perform

preliminary analysis using the finite element method. This method has been used to model

various structures in civil and mechanical engineering since the 1950s, but it is not widely

used in design of wooden furniture frame. Indeed, with the finite element analysis it is

possible to spare time and money, to carry out several modifications on a virtual model in

order to obtain an optimized design of structure, and it minimizes the need for full-scale

testing. Three configurations of sofa frames with two types of connections under three

levels of acceptance loads were modeled using the commercial finite element software

SAP2000 (1995). The properties of the connections were determined from tests presented

in Chapters 3 to 6. It does remain to validate the model predictions using experimental tests

on a real sofa. This chapter is a preliminary attempt of what can be accomplished using

computer assisted design of upholstered furniture.

7.2 Methodology

1) Mathematical model

The governing equations used in the model are described below. In the elastic domain, the

mechanical behaviour of OSB can be described by Hooke’s law. The linear relationship

between stress and strain for a bar in simple tension or compression can be expressed by

the equation:

εΕ=σ

(7.1)

Where: σ: stress (Pa)

E: modulus of elasticity for OSB (Pa)

ε: strain

In this study, an orthotropic version of Euation 7.1 was used for OSB, then Euation 7.1

becomes:

εσ C= (7.2)

Where:

C: elastic stiffness matrix for OSB (Pa)

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The equations for the joints (spring links): In a joint local coordinate system, the spring

forces and moments F1, F2, F3, M1, M2, and M3, at a joint are given by:

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

=

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

⎪⎪⎪⎪

3

2

1

3

2

1

3

2

1

3

2

1

3322.31211332313332221232231211131211

rrruuu

rrrrsymrrrrrrururuurururuuuurururuuuuuu

MMMFFF

where u1, u2, u3, r1, r2 and r3 are the joint displacements and rotations, and the terms u1,

u1u2, u2, … are the specified spring stiffness coefficients.

2) Description of the model and boundary conditions

Figure 7.1 shows the configuration of a typical three-seat sofa frame produced at one of the

upholstered furniture factories in Quebec. A typical sofa frame has structural components

such as front rail, back rail, front stump, back post, arm rail, top rail, etc. These are mainly

constructed with solid lumber or plywood as frame members connected by either screws,

or staples or metal-plates or gusset-plates and glue or a combination of thereof. All these

components must have sufficient strength and stiffness to resist the in-plane and out-of-

plane horizontal and vertical loads caused by people sitting or lying, and potentially,

impact forces due to children jumping on the sofa.

In this study, the sofa frame made entirely of OSB is modeled using finite element

commercial software SAP2000. The design of a three-seat sofa frame is using all

components of 23/32-in (18-mm) thick, 6-in (152-mm) wide OSB bars. The width of the

OSB members is based on recommendations by Chen (2003). The sofa frame is

represented by the 3D linear frame-type elements (beam element), and the connections

between the frames are represented by link elements (including screw, staple, metal-plate,

or gusset-plate, etc.). Here, each link element is a two-joint connecting link, which means a

link connecting two points. In this study, two types of links are used: rigid and semi-rigid.

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In rigid connection, all degrees of freedom are fixed. In semi-rigid connection, each

element is assumed to be composed of six separate “springs”, one for each of six

deformational degrees of freedom (axial, shear, torsion, and pure bending). Each of these

springs possesses a dual set of properties, either linear or nonlinear. In our case, multi-

linear elastic force-deformation characteristics are defined for the link element, and a

nonlinear static analysis is used in this model. The link element length for screw and staple

is chosen as 1-in (25-mm). While for metal-plate it is chosen as 3-in (76-mm). Table 7.1

presents the material properties of members and joints used in the model.

The boundary conditions for the OSB sofa model were:

• The two front feet of sofa frame are assumed as two roller connections which are

free to rotate on x, y and z directions, and no translation on z direction.

• The two back feet are presumed as two pin connections which can only rotate in x,

y, and z directions, but no translation.

Figure 7.1 Typical three-seat sofa frame.

Top Rail

Front Stump

Top Arm Rail

Back Posts

Front Rail

Front Spring Rail

Stretcher

Upright

Middle Side Rail

Bottom Side Rail

Back Rail Back

Spring Rail

BACK FRAME SYSTEM

SEAT FRAME SYSTEM

SIDE FRAME SYSTEM

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Table 7.1 Material properties of members and joints used in the finite element model.

Components Elements Properties

OSB members 3D frames E1 = 4740 MPa, E2 = 6330 MPa, A = 152 * 18 mm2,

I1 = 5267712 mm4, I2 = 73872 mm4

Gusset-plate

(OSB)

3D frames E1 = 5180 MPa, E2 = 6330 Mpa, A = 152 * 11 m m2,

I1 = 3219157 mm4, I2 = 16859 mm4

Metal-plate

connectors

Two joint link

Multi-linear

elastic

Rotation R2, R3 (See Figure 7.2 and Table II-1 in Appendix II)

Multi-linear elastic effective stiffness in translation directions

U1, U2 and U3 were assumed between free (0) to fixed (∞).

Screw Two joint link

Multi-linear

elastic

(for one screw)

U1a: Pmax = 890 N, ∆Pmax = 2 mm (Taking from Table 3.3

ave. screw edge withdrwal for 18-mm OSB)

Pfailure = 0.5 Pmax = 445 N, ∆Pfailure = 10 mm

U2 = U3: Pmax = 2224 N, ∆Pmax = 2 mm (Taking from Table 3.3

ave. screw lateral resistance for 18-mm OSB)

Pfailure = 0.5 Pmax = 1112 N, ∆Pfailure = 10mm

Multi-linear elastic effective stiffness in rotation directions R1,

R2 and R3 were assumed between free (0) to fixed (∞).

Staple Two joint link

Multi-linear

elastic

(for two staples

together =1.6

P1b)

U1: Pmax = 890 N, ∆Pmax = 1.5 mm (Taking from Table

3.4 ave. staple edge withdrwal for 18-mm OSB)

Pfailure = 0.5 Pmax = 445 N, ∆Pfailure = 10 mm

U2 = U3: Pmax = 1779 N, ∆Pmax = 1.5 mm (Taking from Erdil

et al. 2003a, ave. staple lateral resistance for OSB)

Pfailure = 0.5 Pmax = 889.5 N, ∆Pfailure= 10 mm

Multi-linear elastic effective stiffness in rotation directions R1,

R2 and R3 were assumed between free (0) to fixed (∞).

Notes: a U1, U2 and U3 are translation displacements. b P1 is the strength per staple.

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-1500000

-1000000

-500000

0

500000

1000000

1500000

-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25

Rotation (rad.)

Mom

ent (

N-m

m)

In-planeOut-of-plane

Figure 7.2 Two of 2 x 6 metal-plate joint in-plane and out-of-plane rotation-moments (R3 and R2).

3) Loads Applied on the Sofa Frame

In order to conform to durability performance test standards such as the General Service

Administration (GSA) test regimen FNAE-80-214A (GSA 1998), design of upholstered

furniture frames requires information about the performance of each joint in a sofa frame.

According to the GSA, both in-plane and out-of-plane bending moments acting on the front

and back rails are considered. On a 72-in (1.83-m) long three-seat sofa of light-duty

category, three concentrated vertical loads of 300 lbf (1334 N) are applied to the front-rail

with a total of 900 lbf (4003 N) (Table 7.2). There are 15 springs attached to the front and

back rails to carry the loads, i.e. 5 springs per seat which carry the distributed vertical and

horizontal loads shown in Table 7.3 (Tackett and Zhang 2007) and Figure 7.3. It has to be

noticed that since the worse cases were chosen, the sum of vertical loads on the front and

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back rails was 63% higher than each service acceptance level loads (300, 400 and 600 lbf)

(1334, 1779 and 2669 N).

Table 7.2 Acceptance performance level of upholstered furniture in accordance with GSA (1998).

Test Initial Loads

Load Increments

Number of Loads

Light-service

Acceptance Level

Medium-service

Acceptance Level

Heavy-service

Acceptance Level

(lbf) (lbf) (lbf) (lbf) (lbf) Cyclic Vertical Load Test on -- Front Rail

100 100 3 300 400 600

-- Back Rail 100 100 3 200 300 500

1.000 lbf = 4.448 N. Table 7.3 Distributed loads applied on each spring of a sofa seat for light, medium, and

heavy-service acceptance levels (from Tackett and Zhang 2007).

Spring 1 Spring 2 Spring 3 Spring 4 Spring 5 Load direction (lbf) Horizonta

l 61 76 81 76 61 Light-service acceptance

level (300lbf) Vertical 30 60 65 60 30

Horizontal 81.3 101.3 108 101.3 81.3 Medium-

service acceptance

level (400lbf) Vertical 40 80 86.7 80 40

Horizontal 101.7 126.7 135 126.7 101.7

(500lbf) Vertical 50 100 108.3 100 50

Horizontal 122 152 162 152 122 Heavy-service

acceptance level (600lbf) Vertical 60 120 130 120 60

1.000 lbf = 4.448 N.

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Fi

gure

7.3

Lig

ht-s

ervi

ce a

ccep

tanc

e le

vel l

oads

dis

tribu

ted

on a

sofa

fram

e m

odel

.

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4) Resistance Criteria

To verify if the frame elements can pass the resistance criteria, such as bending, axial

tension or compression, shear-through-thickness, and in-plane shear, the specified

capacities of OSB structural rated panels from the CSA-O86 standard (Wood Design

Manual 2001) shown in Table 7.4 were recalculated to the average short-term values using

the following formulae.

Table 7.4 Specified Strength, Stiffness, and Rigidity Capacities for Type 1 (Standard) Design OSB (Nominal thickness 18.5mm, Rating grade B) (Adapted from Table 7.3C CSA-O86) Unit Capacities relative to major axis at

0o Bending mp N-mm/mm 910 Axial tension tp N/mm 120 Axial compression pp N/mm 120 Shear-through-thickness Vp N/mm 59 Planar shear, bending Vpb N/mm 7.9 Planar shear, shear in-plane Vpf MPa 0.64

X05 = aXmean (1-1.645CV)

where,

X0.5 = 5th percentile value based on a normal distribution on 75% confidence level, from

Table 7.3C CSA-086;

a = 0.8, load duration factor to convert from short-term to standard term load;

CV = 15%, coefficient of variation assumed for OSB.

Recalculating for the width b = 1mm:

1) Bending: (N/mm2) σ = 6M / (bh2)

fb = 910 N-mm/mm x 6 / (bh2)

= 910 N-mm/mm x 6 / (18.5mm)2 = 15.95 N/mm2

fb, mean = fb / (1-1.645x15%) / a = 15.95 N/mm2 / 0.75325/ 0.8 = 26.5 N/mm2

2) Axial tension or compression: (N/mm2) σ = N / (bh)

fa = 120 N/mm / (1 x 18.5mm) = 6.49 N/mm2

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fa, mean = fa / (1-1.645x15%) / a = 6.49 N/mm2 / 0.75325/ 0.8 = 10.8 N/mm2

3) Shear-through-thickness τ = F / (bh)

fvt = 59 N/mm / (1 x 18.5mm) = 3.19 N/mm2

fvt, mean = fvt / (1-1.645x15%) / a = 3.19 N/mm2 / 0.75325/ 0.8 = 5.3 N/mm2

4) Shear in-plane τ = F / (bh)

fvip = 7.9 N/mm / (1 x 18.5mm) = 0.43 N/mm2

fvip, mean = fvip / (1-1.645x15%) / a = 0.43 N/mm2 / 0.75325/ 0.8 = 0.7 N/mm2 (planar shear,

bending)

or fvip, mean = fvip / (1-1.645x15%) / a = 0.64 N/mm2 / 0.75325/ 0.8 = 1.1 N/mm2 (planar

shear, shear in plane)

5) Torsion

τ max = T / (α dl (dc)2) < fvip, mean

dl/dc = 6/(23/32) = 8.35 α = 0.30

τ max = T / (0.30 x 6 x (23/32)2) (shear, torsion)

Therefore, Table 7.5 shows the average short-term strength values of bending, axial tension

or compression, shear-through thickness, and shear in-plane, and they are the criteria which

should be compared with results of the analyses.

Table 7.5 The average short-term strength values

Type of strength N/mm2

Bending fb, mean 26.5

Axial tension or compression fa, mean 10.8

Shear-through-thickness fvt, mean 5.3

Shear in-plane fvip, mean 0.7

A total of three configurations were analyzed under light-service acceptance level load, and

then the optimized configuration was used to evaluate the performance under medium and

heavy-service acceptance levels loads. Figure 7.4 shows three configurations of a typical

three-seat OSB sofa frame which has the same size as the wooden one: 72-in (1.83-m)

long, 34-in (864-mm) wide and 27-in (686-mm) high. Two types of connections are used in

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the model, either all joints with screws or staples with the exception of four metal-plates on

the bottom. The 1.5-in (38-mm) long screws or staples, and 6-in (152-mm) long metal-

plates are chosen as connectors in the frames. Figure 7.5 shows the types of connections

used in the model.

(a)

(b)

(c)

Figure 7.4 Configurations (a), (b) and (c) of a three-seat sofa made of OSB

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(a

) A

ll jo

ints

with

scre

ws e

xcep

t fou

r met

al-p

late

s on

the

botto

m.

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(b

) All

join

ts w

ith st

aple

s exc

ept f

our m

etal

-pla

tes o

n th

e bo

ttom

.

Figu

re 7

.5 T

ypes

of c

onne

ctio

ns u

sed

in so

fa fr

ame

mod

el.

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7.3 Results and Discussion 1. Sofa frame model under light-service acceptance level load.

1) Configuration optimization with rigid joints

The sofa frame is analyzed making the assumption that all joints are rigid (fixed

connections). Table II-2 in Appendix II shows stresses in the frame elements. The

maximum torsion stress is 3.6 N/mm2 (in red) in the two bottom stretchers. In comparison

with the calculations of shear in-plane (0.7 N/mm2) in Table 7.5, it becomes clear that

configuration (a) in Figure 7.4 does not work, since two bottom stretchers are over-

stressed, as can be seen in Figure 7.6 (a).

With the same proceeding, configuration (b) was analyzed and results from Table II-3 in

the Appendix II demonstrate that the maximum torsion stress is still too large (about 2

N/mm2), which appears on the two front stumps and back posts, as can be seen in Figure

7.6 (b). When two more pieces of stretchers are added, as shown in configuration (c) in

Figure 7.4, the stress level is reduced and then becomes 0.2 N/mm2, as given in Table II-4

in the Appendix II and Figure 7.6 (c). It can be concluded that the configuration (c) is the

optimum among the three configurations.

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(a)

(b)

(c)

Figure 7.6 OSB sofa frame with torsion stress bars for configurations (a), (b) and (c).

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2) Semi-rigid joints

The sofa frame is then analysed with the assumption that all joints are semi-rigid. The

properties of each type of joint are used as inputs into the finite element model for the

frame of configuration (c). The results of joint displacements are given in Table 7.6. And

the results of element joint forces in the links are shown in Table 7.7.

Table 7.6 Joint displacements under light-service acceptance level load. Type of joint Translation displacement Rotation displacement

Effective stiffness

(N/mm) U1 (mm) U2 (mm) U3 (mm) R1(Radians) R2(Radians) R3(Radians)

Metal Screw/Staplea Screw/Staple Screw/Staple Screw/Staple Screw/Staple Screw/Staple Screw/Staple

fixed fixed 7.7/7.7 0.8/0.8 8.7/8.7 0.0079/0.0079 0.0170/0.0170 0.0086/0.0086

5000 fixed 10.6/10.6 0.7/0.7 9.6/9.6 0.0058/0.0058 0.0241/0.0241 0.0115/0.0115

1000 fixed 10.6/10.6 0.7/0.7 10.9/10.9 0.0060/0.0060 0.0241/0.0241 0.0115/0.0115

5000 1000 13.9/13.9 3.1/4.2 10.7/10.7 0.0067/0.0067 0.0311/0.0311 0.0339/0.0362

5000 500 13.9/13.9 3.1/4.2 10.7/10.7 0.0067/0.0067 0.0311/0.0311 0.0339/0.0362

1000 1000 13.9/13.9 3.1/4.2 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365

1000 500 13.9/13.9 3.1/4.2 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365

1000 200 13.9/ 3.1 12.0 0.0067 0.0311 0.0342

1000 100 13.9/13.9 3.1/4.1 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365

1000 50 13.9/13.9 3.0/4.1 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365

1000 10 13.9/13.9 10.4/12.6 12.0/12.0 0.0067/0.0067 0.0311/0.0311 0.0342/0.0365

1000 8 13.9/13.9 13.5/16.3 12.0/12.0 0.0067/0.0066 0.0311/0.0311 0.0342/0.0365

1000 7 13.9 15.6 12.0 0.0067 0.0311 0.0342

1000 5 13.9/13.9 22.3/27.0 12.0/12.0 0.0067/0.0066 0.0311/0.0311 0.0342/0.0365

1000 1 13.9/13.9 95.1/117 12.0/12.0 0.1295/0.1600 0.0311/0.0311 0.0342/0.0365

1000 0 13.4/14.4 359/509 12.0/16.9 19.1/0.6740 0.0311/0.0311 0.0342/0.0366

400 100 14.0/14.0 3.0/4.1 14.5/14.5 0.0068/0.0067 0.0311/0.0311 0.0347/0.0369

400 10 14.0/14.0 14.5/13.5 14.5/14.5 0.0248/0.0221 0.0197/0.0311 0.0369/0.0347

300 100 14.0/14.0 3.0/4.1 15.8/15.8 0.0068/0.0067 0.0311/0.0311 0.0350/0.0371

200 100 14.1/14.1 3.0/4.1 18.5/18.5 0.0070/0.0068 0.0311/0.0311 0.0354/0.0375

100 100 14.3 3.0 26.7 0.0074 0.0385 0.0364

a All screws or staples joints except four bottom metal-plate joints.

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Table 7.7 Element joint big forces in the links under light-service acceptance level load.

Translation Rotation Link

F1 F2 F3 M1 M2 M3

Discription No. (N) (N-mm)

4 399

4 -399

5 -521

Two joints

between upright

with top rail 5 521

10 1635

10 -1635 -124565 8209

11 1619 -192001

11 -1619 -8211

12 -1634 124565 -14646

12 1634

13 -1616 14645

Four joints

between front

rail with front

stump or back

rail with back

post

13 1616 108924

18 1758

18 -1758

19 1740

19 -1740

24 1740

24 -1740

25 1758

Four joints

between front

rail with

stretcher or

back rail with

stretcher

25 -1758

Compare with 890 1779 1779 210209 607376

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From Table 7.6, with the exception of four metal-plate joints on the bottom of the sofa

frame, the joints using either screws or staples do not influence joint displacements. When

1000 N/mm used as metal-plate multi-linear elastic effective stiffness in U1, U2 and U3, the

multi-linear elastic effective stiffness of screw or staple in R1, R2 and R3 could be chosen

even as small as 10N/mm, the displacements were still acceptable (the blue line in Table

7.6) compared with the first line (when all joints are fixed). When metal-plate multi-linear

elastic effective stiffness in U1, U2 and U3, changed to 400N/mm, and the multi-linear

elastic effective stiffness of screw or staple in R1, R2 and R3 were 10N/mm, the results of

displacements were also acceptable. So that 400N/mm was the minimum multi-linear

elastic effective stiffness in U1, U2 and U3 for the metal-plate joint, and 10N/mm was the

minimum stiffness in R1, R2 and R3 for the screw or staple joint.

As can be seen in Table 7.7, the biggest axial force F1 was 521 N and it happened at the

joint between upright with top rail. Compared with screw or staple withdrawal forces (890

N) from Table 7.1, either screw or staple can hold this force. The biggest lateral forces (F2

and F3) were 1758 N and 1635 N, and they were at the four joints between front rail with

front stump and back rail with back post. Compared with screw or staple lateral forces

(2224 N or 1779 N) from Table 7.1, both screw and staple can support this force. The same

for the moment, the biggest out-of-plane moment was 192001 N-mm (M2), it also

happened at the joint between front rail with front stump and back rail with back post.

Comparison was made with G3 (two pairs of 51 by 152-mm) metal-plate out-of-plane

moment (210209 N-mm) from Table 6.3, this metal-plate joint can be used here. The

biggest in-plane moment (M3) (14646 N-mm) was at the joint between front rail with front

stump or back rail with back post, and it far smaller than any tested metal-plate in-plane

moment (min. 607376 N-mm) from Table 5.5. But be noticed that all these forces were

from either static analyse or static tests, if taking into account of fatigue effects (about

double of forces or moments), other stronger joints had to be found.

2. Sofa frame model under medium-service acceptance level load.

Table 7.8 presents the joint displacement under medium-service acceptance level load.

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Table 7.8 Joint displacements under medium-service acceptance level load. Type of joint a Translation displacement Rotation displacement

Effective stiffness (N/mm) U1 U2 U3 R1 R2 R3

Metal Screw (mm) (mm) (mm) (Radians) (Radians) (Radians)

fixed fixed 10.2 1.0 11.7 0.0105 0.0227 0.0115

5000 fixed 14.2 0.9 12.7 0.0078 0.0321 0.0154

1000 fixed 14.2 0.9 14.5 0.0080 0.0321 0.0154

5000 5000 18.5 5.4 14.3 0.0089 0.0415 0.0485

5000 1000 18.5 5.6 14.3 0.0089 0.0415 0.0483

1000 2000 18.6 5.5 16.0 0.0089 0.0415 0.0487

1000 1000 18.6 5.6 16.0 0.0089 0.0415 0.0487

fixed 1000 11.7 5.4 13.0 0.0120 0.0256 0.0417

fixed 100 11.7 6.1 13.1 0.0132 0.0256 0.0416

fixed 50 11.7 12.5 13.3 0.0237 0.0256 0.0416

fixed 45 11.7 14.3 13.4 0.0260 0.0256 0.0416

fixed 40 11.7 16.5 13.5 0.0289 0.0256 0.0416

fixed 10 11.7 75.0 15.4 0.1057 0.0256 0.0416

fixed 1 11.7 632 34.0 0.8364 0.0256 0.0419 a All screws joints except four bottom metal-plate joints.

From Table 7.8, the results of joint displacements under medium-service acceptance level

load were rather different from the light-service acceptance level. When metal-plate multi-

linear elastic effective stiffness in U1, U2 and U3 were chosen 1000 N/mm, the multi-linear

elastic effective stiffness of screw or staple in R1, R2 and R3 should be fixed, then the

displacements were acceptable (the blue line in Table 7.7) comparing with the first line

(when all joints are fixed). But it is more reasonable to think that the screw multi-linear

elastic effective stiffness in R1, R2 and R3 were used 45N/mm, and metal-plates should be

fixed, these four critical joints on the bottom (front rail – front stump, back rail – back

post) should be reinforced (glued with corner block etc.) to create rigid connections.

Also, Table II-5 in the Appendix II gives stresses in the frame elements. The maximum

bending stress is 23.2 N/mm2 (in red). In comparison with the bending strength (26.5

N/mm2) in Table 7.5, it is found that this frame can serve the medium-service acceptance

level load, but it is close to the limit.

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In addition, as can be seen in Table II-6 in Appendix II, the biggest lateral forces (F2) were

2307 N, and they were at the four joints between front rail with stretcher and back rail with

stretcher. Compared with screw or staple lateral forces (2224 N or 1779 N) from Table 7.1,

neither screw nor staple can support this force.

3. Sofa frame model under heavy-service acceptance level load.

The joint displacements under heavy-service acceptance level load presented in Table 7.9,

which showed that even if all joints are fixed, the displacements are still too large. Table II-

7 in the Appendix II shows stresses in the frame elements. The maximum bending stress is

34.8 N/mm2 (in red), higher than the bending strength (26.5 N/mm2) in Table 7.5. Also, the

maximum torsion stress is 2.6 N/mm2 (in red), which exceeds the shear in-plane strength

(0.7 N/mm2) in Table 7.5. Consequently, the frame can not serve this heavy-service

acceptance level load.

In addition, from Table II-8 in Appendix II, the biggest lateral forces (F2) were 3461 N and

at the four joints between front rail with stretcher and back rail with stretcher. They were

much bigger than screw or staple lateral forces (2224 N or 1779 N) from Table 7.1, neither

screw nor staple can support this force.

Table 7.9 Joint displacements under heavy-service acceptance level load.

Type of joint a Translation displacement Rotation displacement

Effective stiffness (N/mm) U1 U2 U3 R1 R2 R3

Metal Screw (mm) (mm) (mm) (Radians) (Radians) (Radians)

fixed fixed 15.4 1.0 17.5 0.0158 0.0341 0.0172

5000 fixed 21.3 1.4 19.1 0.0117 0.0481 0.0231

1000 1000 27.9 8.4 24.0 0.0133 0.0623 0.0730 a All screws joints except bottom four metal-plate joints.

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7.4 Conclusions and Recommendations Three configurations of a three-seat sofa frame made of OSB with two types of joints

(screws with metal-plates and staples with metal-plates) under three levels of service

acceptance loads were modeled. Two types of connections were used in the model: rigid

(fixed) and semi-rigid (with real properties of connections). Results allowed making the

following conclusions.

1) The orientation of the components of the sofa frame has a strong impact on the

resistance.

2) When the sofa frame model is under light-service acceptance level load, using either

screws with four metal-plate joints or staples with four metal-plate joints does not change

the joint displacements remarkably. Regarding the inputs in semi-rigid joints model,

400N/mm was the minimum multi-linear elastic effective stiffness in U1, U2 and U3 for

metal-plate joint, and 10N/mm was the minimum effective stiffness in R1, R2 and R3 for

screw or staple joint. The biggest axial force F1 was smaller than screw or staple

withdrawal resistance. The biggest lateral forces F2 and F3 were smaller than screw or

staple lateral resistance. Out-of-plane moment M2 was less big than metal-plate (G3) out-

of-plane moment tested before. In-plane moment M3 was smaller than any metal-plate in-

plane moment tested. It could be concluded that using either all screws or all staples except

four metal-plate joints on the bottom of sofa frame can support light-service acceptance

level load.

3) When the sofa frame model is under medium-service acceptance level load, the limit

screw multi-linear elastic effective stiffness in R1, R2 and R3 could be 45N/mm, and metal-

plate should be fixed. In order to pass this acceptance level load, the four critical joints on

the bottom (front rail – front stump, back rail – back post) should be reinforced (e.g., glued

with corner block etc.) to create rigid connections. The biggest lateral forces (F2) were

bigger than screw or staple lateral resistance. Either screw or staple had difficulty to hold

this force.

4) It was found that the frame of configuration (c) could not serve the heavy-service

acceptance level load, because the bending strength of the frame material was exceeded

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(34.8 vs. 26.5 N/mm2). The biggest lateral forces (F2) were much bigger than screw or

staple lateral resistance. Neither screw nor staple can support this force.

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Summary and Conclusions

Summary

Designing, testing and modeling of joints and attachment systems for the use of OSB in

upholstered furniture frames is the focus of this dissertation. The key objective of the study

is to develop the information needed for the engineered design of joints used in upholstered

furniture frames constructed of OSB. To achieve the main objective, five aspects were

studied:

1. Localized OSB panel properties and fastener characteristics.

Basic material properties (density, density profile, internal bond, MOE, MOR and moisture

content) were evaluated in order to be used as input for the modeling of joints of OSB sofa

frame. The localized density effects on fastener holding capacities in wood-based panels

under static and cyclic loading were evaluated. The panels were: 11-mm OSB, 15-mm

OSB, 18-mm OSB, 16-mm MDF and 16-mm PB. Screws and staples were chosen as they

are common types of fasteners in upholstered furniture industry to determine their

performance in OSB joints. The tests including screw and staple face and edge withdrawal,

screw lateral resistance, and screw and staple head pull-through.

2. Moment capacities of OSB gusset-plate joints for upholstered furniture under

static and fatigue loads.

A) The static moment capacity of T-shaped, end-to-side joints with two gusset-plates was

determined experimentally and analytically for gusset-plates of different lengths (102, 152,

203, 254 and 305-mm) (4, 6, 8, 10 and 12-in) attached with 25-mm (1.0-in) and 38-mm

(1.5-in) long staples with and without adhesive. Effects of gusset-plate length, number and

length of staples, placement of staples, and glue application on the static load capacity of

T-shape OSB gusset-plate joints were investigated.

B) The fatigue performance of T-shaped, end-to-side gusset-plate joints made of OSB was

investigated. A total of 108 stapled and glued-stapled joints with gusset-plates of different

lengths (152, 203 and 254-mm) (6, 8 and 10-in) were subjected to one-side fatigue stepped

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bending loads, and comparisons with their static moment resistance were made to

determine the influence of the gusset-plate size, material and fastening system on the static-

to-fatigue moment capacity ratio and on failure modes of the joints.

3. Static and fatigue bending resistance of metal-plated joints constructed of OSB for

upholstered furniture.

Metal-plate connectors are commonly used to connect critical joints in upholstered

furniture frames due to their high load resistance, rapid assembly, and easy connection of

members with uniform thickness.

A) Static moment capacity of T-shaped joints with metal-plates was determined

experimentally for six different configurations. Effects of metal-plate width and number of

metal-plates on the static bending resistance of T-shaped OSB metal-plated joints were

investigated.

B) The fatigue performance of T-shaped, end-to-side, metal-plated joints made of OSB was

evaluated. A total of 80 joints with metal plates of different configurations were subjected

to one-side fatigue stepped bending loads, and comparisons with their static moment

resistance were made to determine the influence of the metal-plate configuration, material

and fastening system on the static-to-fatigue moment capacity ratio and on failure modes of

the joints.

4. Static out-of-plane bending resistance of gusset-plate and metal-plate joints

constructed of OSB for upholstered furniture frames

The out-of-plane moment capacity of OSB joints is needed in upholstered furniture

designs, since the load acts on the sofa seat springs which transfer the out-of-plane bending

on the front rail. Static out-of-plane moment capacity of T-shaped joints with gusset-plates

and metal-plates were determined experimentally for different configurations, and the

comparison with the in-plane moment capacities were also made.

5. Finite element model of sofa frame made of OSB

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In order to use a new material in the assembly of a conventional sofa structure, it is useful

to perform preliminary modeling using the finite elements method. Modeling allows the

elimination of numerous experimental tests and opens a new way to optimize the sofa

structure by the assistance of computer. Three configurations of three-seat sofa frame made

of OSB with two types of connections under three service level acceptance loads were

modeled using commercial finite element software SAP 2000. Two types of links were

used in the models: rigid (fixed) and semi-rigid (with the properties of joints determined

experimentally).

Conclusions

Based on the observations and results of experimental tests and finite element modeling,

the following conclusions were made about joints and attachment systems performance for

the use of OSB in upholstered furniture frames.

1 The localized density effects on fastener holding capacities in wood-based panels

under static and cyclic loading

• The composition of panel material was the most important factor for the fastener

holding capacity, but for the same type of panel and the same type of fastener

holding capacity, localized density was an importance factor.

• Among tested panels, OSB showed the highest density variation in plane and

through thickness, which was more critical to the screw than to the staple holding

capacities. The density of MDF panels varied the least, which generally led to a

more uniform fastener holding capacity.

• Cyclic tests of fasteners in wood-based panels showed similar results to the

corresponding static tests. For the type of cyclic loading regimes used in this study

(90 cycles at different load levels), no significant differences were observed

between static and cyclic behavior in terms of ultimate fastener holding capacity in

most cases.

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• Generally, fasteners driven in low density zones fail at lower load levels than those

driven in high density zones. Increasing panel density will ultimately improve the

fastener holding capacity. However, reducing the variation in localized density by

producing panels with more consistent and uniform density distribution for use in

the upholstered furniture industry could be more effective and possibly more

economical for improving the fastener performance.

2 Moment capacities of OSB gusset-plate joints for upholstered furniture

• The application of glue was the most important factor affecting the performance of

the joints allowing strength increase up to 27%.

• For the tested configurations, an increase in length of gusset-plate from 102 to 203-

mm (4 to 8-in) increased the peak load for both glued and unglued joints, but

further increase of the gusset-plate length did not enhance the strength of the joints.

• Twice as many 25-mm (1.0-in) long staples had to be used to achieve similar load

levels with 38-mm (1.5-in) long staples for unglued gusset-plate joints.

• Changing positions of staples in gusset-plates did not affect the strength of the

joints of tested configurations.

• Failure modes depended on the size of the gusset-plates.

• Predicted and experimental reference resistance values for stapled joints were in

satisfactory agreement.

• The average value of 2.1 can be used as the passing static-to-fatigue ratio for design

of upholstered furniture frames with OSB gusset-plate joints. In other words, it is

advised to design gusset-plate joints so that they will not be loaded to more than 48

percent of their static moment capacity.

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• In the stapled joints, the higher ratios were associated with the staple withdrawal as

dominating failure mode. In the glued-stapled joints lower ratios were associated

with in-plane shear, and the higher ratios – with the rupture of the OSB panels.

3 Static and fatigue bending resistance of metal-plate joints constructed of OSB for

upholstered furniture

• For the same total width of metal-plates, the use of two pairs of plates was the most

important factor that affected the performance of the joints, allowing for strength

increase up to 50% in comparison with one pair of plates.

• An increase in the width of metal-plates from 51 to 102-mm (2 to 4-in) increased

the mean ultimate load considerably for both one and two pairs of plates. In

assemblies with one pair of 152 by 152-mm (6 by 6-in) metal-plates, the mean

ultimate load was slightly lower than that for assemblies with two pairs of 51 by

152-mm (2 by 6-in) plates.

• The stiffness values for the joints with one pair of plates were lower than those for

joints with two pairs of plates. The type of failure modes observed depended on the

size and configuration of the plates. Among the tested configurations, the joint with

two pairs of 51 by 152-mm (2 by 6-in) plates was the strongest and showed the

highest stiffness.

• A static-to-fatigue ratio of 2.5 can be adopted as the passing ratio for design of

upholstered furniture frames with metal-plated joints. In other words, it is advised

to design metal-plate joints so that they will not be loaded to more than 40 percent

of their static moment capacity.

• In joints with two pairs of plates, a mixture of metal-plate yield and shear-out of

OSB was the dominant failure mode. In joints with one pair of plates, lower fatigue

life was associated with predominantly metal-plate yielding.

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4 Static out-of-plane bending resistance of gusset-plate and metal-plate joints

constructed of OSB for upholstered furniture frames

• In general, all metal-plate and gusset-plated joints out-of-plane moment capacities

were, on average, 1/4 of the in-plane moment capacities.

• For the same width of metal-plates, the use of two pairs of plates affected

significantly the performance of the joints, allowing for strength increase up to 14%

in comparison with one pair of plates.

• An increase in the width of metal-plates from 51 by 102-mm (2 to 4-in) increased

the mean ultimate load considerably (19% and 15%) for both one pair and two pairs

of metal-plate joints.

• Assemblies with two pairs of 51 by 152-mm (2 by 6-in) metal-plates had the

highest ultimate unit load among all metal-plate configurations tested.

• The stiffness values for the joints with metal-plates demonstrated similar tendency

as the values of the ultimate load. Similar stiffness values were observed for metal-

plate joints and unglued gusset-plate joints.

• For gusset-plate joints, application of glue was the most important factor affecting

the stiffness of the joints, which allowed for stiffness increase up to 87%, but not

for the mean ultimate load of the joints.

• An increase in length of gusset-plate from 102 by 203-mm (4 to 8-in) increased the

peak load for both glued and unglued joints, but further increase of gusset-plate

length did not enhance the strength of the joints. Changing positions of staples in

gusset-plates did affect the strength of the joints of tested configurations.

• The gusset-plate joints resisted higher out-of-plane moments than the metal-plate

joints (max. 979 N (220 lbf) vs. max. 596 N (134 lbf)). It can be concluded that

metal-plates do not resist out-of-plane moment well.

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5 Finite element model of sofa frame made of OSB

• The orientation of the components of the sofa frame has a strong impact on the

resistance.

• When the sofa frame model is under light-service acceptance level load, using

either screws with four metal-plate joints or staples with four metal-plate joints

does not change the joint displacements remarkably. Concerning the inputs in semi-

rigid joints model, 400N/mm was the minimum multi-linear elastic effective

stiffness in U1, U2 and U3 for metal-plate joint, and 10N/mm was the minimum

effective stiffness in R1, R2 and R3 for screw or staple joint.

• When the sofa frame model is under medium-service acceptance level load, the

limit screw multi-linear elastic effective stiffness in R1, R2 and R3 could be

45N/mm, and metal-plate should be fixed. In order to pass this acceptance level

load, the four critical joints on the bottom (front rail – front stump, back rail – back

post) should be reinforced (e.g., glued with corner block etc.) to create rigid

connections.

• It was found that the frame of configuration (c) could not serve the heavy-service

acceptance level load, because the bending strength of the frame material was

exceeded (34.8 vs. 26.5 N/mm2).

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Recommendations for Future Work

Finite element modeling should be continued, and the experimental tests on the real-scale

sofa frame should be done for the verification and validation of the model.

For the experimental tests on joints and full-scale sofas, different types of joints should be

tested in various directions to obtain more data for modeling (e.g., face to face and face to

edge staples with glue, screws with glue; solid wood corner block glued and screwed

joints, etc.). Shear tests of joints could be included. Joints made with the use of other

materials, such as oriented strand lumber (OSL) or laminated strand lumber (LSL) could be

tested as well.

With the use of FEM, different sofa configurations should be designed and analyzed. Other

types of loading should be applied to the model, for instance, cyclic fatigue loads.

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Bibliography Anonymous. 1980. MDF-Basic Properties and Performance. Furniture Industry Research

Association. FIRA Handbook No.1. APA – The Engineered Wood Association (APA). 1982. Technical Note E830A. Fastener

loads for plywood - screws. Tacoma, WA. ___________. 1993. Technical Topics. Form No. TT-051. Screw withdrawal from APA-

trademarked OSB. Tacoma, WA. ___________. 1997. Take a seat with engineered wood: wood structural panels add

strength and quality to furniture framing. American Society for Testing and Materials (ASTM). 2003a. D1037 Test methods for

evaluating properties of wood-base fiber and particle panel materials. Annual Book of ASTM Standards. West Conshohocken, PA.

___________. 2003b. D1761 Test methods for evaluating mechanical fasteners in wood.

Annual Book of ASTM Standards. ASTM, West Conshohocken, PA. ____________. 2003c. D4442. Test methods for direct moisture content measurement of

wood and wood-base materials. Annual Book of ASTM Standards. West Conshohocken, PA.

___________. 2005a. D1037-99 Test methods for evaluating properties of wood-base fiber

and particle panel materials. Annual Book of ASTM Standards. West Conshohocken, PA.

___________. 2005b. D5457-04 Standard specification for computing the reference

resistance of wood-based materials and structural connections for load and resistance factor design. Annual Book of ASTM Standards. West Conshohocken, PA.

Bao, Z, and C. A. Eckelman. 1995. Fatigue Life and Design Stresses for Wood Composites

Used In Furniture. Forest Products Journal 45 (7/8): 59-63. BIFMA-the Business and Institutional Furniture Manufacturer’s Association (BIFMA).

2001. Grand Rapids, MI. Canadian Standards Association (CSA). 2003 Rev. CAN/CSA-0325.0-92. Construction

Sheathing. Canadian Wood Council. 2005. Wood Design Manual – Canadian Standard Association

(CSA-O86). Engineered Design in Wood. Mississauga, ON, Canada.

Page 224: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

206

Chen, B. 2003. Fatigue performance of wood-base composites as upholstered furniture frame stock. M.S. thesis. Mississippi State University, Starkville, MS, USA. 82 pp.

Chow, P., J. D. McNatt, S. J. LAmbrechts, and G. Z. Gertner. 1988. Direct withdrawal and

head pull-through performance of nails and staples in structural wood-based panel materials. Forest Prod. J. 38 (6): 19-25.

Composite Panel Association (CPA). 1999. American National Standard ANSI A208.1.

Particleboard. CPA, Gaithersburg, MD. ________________________(CPA). 2002. American National Standard ANSI A208.2.

Medium density fiberboard (MDF) for interior applications. CPA, Gaithersburg, MD.

Desroches-Noblecourt, C. 1963. Tutankhamen. New York Graphic Society, New York. Eckelman, C. A. 1967. Furniture mechanics: chair frame analysis and design. Forest Prod.

J. 17 (9): 100-106. ________. 1968. Furniture frame analysis and design. Unpublished Ph. D. thesis. Purdue

Univ., W. Lafayette, Ind. USA. 231 pp. ________. 1969. Engineering concepts of single-pin dowel joint design. Forest. Prod. J. 19

(12): 52-60. ________. 1970a. The fatigue strength of two-pin moment-resisting dowel joints. Forest

Prod. J. 20 (5):42-45. ________. 1970b. CODOFF-computer design of furniture frames-user’s manual. Purdue

Univ. Agri. Expt. Sta. Res. Bul. No.857, West Lafayette, Ind. USA. ________. 1970c. CODOFF-computer design of furniture frames-engineering concepts.

Purdue Univ. Agri. Expt. Sta. Res. Bul. No.863, West Lafayette, Ind. USA. ________. 1971a. Bending strength and moment-rotation characteristics of two-pin

moment-resisting dowel joints. Forest Prod. J. 21(3): 35-39. ________. 1971b. CODOFF-computer design of furniture frames-program documentation.

Purdue Univ. Agri. Expt. Sta. Res. Bul. No.876, West Lafayette, Ind. USA.

________. 1971c. Designing joints with gusset plates. Furniture Design and manufacturing 43(9): 72-79.

________. and M. D. Hill. 1971. Textured versus plain dowels-Which are stronger?

Furniture Design and Manufacturing, Vol. 43, No.4.

Page 225: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

207

________. 1974. Reasonable design stresses for woods use in furniture. Purdue Univ. Agri. Expt. Sta. Res. Bul. No.916, West Lafayette, Ind. USA.

________. 1977. Evaluating the strength of library chairs and tables. Library Technology

Reports 13(4): 341-433. ________. 1978a. Strength design of furniture. Tim Tech, Inc., West Lafayette, Ind. USA.

231pp. ________. 1978b. Predicting withdrawal strength of sheet-metal-type screws in selected

hardwoods. Forest Prod. J. 28 (8): 25-28. ________. 1979. Withdrawal strength of dowel joints: Effect of shear strength. Forest

Prod. J. 29 (1): 48-52. ________, W. L. Hoover, R. W. Jokerst, and J. A. Youngquist. 1979. Utilization of red oak

press-lam as upholstered furniture frame stock. Forest Prod. J. 29 (5): 30-40. ________. 1980. The bending strength of furniture joints constructed with metal tooth

connector plates. International Journal of Furniture Research 2(1): 12-14 and 2(2): 40-42.

________, and D. Cassens. 1985. Withdrawal strength of dowels from wood composites.

Forest Prod. J. 35 (5): 55-60. ________. 1987. Bending strength, fatigue strength, stiffness, and allowable design

stresses for engineered strand lumber, oriented strand lumber plus, and engineered strand panel. A report prepared for the Weyerhauser Company. Furniture research center, Purdue Univ., West Lafayette, Ind. USA.

________. 1988a. The withdrawal strength of screws from a commerciality available

medium density fiberboard. Forest Prod. J. 38 (5): 21-24. ________. 1988b. Performance testing of furniture. Part II. A multipurpose universal

structural performance test method. Forest Prod. J. 38(4): 13-18. ________. 1989a. Strength of furniture joints constructed with through-bolts and dowel

nuts. Forest Prod. J. 39 (11/12): 41-48. ________. 1989b. Effective principles of product engineering and strength design for

furniture manufacturing. Product engineering and strength design manual presented Dec. 5-7, Grand Rapid, Michigan, USA.

________. 1991. Textbook of product engineering and strength design of furniture. Purdue

Univ., West Lafayette, Ind. USA.

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208

________, and J. Zhang. 1995. Uses of the Gerneral Service Administration performance test method for upholstered furniture in the engineering of upholstered furniture frames. Holz als Roh-und Werkstoff 53: 261-267.

________. 1998. Holding strength of T-nuts in solid wood and wood composites. Holz als

Roh-und Werkstoff 56(1998):253-258. ________, and Y. Z. Erdil. 1998. Joint design manual for furniture frames constructed of

plywood and oriented strand board. 33 pp. ________, Y. Z. Erdil and J. Zhang. 2002. Withdrawal and bending strength of dowel

joints constructed of plywood and oriented strand board. Forest Prod. J. 52 (9): 66-74.

EN 1995-1-1: 2004 (E). 2004. Eurocode 5: Design of timber structures. European

Committee for Standardization (CEN), Brussels, Belgium. Erdil, Y. Z. 1998. Strength analysis and design of joints of furniture frames constructed of

plywood and oriented strand board. M. S. thesis. Purdue Univ., W. Lafayette, Ind. USA. 145 pp.

________, J. Zhang, and C. A. Eckelman. 2002. Holding strength of screws in plywood

and oriented strand board. Forest Prod. J. 52 (6): 55-62. ________, J. Zhang, and C. A. Eckelman. 2003a. Staple holding strength of furniture frame

joints constructed of plywood and oriented strand board. Forest Prod. J. 53 (1): 70-75.

________, J. Zhang and C. A. Eckelman. 2003b. Withdrawal and bending strength of

dowel-nuts in plywood and oriented strand board. Forest Prod. J. 53 (6): 54-57. Fakopp Enterprise. 2005. Screw withdrawal force meter. www.fakopp.com. Gebremedhin, K. G., M. C. Jorgensen, and C. B. Woelfel. 1992. Load-slip characteristics

of metal plate connected wood joints tested in tension and shear. Wood and Fiber Sciences, 24(2), 1992, pp. 118-132.

General Service Administration (GSA). 1998. Upholstered furniture test method. FNAE-

80-214A. Furniture Commodity Center, Federal Supply Services, Washington, D.C.

Geschwindner, L. F., R.O. Disque, and R. Bjorhovde. 1994. Load and resistance factor

design of steel structures. Prentice-Hall, Inc. Englewood Cliffs, N. J. USA. 456pp. Hayashi, T., H. Sasaki, and M. Masuda. 1980. Fatigue properties of wood butt joints with

metal plate connectors. Forest Prod. J. 30(20: 49-54.

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209

Hill, M. D. and C. A. Eckelman. 1973. Flexibility and bending strength of mortise and tenon joints. Furniture design and manufacturing, Vol. 45, No.1 and 2. Journal # 4758.

Johansen, K. W. 1949. Theory of timber connections. International Association for Bridge

and Structural Engineering, 9: 249-262. Johnson, J. W. 1967. Screw-holding ability of particleboard and plywood. Oregon State

School of Forestry. Forest Resources Lab. Rep. T-22. Moura, J. D. D. M., C. Bastian, G. Duchanois, J. M. Leban, and P. Triboulot. 1995. The

influence of wood density on metal-plate connector mechanical behavior under cyclic loading. Forest. Prod. J. 45(11/12): 74-82.

Picado, F. 1988. Development of an expert system for upholstered furniture. Unpublished

M. S. thesis. Purdue Univ., West Lafayette, Ind. USA. 166pp. Rajak, Z. I. B. H. A., and C. A. Eckelman. 1993. Edge and face withdrawal strength of

large screws in particleboard and medium density fiberboard. Forest Prod. J. 43(4):25-30.

Resource Information Systems, Inc. (RISI). 2004. North American Wood Panels Forecast.

Volume 4, Number 1. Rosowsky, D. V. and M. O. Hunt. 1995. Increasing the competitiveness of structural wood

composites using probabilistic methods. Forest Prod. J. 45 (11/12): 83-86. Sackey, E., K. Semple, H. Park, and G. Smith. 2005. Properties survey of furniture grade

particleboard Part 1- Variation within M2 grade and a reassessment of the relationships between density, bond strength, and screw withdrawal resistance. Forest Products Society 59th international convention, June 19-22, 2005. Quebec city, Quebec, Canada.

Salmon, C. S. and J. E. Johnson.1990. Steel structures. 3rd ed. Harper Collins Publ. Inc.

New York, N. Y. USA. 1086 pp. SAP 2000. Structural Analysis Program. Computers and Structures., Inc. 1995 University

Ave., Berkeley, CA 94704, USA Website: csiberkeley.com Semple K., E. Sackey, H. Park, and G. Smith. 2005. Properties survey of furniture grade

particleboard Part 2- MS and M2 grade comparison and a practical in-situ test for internal bond strength. Forest Products Society 59th international convention, June 19-22, 2005. Quebec city, Quebec, Canada.

Structural Board Association (SBA). 2004. OSB expending beyond commodity sheathing

applications. http://www.osbguide.com/pdf_news/SBA-0407newsrelease.pdf

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Tabarasi, E. 2002. Suitability of Oriented Strand Board for Upholstered Furniture: Market Analysis. Forintek Canada Corp. report No. 3251.

Tackett, B. and J. Zhang, 2007. A biaxial load cell design for simultaneous measurement of

horizontal and vertical spring forces in sinuous spring-supported seating. Journal of Testing and Evaluation, Vol. 35, No. 4 Paper ID JTE100112. Available online at: www.astm.org

Wang, S. and R. M. Knudson. 2002. Suitability of oriented strand board for upholstered

furniture technical analysis. Forintek report No. 3251. Canadian forest service value-added report . 64pp.

Wang, X., A. Salenikovich, and M. Mohammad. 2007a. Localized density effects on

fastener holding capacities in wood-based panels. Forest Prod. J. 57(1/2): 103-109. ________, A. Salenikovich, M. Mohammad, C. Echavarria, and J. Zhang. 2007b. Moment

capacity of oriented strandboard gusset-plate joints for upholstered furniture. Part 1. Static Load. Forest Prod. J. 57(7/8): 39-45.

________, A. Salenikovich, M. Mohammad, and J. Zhang. 2007c. Moment capacity of

oriented strandboard gusset-plate joints for upholstered furniture. Part 2. Fatigue Load. Forest Prod. J. 57(7/8): 46-50.

________, M. Mohammad, A. Salenikovich, R. Knudson, and J. Zhang. 2007d. Static

bending strength of metal-plate joints constructed of oriented strandboard for upholstered furniture frames. Submitted to Forest Prod. J. February 2007.

________, M. Mohammad, A. Salenikovich, R. Knudson, and J. Zhang. 2007e. Fatigue

bending strength of metal-plate joints constructed of oriented strandboard for upholstered furniture frames. Accepted by Forest Prod. J. February 2007.

Williams, D. and R. Nielson. 1999. Machining and fastener withdrawal tests of MDF, OSB

and Plywood. Forintek report No. W-1882, 12 pp. Wood Handbook, 1999: wood as an engineering material, Forest products Laboratory.

Department of Agriculture, Forest Service. Madison, WI. 463p. Zhang, J. 1995. Structural analysis and design of sofa front rail. Unpublished Ph. D. thesis.

Purdue Univ., W. Lafayette, Ind. USA. 156 pp. ________. 2000. Research provides solutions for upholstered seating frame failures.

Modern Woodworking Magazine. 14(6): 33-36. ________, F. Quin, and B. Tackett. 2001a. Bending fatigue life of two-pin dowel joints

constructed of wood and wood composites. Forest Prod. J. 51 (10): 73-78.

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________, D. Lyon, F. Quin, and B. Tackett. 2001b. Bending strength of gusset-plate joints constructed of wood composites. Forest Prod. J. 51(5): 40-44.

________,Y. Z. Erdil, and C. A. Eckelman. 2002a. Lateral holding strength of dowel joints

constructed of plywood and oriented strand board. Forest Prod. J. 52 (7/8): 83-89. ________, Y. Z. Erdil, and C. A. Eckelman. 2002b. Torsional strength of dowel joints

constructed of plywood and oriented strand board. Forest Prod. J. 52 (10): 89-94. ________, F. Quin, and B. Tackett. 2002c. Direct withdrawal strength of multi-staple joints

in pine plywood. Forest Prod. J. 52 (5): 61-66. ________, F. Quin, B. Tackett, and S. Park. 2002d. Direct withdrawal strength of single-

staple joints in pine plywood. Forest Prod. J. 52 (2): 86-91. ________, V. Yadama, and F. Quin. 2002e. Resistance of southern yellow pine to direct

withdrawal of staples. Forest Prod. J. 52 (9): 75-81. ________, G. Li, and T. Jr. 2003. Bending fatigue life of two-pin dowel joints in furniture

grade pine plywood. Forest Prod. J. 53 (6): 1-7. ________, and M. Maupin. 2004. Face lateral and withdrawal resistances of staple joints in

furniture-grade pine plywood. Forest Prod. J. 54(6): 40-46. ________, Y. Yu, and F. Quin. 2005. Moment capacity of metal-plate-connected joints in

furniture grade pine plywood. Forest Prod. J. 55(5): 45-51. ________, Y. Yu, and F. Quin. 2006. Bending fatigue life of metal-plate-connected joints

in furniture-grade pine plywood. Forest Prod. J. 56(11/12): 62-66.

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APPENDIX I Visiting Several Upholstered Furniture

Companies

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I.1 Objective of the Visit We visited upholstered furniture companies in order to understand the context of this

segment of the furniture industry and to see what are the industry issues of concerns

relating to the usage of OSB for framing material and whether it is possible to work

together to improve frame designs.

I.1.1 Berkline Upholstered Furniture

I.1.1.1 Profile

Berkline (Canada) is a branch of Berkline Furniture, a Moorestown, Tennessee, U.S. based

company. The Canadian branch has over 150 employees in Montréal. We observed that

Berkline (Canada) is a small traditional furniture company doing a lot of manual work.

Their total production in one year is equal to a week’s production at the company’s main

site in the United States.

Berkline (Canada) produces mainly recliners for one, two or three persons. The company

uses solid wood, plywood, OSB, particle board, MDF and combinations of these.

I.1.1.2 Design

New designs are usually not made by Berkline (Canada). If there is a new design, its

mechanical performance has to be tested in the head office in the U.S.

I.1.1.3 Material A combination of solid wood with all kinds of wood based panels is being used. The focus

is on plywood, however.

(1) Solid Wood Berkline (Canada) does not use panel products for the front and back rails, but soft or hard

wood depending on the model and shape. The three person sofa, for instance, uses 3” (76

mm) hardwood.

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(2) Plywood Two types of plywood are used for the backs and seat frames.

a) Russian Plywood Berkline (Canada) used to rely on poplar plywood. After many call-backs due to broken

legs, the company switched to Russian birch plywood, No.1 or No.2, 1525 x 1525, 13

plies, 5/8” (16 mm) thickness. The company appreciates the high quality of the plywood,

and assures that it hardly has any problems with it.

b) SYP Plywood Apart from Russian birch plywood, Southern Yellow Pine plywood mixed with other hard

woods imported from the United States is also used. That plywood being used by Berkline

(Canada) is made of SYP for the exterior plies, while the interior is mostly made of yellow

poplar. More precisely, SYP is used for the front rail base of the sofas. It is 2” (51 mm)

thick. The back seat bases use plywood with clips on it, for back frames solid wood is

mixed with plywood.

(3) OSB OSB is only used for less structurally critical sections. The OSB used by Berkline (Canada)

is sources from Goodfellow, it is of the No. 1 Common sheathing panel grade, which is not

specially produced for furniture. Grade 1 has a uniform thickness of 3/8” (16 mm) for front

and 7/16” (11 mm) for back rails, while grade 2 has a high variation of thickness and

density.

The major problem of the company associated with OSB use is the splitting due to

fastening on edge. If there is too much glue inside the OSB, there can also be a problem

with staples bending. Moreover cutting OSB results in a considerable wear and tear on

saws and knives compared to plywood or solid wood.

(4) Particle Board

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Berkline (Canada) uses particle board mainly for less structurally demanding parts,

particularly to make foot and arm rests. Since particle board is not expensive and not too

heavy (i.e. we have to think of the whole seat for the balance of a rocking mechanism),

MDF with its weight is often inappropriate.

The company staples on the face and edge of the particle board, without any signs of

splitting. A bending test of 60 lbf (27 kg) is done for typical particle board while 45 lbf (20

kg) is used to test lower grades.

(5) MDF MDF used by Berkline is made by Uniboard and is preferred due to its weight and its light

colour. Berkline (Canada) uses a combination of MDF and plywood for arm rails,

connected with staples. For a three person sofa, the middle seat is made of MDF because it

does not move. It is painted in black to make it invisible for the customer.

I.1.1.4 Joints Staples are the main type of fastener used in jointing the main frame members together

since they can be inserted quickly. Apart from staples, screws, dowels, t-nut, toothed metal

connector plates and a kind of tenon-mortise are used as well.

(1) Staples Berkline (Canada) uses standard staples grade 19 from SENCO with 1 ¾” (44 mm) legs

and 1 ½” (38 mm) crown. Most staples are inserted with glue, however some are used in a

combination with metal gang nail plates.

(2) Dowels Birch dowels are used for solid wood and solid wood and plywood connections. Some

wood dowels are also used for crossing and rocking sections. Solid wood dowels are being

used on solid wood 5/4 front rails.

(3) Screws

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Screws manufactured by Robertson, are mainly used to reinforce certain glued joints in

some models. Nails are not used.

(4) Glue Berkline (Canada) uses Woodlok 40-0304 PVA (Polymer Vinyl Acetate) glue produced by

NACAN Ltd.

(5) Clips Clips made by Sigmatools Manufactory, Toronto, are used to attach springs for backs and

seats.

I.1.1.5 Testing

Mechanical tests are not conducted in the Canadian branch of the company. There are,

however, occasional drop tests, in which a sofa with a box is dropped from a height of 8

feet (2.44 m).

I.1.1.6 Recalls

With the poplar plywood previously used, leg joints often broke. Since the company has

switched to Russian plywood, broken leg joints have become very rare. Sometimes metal

plates are broken, though.

I.1.1.7 Possibility of switching to OSB instead of plywood The major problem with OSB at Berkline (Canada) is splitting once fasteners (i.e. staples,

screws) are driven in the panel edge. If there is too much glue inside, OSB staples can also

be bent due to the rigidity of the resin. Moreover, OSB cutting increases the wear and tear

on saws and knives. With wood material, the company saws 2000 to 3000 linear feet

without replacing the saw blade, while with OSB, after 400 feet, it has to be changed.

Cooperating with this small traditional furniture company with the aim of replacing the

materials used is difficult. My thought on this is that working with this company might be

easier but the benefit and impact on industry would be very limited because this company

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is a tiny subsidiary of a large American company. Hence the technology transfer potential

of our work with it would be very limited. Plus, since they use many materials already, the

improvements we could have would be only incremental (marginal). They already use

OSB to a limited extent and all they could do is use a little more of it. The impact of our

work in such context would be limited.

Contact:

Luc Fernandez

Directeur d’usine

Berkline inc.

8491 Ernest Cormier, Ville d’Anjou, Qc, H1J 1B5

[email protected]

I.1.2 Elran Upholstered Furniture

I.1.2.1 Profile Elran has been in the upholstery furniture business for about 36 years. Since 1988 they

have used a 250,000 square feet (2.3 hectares) building located in Pointe Claire, Montréal.

It has 750 employees and 12 production lines. Our observation is that Elran is a quite large,

modern and efficient furniture company.

Elran produces mainly (90%) recliners for one (lazy boy), two (love seats) or three (sofa)

persons. They are the 7th biggest recliner company in the world and the leader in Canada in

their category. Recliners hold 20% of the upholstered furniture market in North-America.

They produce 135,000 pieces/year (with an average of 2.2 seats per piece). More than 50%

of the production is made of leather and the rest in other types of fabric. Their products are

exported to Europe, the USA, Israel, Japan and other countries. 20-25% of the exports go

to the United States.

I.1.2.2 Design There are currently 15 people working in the research and development department of the

company. They do create new designs, but most products are based on standard frames.

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Backs and seats are all standardized, using the same frame concept design for all models.

The core of recliners is hence standardized and hundreds of options can be added to the

basic design to produce customized styles. The standard frame components are produced

on a continuous basis on stock while the custom options are produced on a Kanban basis.

I.1.2.3 Material They use plywood for most parts and timberstrand for a limited number of more

mechanically demanding applications. Particle board and OSB are sometimes used but to a

much lesser extent and mainly for non-structural or less structurally demanding parts.

(1) Timberstrand Elran uses Timberstrand for front and back rails with 7/8” (22 mm) thickness.

Timberstrand is not only 30% cheaper than solid wood, but it is also stronger than

plywood. Elran receives pre-cut pieces of Timberstrand from Weyerhaeuser with the

appropriate section. Thus Elran does not need machinery to cut the pieces for themselves

and there is no waste. Spring clips are inserted in the edges of the Timberstrand. There are

five springs on the seat frame with a 40 lbf (18 kg) load on each spring, totalling 200 lbf

(91 kg) in tension and the load of the people sitting on the furniture.

(2) Plywood Elran has used plywood for 25 years. The material is used for most frame parts. The

plywood is poplar plus pine or spruce with 6 or 5 plies, ¾” (19 mm) thick, of construction

sheathing grade, provided by Weyerhaeuser and Slocan, two domestic plywood

manufacturers not specialized on furniture.

(3) Particle Boards Elran uses particleboard mainly for less structurally demanding parts such as footrests,

because particleboard is cheap and not very heavy. MDF would be too heavy to get a

balance in the rocking mechanism. The company also uses particleboard for the drawer

underneath the central seat of 3-pieces sofa.

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(4) OSB OSB is only used for reinforcing the sides since it is cut in one piece rather than having a

joint.

I.1.2.4 Joints Most connections are staples with glue, which does not take a long time. Screws and

dowels are also used for certain parts.

(1) Staples Staples and glue are their main material for joints. Those are mainly standard crown

galvanized ½ inch staples. Bigger staples are used to produce strong joints for certain

structurally demanding areas.

(2) Wood dowels Wood dowels are only used for the drawer underneath the middle seat of the sofa. Those

are mainly made of hardwoods (i.e. Birch) and have a spiral profile.

(3) Screws Screws—made by Robertson—are used additionally in critical places where twist is

significant.

(4) T-nuts T-nuts are being used for locations where extra connection strength is required, especially

to fix the seat to the mechanism frame. T-nuts are supplied by Sigma Tool

(www.sigmatool.com).

(5) Glue The type of glue used is Dural CL. 3132 G-2672.

(6) Clips

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Clips are used to attach springs for backs and seats. The teeth of the clips are staggered to

avoid splitting of timber-strand.

I.1.2.5 Production lines

Elran has automated production lines with a Taylor CNC band saw, which has a 102°

rotation angle cutting 17 boards at same time. This method is very fast. In fact it has been

optimized, using up to 90% wood and only 10% waste. Elran is one out of only two or

three companies in Canada that run such CNC bandsaw. Such a machine costs about half a

million dollars, but its high efficiency makes it profitable, it allows the same throughput as

was achieved prior to its acquisition, with 12 less people.

Elran has 12 production lines with automated assembly machines to staple and apply glue

automatically. The T-nuts inserted by the machine are made by Sigma Tool, Toronto.

Some of the production lines are dedicated to the backs and seats of sofas. Two shifts are

operated every day.

I.1.2.6 Testing

Mechanical testing is not carried out at the company, but by the distributors and customers,

though there are occasional human test with people jumping up and down on the furniture.

I.1.2.7 Recalls The total annual revenue of the company is 100 million dollars with 1–1.5% recalls. The

main areas where recall occurs are (in decreasing order of frequency): leather and fabric,

mechanism, foam and wood frame structure. There are very few recalls related to the

structural frames.

I.1.2.8 Possibility to Change all Material to OSB

When asked about the potential change from plywood and Timber-strand to OSB, the R&D

manager replied that plywood is currently cheaper than OSB, but the company would

consider changing to OSB if its price decreased. However, Elran management does not

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believe all seats and sofa parts could be made of OSB. They think only parts where the

fastener can be applied on a face is suitable to use OSB. They think everywhere a fastener

would have to be applied on edge, OSB would not be suitable.

On the other hand, it would be difficult for the company to envisage using two main

materials (plywood and OSB). This is due to the use of a Taylor CNC bandsaw, which

works more efficiently if all components are made of the same material. Using OSB and

plywood would increase the sawing time and significantly decrease the output. OSB is

currently used only to reinforce the sides because it is cut in one piece without joints.

The company has two main concerns regarding the reliability of OSB in critical places

such as side rails, especially at the location of attachment to the reclining mechanism:

(1) OSB can not carry as much load as plywood;

(2) Fasteners in OSB edges (staples and screws) are weak points.

With improved mechanical properties of OSB (fastener retention, end splitting, consistency

of thickness as well as structural resistance) or through appropriate design, the company

would consider using OSB in upholstery furniture frames, provided its cost would go down

again. Their aim is to save on costs as well as ensuring the required dynamic performance

of the frames.

We asked Elran to send us a sofa frame out of their real production in order to make some

mechanical tests in our laboratory. We also asked the company to make a sofa frame

entirely of OSB, so we can execute the same test twice, checking whether the whole sofa

could be made of OSB.

Contacts:

Yvan Tremblay

Directeur R&D

Elran, 2751 route Transcanadienne

Pointe-Claire, Qc, H9R 1B4

[email protected]

Marie-Claude Desjardins (graduate from UdeM in Industrial design)

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[email protected]

Figure I.1 Three-set sofa frame made in Jaymar furniture company.

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APPENDIX II Tables in finite element modelling

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Table II-1: Rotation-Moment of Metal-plate connectors

Rotation (rad.) Moment (N-mm)Rotation (rad.) Moment (N-mm)-0.0368 -5.19E+05 -2.30E-01 -1.77E+05-0.0122 -1.22E+06 -2.23E-01 -1.80E+05-0.0118 -1.22E+06 -2.08E-01 -1.87E+05

-9.86E-03 -1.15E+06 -2.07E-01 -1.86E+05-7.95E-03 -1.09E+06 -1.92E-01 -1.98E+05-6.56E-03 -1.02E+06 -1.77E-01 -2.02E+05-5.44E-03 -9.44E+05 -1.62E-01 -2.06E+05-4.44E-03 -8.72E+05 -1.48E-01 -2.10E+05-3.67E-03 -7.98E+05 -1.43E-01 -2.08E+05-3.18E-03 -7.27E+05 -1.28E-01 -2.08E+05-2.75E-03 -6.61E+05 -1.14E-01 -2.03E+05-2.37E-03 -5.90E+05 -1.00E-01 -1.97E+05-1.91E-03 -4.89E+05 -8.69E-02 -1.87E+05-1.51E-03 -4.20E+05 -7.35E-02 -1.78E+05-1.14E-03 -3.33E+05 -6.13E-02 -1.63E+05-7.89E-04 -2.50E+05 -4.95E-02 -1.43E+05-5.52E-04 -1.74E+05 -3.85E-02 -1.22E+05-3.36E-04 -1.11E+05 -2.79E-02 -9.92E+04-1.84E-04 -64378.8 -0.0177 -72129.5-8.07E-05 -34324.8 -8.43E-03 -47770-2.69E-05 -16292.41 -8.90E-04 -21670.490.00E+00 0 0.00E+00 02.69E-05 16292.414 8.90E-04 21670.4928.07E-05 34324.79 8.43E-03 47769.991.84E-04 64378.76 1.77E-02 72129.523.36E-04 110566.96 2.79E-02 99178.095.52E-04 173522.12 0.0385 122114.017.89E-04 2.50E+05 4.95E-02 143468.151.14E-03 3.33E+05 6.13E-02 162765.961.51E-03 4.20E+05 7.35E-02 1.78E+051.91E-03 4.89E+05 8.69E-02 1.87E+052.37E-03 5.90E+05 1.00E-01 1.97E+052.75E-03 6.61E+05 1.14E-01 2.03E+053.18E-03 7.27E+05 1.28E-01 2.08E+053.67E-03 7.98E+05 1.43E-01 2.08E+054.44E-03 8.72E+05 1.48E-01 2.10E+055.44E-03 9.44E+05 1.62E-01 2.06E+056.56E-03 1.02E+06 1.77E-01 2.02E+057.95E-03 1.09E+06 1.92E-01 1.98E+059.86E-03 1.15E+06 2.07E-01 1.86E+051.18E-02 1.22E+06 2.08E-01 1.87E+051.22E-02 1.22E+06 2.23E-01 1.80E+05

0.0368 5.19E+05 2.30E-01 1.77E+05

In-plane Out-of-plane

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225

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Page 244: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

226

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

amSt

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nput

CaseT

yP

V2V3

TM

2M

3m

eEem

Stat

ion

6M33

/(bh2

)6M

22/(h

b2)s

umfle

xion

3V33

/(2bh

)3V

22/(2

bh)P

/(bh)

T/(a

lfa*d

l*dc2

)Te

xtm

mTe

xtTe

xtN

NN

N-m

mN

-mm

N-m

mTe

xtm

mh

bN

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

3N

/mm

21

0Po

inLin

St27

7.05

-161

0-7

96.5

1189

.97

-983

27.8

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337

220

152

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43-1

1.61

023

-18.

3917

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2931

9-0

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001

0.1

0.07

8059

946

110

2Po

inLin

St27

7.05

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0-7

96.5

1189

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101.

615

218

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6629

2-2

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236

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1953

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2931

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001

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8059

946

110

2Po

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St27

7.05

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7-5

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236

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1953

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8306

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0.1

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8059

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3Po

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2441

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203

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277.

05-1

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2220

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1.89

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130

5Po

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7.05

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6.48

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130

5Po

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7.05

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406

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277.

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9311

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20

PoinL

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272.

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102

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272.

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272.

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6666

310

2Po

inLin

St27

7.05

520.

52-7

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9.9

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1172

5124

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615

218

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6666

310

2Po

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St27

7.05

653.

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9.9

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6587

73-1

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349

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7560

70.

3525

030.

1-0

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0566

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203

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inSt

277.

0565

3.97

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349.

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831.

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203.

215

218

0.71

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4.41

0148

5.12

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7560

70.

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203

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277.

0592

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203.

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0.71

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4.41

0148

5.12

9369

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0.49

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0.1

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7805

6666

330

5Po

inLin

St27

7.05

920.

86-1

73.2

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9.9

5495

4.7

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40.9

2430

4.8

152

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678

6.48

8881

5.88

4203

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5Po

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St27

7.05

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290.

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406

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277.

0512

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9.9

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4.24

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1.90

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0.10

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0.65

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0.1

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6666

340

6Po

inLin

St27

7.05

1476

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9.9

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4.24

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1.90

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0.28

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0.79

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0.1

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7805

6666

350

8Po

inLin

St27

7.05

1476

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5.1

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9.9

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04-3

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5501

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2830

560.

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663

508

PoinL

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277.

0516

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5-1

189.

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361

0Po

inLin

St27

7.05

1610

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6.5

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9.9

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0Po

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410

2Po

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St-1

89.7

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463

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529

2510

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102

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PoinL

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5Po

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89.7

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1.29

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508

PoinL

inSt

-189

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28.6

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8.85

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1145

73.8

2550

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218

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2.06

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3.68

2507

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70.

0497

7923

Page 245: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

227

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

amSt

atio

nput

CaseT

yP

V2V3

TM

2M

3m

eEem

Stat

ion

6M33

/(bh2

)6M

22/(h

b2)s

umfle

xion

3V33

/(2bh

)3V

22/(2

bh)P

/(bh)

T/(a

lfa*d

l*dc2

)Te

xtm

mTe

xtTe

xtN

NN

N-m

mN

-mm

N-m

mTe

xtm

mh

bN

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

3N

/mm

24

508

PoinL

inSt

-189

.7-9

5.17

-796

.975

8.85

1745

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Page 246: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

228

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Page 247: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

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Page 248: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

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Page 249: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

231

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Page 250: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

232

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

ameS

tatio

npu

tCase

TyP

V2V3

TM

2M

3m

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ion

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b2)s

umfle

xion

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22/(2

bh)P

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T/(a

lfa*d

l*dc2

Text

mm

Text

Text

NN

NN

-mm

N-m

mN

-mm

Text

mm

hb

N/m

m2

N/m

m2

N/m

m2

N/m

m2

N/m

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N/m

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Page 251: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

233

T

able

II -

4. E

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for

conf

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ame

Page 252: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

234

TAB

LE:

Elem

ent F

orce

s - F

ram

esra

mSta

tionp

utCas

eTy

PV2

V3T

M2

M3

ameE

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umfle

xion

3V33

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2/(2

bh)

P/(b

h)T/

(alfa

*dl*d

c2)

Text

mm

Text

Text

NN

NN

-mm

N-m

mN

-mm

Text

mm

mm

mm

N/m

m2

N/m

m2

N/m

m2

N/m

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N/m

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Page 253: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

235

TAB

LE:

Elem

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N-m

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mm

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641

Page 254: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

236

TAB

LE:

Elem

ent F

orce

s - F

ram

esra

mSta

tionp

utCas

eTy

PV2

V3T

M2

M3

ameE

lemSt

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hb

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22/(h

b2)s

umfle

xion

3V33

/(2bh

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2/(2

bh)

P/(b

h)T/

(alfa

*dl*d

c2)

Text

mm

Text

Text

NN

NN

-mm

N-m

mN

-mm

Text

mm

mm

mm

N/m

m2

N/m

m2

N/m

m2

N/m

m2

N/m

m2

N/m

m3

N/m

m2

3540

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Page 255: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

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Page 256: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

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4

Page 257: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

239

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

amSt

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nput

CseT

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V2V3

TM

2M

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bh)P

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T/(a

lfa*d

l*dc2

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mN

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mTe

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mh

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2

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635

Page 258: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

240

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

amSt

atio

nput

CseT

yP

V2V3

TM

2M

3m

eEm

Stat

ion

6M33

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)6M

22/(h

b2)s

umfle

xion

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22/(2

bh)P

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T/(a

lfa*d

l*dc2

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xtm

mTe

xtTe

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NN

N-m

mN

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N-m

mTe

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mh

bN

/mm

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Page 259: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

241

Table II - 6. Element joint forces –Links for configuration (c) sofa frame under medium-service acceptance level load TABLE: Element Joint Forces - LinksLinkLinkElemJoint utputCaCaseType F1 F2 F3 M1 M2 M3Text Text Text Text Text N N N N-mm N-mm N-mm

1 5 405 PonctuLinStatic 476 1 5 -34 12082 -21 5 5 PonctuLinStatic -476 -1 -5 0 0 23 6 346 PonctuLinStatic 0 -25 0 -27 1 23 6 9 PonctuLinStatic 0 25 0 -1 -1 -24 7 286 PonctuLinStatic 336 -1 -5 34 8547 04 7 312 PonctuLinStatic -336 1 5 0 0 05 8 285 PonctuLinStatic -336 -1 -5 34 -8547 05 8 313 PonctuLinStatic 336 1 5 0 0 06 9 406 PonctuLinStatic -476 1 5 -34 -12082 26 9 6 PonctuLinStatic 476 -1 -5 0 0 -27 10 379 PonctuLinStatic 0 -25 0 11 -1 -27 10 8 PonctuLinStatic 0 25 0 -1 1 28 11 225 PonctuLinStatic 0 -171 0 1 -1 -28 11 4 PonctuLinStatic 0 171 0 -1 1 29 12 159 PonctuLinStatic 0 1199 0 1 -1 -29 12 36 PonctuLinStatic 0 -1199 0 -1 1 210 1 2 PonctuLinStatic 0 0 0 0 0 010 1 21 PonctuLinStatic 0 0 0 0 0 011 2 1 PonctuLinStatic 0 0 0 0 0 011 2 56 PonctuLinStatic 0 0 0 0 0 012 3 35 PonctuLinStatic 0 0 0 0 0 012 3 3 PonctuLinStatic 0 0 0 0 0 013 4 36 PonctuLinStatic 0 0 0 0 0 013 4 4 PonctuLinStatic 0 0 0 0 0 016 13 160 PonctuLinStatic 0 -171 0 1 1 216 13 1 PonctuLinStatic 0 171 0 -1 -1 -217 14 126 PonctuLinStatic 0 1199 0 1 1 217 14 56 PonctuLinStatic 0 -1199 0 -1 -1 -218 15 464 PonctuLinStatic 0 2307 0 2 0 018 15 10 PonctuLinStatic 0 -2307 0 -2 0 019 16 431 PonctuLinStatic 0 2307 0 2 0 019 16 7 PonctuLinStatic 0 -2307 0 -2 0 020 17 2 PonctuLinStatic 0 -171 0 -1 1 220 17 192 PonctuLinStatic 0 171 0 1 -1 -221 18 21 PonctuLinStatic 0 1199 0 -1 1 221 18 94 PonctuLinStatic 0 -1199 0 1 -1 -222 19 35 PonctuLinStatic 0 1199 0 -1 -1 -222 19 127 PonctuLinStatic 0 -1199 0 1 1 223 20 3 PonctuLinStatic 0 -171 0 -1 -1 -223 20 193 PonctuLinStatic 0 171 0 1 1 224 21 11 PonctuLinStatic 0 2307 0 -1 0 024 21 463 PonctuLinStatic 0 -2307 0 1 0 025 22 12 PonctuLinStatic 0 2307 0 -1 0 025 22 496 PonctuLinStatic 0 -2307 0 1 0 026 23 242 PonctuLinStatic 0 -25 0 641 1 126 23 13 PonctuLinStatic 0 25 0 1 -1 -127 24 259 PonctuLinStatic 0 -25 0 641 -1 -127 24 15 PonctuLinStatic 0 25 0 1 1 1

Max. 476 2307 5 641 12082 2Min. -476 -2307 -5 -34 -12082 -2

Page 260: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

242

T

able

II -

7. E

lem

ent f

orce

s –fr

ames

for

conf

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atio

n (c

) sof

a fr

ame

unde

r he

avy-

serv

ice

acce

ptan

ce le

vel l

oad

Page 261: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

243

TAB

LE:

Elem

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s - F

ram

esFr

amSt

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nput

CaseT

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V2V3

TM

2M

3m

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22/(h

b2)s

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)3V

22/(2

bh)P

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T/(a

lfa*d

l*dc2

)Te

xtm

mTe

xtTe

xtN

NN

N-m

mN

-mm

N-m

mTe

xm

mh

bN

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

3N

/mm

220

0Po

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nS-3

269.

31.

6E-1

1-5

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00

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10

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40

2.27

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1.6E

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20

1988

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138

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1988

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2276

.2Po

nLi

nS-3

269.

349

04.9

952

.20

-397

7.5

-373

760

376

.215

2.4

18.2

6-5

.287

779

-0.4

6964

5-5

.757

420.

0281

372.

6438

92-1

.175

023

0Po

nLi

nS-3

269.

6-4

905

52.2

03E

-12

4E-1

04

015

2.4

18.2

65.

68E

-15

3.7E

-16

6.05

E-1

50.

0281

37-2

.643

892

-1.1

750

2338

.1Po

nLi

nS-3

269.

6-4

905

52.2

0-1

988.

818

6880

438

.115

2.4

18.2

62.

6438

9-0

.234

832

2.40

9057

0.02

8137

-2.6

4389

2-1

.175

023

76.2

Pon

LinS

-326

9.6

-490

552

.20

-397

7.6

3737

604

76.2

152.

418

.26

5.28

7779

-0.4

6966

44.

8181

160.

0281

37-2

.643

892

-1.1

750

650

Pon

LinS

-400

8.9

-323

4-1

517

-150

38-1

5295

0-6

2938

35

015

2.4

18.2

6-8

.904

216

-18.

0598

6-2

6.96

41-0

.817

695

-1.7

4321

5-1

.441

-0.9

8648

8165

88.9

Pon

LinS

-400

8.9

-323

4-1

517

-150

38-1

8061

-341

820

588

.92

152.

418

.26

-4.8

3590

5-2

.132

632

-6.9

6854

-0.8

1769

5-1

.743

215

-1.4

41-0

.986

4881

6588

.9Po

nLi

nS-4

008.

9-2

967.

1-9

74.3

-150

38-1

8066

-341

822

588

.92

152.

418

.26

-4.8

3593

8-2

.133

201

-6.9

6914

-0.5

2517

9-1

.599

35-1

.441

-0.9

8648

8165

178

Pon

LinS

-400

8.9

-296

7.1

-974

.3-1

5038

6851

6-7

8149

517

7.8

152.

418

.26

-1.1

0560

98.

0901

916.

9845

82-0

.525

179

-1.5

9935

-1.4

41-0

.986

4881

6517

8Po

nLi

nS-4

008.

9-2

433.

4-2

98.2

-150

3868

516

-781

445

177.

815

2.4

18.2

6-1

.105

542

8.09

0191

6.98

4649

-0.1

6073

1-1

.311

632

-1.4

41-0

.986

4881

6526

7Po

nLi

nS-4

008.

9-2

433.

4-2

98.2

-150

3895

031

1382

255

266.

715

2.4

18.2

61.

9555

4111

.220

9413

.176

48-0

.160

731

-1.3

1163

2-1

.441

-0.9

8648

8165

267

Pon

LinS

-400

8.9

-185

5.1

422.

42-1

5038

9503

113

8225

526

6.7

152.

418

.26

1.95

5541

11.2

2094

13.1

7648

0.22

7693

-0.9

9993

2-1

.441

-0.9

8648

8165

356

Pon

LinS

-400

8.9

-185

5.1

422.

42-1

5038

5747

030

3175

535

5.6

152.

418

.26

4.28

918

6.78

5899

11.0

7508

0.22

7693

-0.9

9993

2-1

.441

-0.9

8648

8165

356

Pon

LinS

-400

8.9

-132

1.3

1098

.6-1

5038

5747

030

3171

535

5.6

152.

418

.26

4.28

9113

6.78

5899

11.0

7501

0.59

2141

-0.7

1220

8-1

.441

-0.9

8648

8165

444

Pon

LinS

-400

8.9

-132

1.3

1098

.6-1

5038

-401

5242

0587

544

4.5

152.

418

.26

5.95

027

-4.7

4100

31.

2092

670.

5921

41-0

.712

208

-1.4

41-0

.986

4881

6544

4Po

nLi

nS-4

008.

9-1

054.

416

41.2

-150

38-4

0147

4205

905

444.

515

2.4

18.2

65.

9503

03-4

.740

433

1.20

987

0.88

4657

-0.5

6834

9-1

.441

-0.9

8648

8165

533

Pon

LinS

-400

8.9

-105

4.4

1641

.2-1

5038

-186

082

5143

455

533.

415

2.4

18.2

67.

2767

14-2

1.97

195

-14.

6952

0.88

4657

-0.5

6834

9-1

.441

-0.9

8648

8172

0Po

nLi

nS-3

399.

7-1

089.

8-1

579

-0.1

6-1

8865

214

1765

60

152.

418

.26

2.00

5626

-22.

2754

9-2

0.26

99-0

.851

146

-0.5

8740

9-1

.222

-1.0

5E-0

572

102

Pon

LinS

-339

9.7

-108

9.8

-157

9-0

.16

-281

8825

2508

610

1.6

152.

418

.26

3.57

2365

-3.3

2829

30.

2440

71-0

.851

146

-0.5

8740

9-1

.222

-1.0

5E-0

572

102

Pon

LinS

-339

9.7

-822

.88

-103

6-0

.16

-281

9325

2505

610

1.6

152.

418

.26

3.57

2326

-3.3

2894

40.

2433

82-0

.558

63-0

.443

549

-1.2

22-1

.05E

-05

7220

3Po

nLi

nS-3

399.

7-8

22.8

8-1

036

-0.1

677

061

3360

766

203.

215

2.4

18.2

64.

7546

499.

0991

3513

.853

78-0

.558

63-0

.443

549

-1.2

22-1

.05E

-05

7220

3Po

nLi

nS-3

399.

7-2

89.0

9-3

60.3

-0.1

677

061

3360

826

203.

215

2.4

18.2

64.

7547

269.

0991

3513

.853

86-0

.194

182

-0.1

5582

6-1

.222

-1.0

5E-0

572

305

Pon

LinS

-339

9.7

-289

.09

-360

.3-0

.16

1136

7036

5459

630

4.8

152.

418

.26

5.17

0346

13.4

2179

18.5

9213

-0.1

9418

2-0

.155

826

-1.2

22-1

.05E

-05

7230

5Po

nLi

nS-3

399.

728

9.18

360.

36-0

.16

1136

7036

5459

630

4.8

152.

418

.26

5.17

0346

13.4

2179

18.5

9213

0.19

4242

0.15

5874

-1.2

22-1

.05E

-05

7240

6Po

nLi

nS-3

399.

728

9.18

360.

36-0

.16

7705

033

6073

640

6.4

152.

418

.26

4.75

4602

9.09

7814

13.8

5242

0.19

4242

0.15

5874

-1.2

22-1

.05E

-05

7240

6Po

nLi

nS-3

399.

782

2.96

1036

.5-0

.16

7705

033

6068

640

6.4

152.

418

.26

4.75

4525

9.09

7814

13.8

5234

0.55

869

0.44

3593

-1.2

22-1

.05E

-05

7250

8Po

nLi

nS-3

399.

782

2.96

1036

.5-0

.16

-282

1525

2488

650

815

2.4

18.2

63.

5720

79-3

.331

585

0.24

0494

0.55

869

0.44

3593

-1.2

22-1

.05E

-05

7250

8Po

nLi

nS-3

399.

710

89.8

615

79.2

-0.1

6-2

8210

2524

916

508

152.

418

.26

3.57

2118

-3.3

3093

40.

2411

840.

8512

050.

5874

57-1

.222

-1.0

5E-0

572

610

Pon

LinS

-339

9.7

1089

.86

1579

.2-0

.16

-188

686

1417

396

609.

615

2.4

18.2

62.

0052

56-2

2.27

945

-20.

2742

0.85

1205

0.58

7457

-1.2

22-1

.05E

-05

800

Pon

LinS

-400

8.8

1054

.49

-164

115

039

-186

063

5143

717

015

2.4

18.2

67.

2770

81-2

1.96

974

-14.

6927

-0.8

8459

20.

5683

92-1

.441

0.98

6504

4880

88.9

Pon

LinS

-400

8.8

1054

.49

-164

115

039

-401

3942

0608

788

.92

152.

418

.26

5.95

057

-4.7

3949

21.

2110

78-0

.884

592

0.56

8392

-1.4

410.

9865

0448

8088

.9Po

nLi

nS-4

008.

813

21.3

8-1

098

1503

9-4

0144

4206

067

88.9

215

2.4

18.2

65.

9505

36-4

.740

061

1.21

0475

-0.5

9207

70.

7122

51-1

.441

0.98

6504

4880

178

Pon

LinS

-400

8.8

1321

.38

-109

815

039

5746

730

3182

717

7.8

152.

418

.26

4.28

9279

6.78

557

11.0

7485

-0.5

9207

70.

7122

51-1

.441

0.98

6504

4880

178

Pon

LinS

-400

8.8

1855

.17

-422

.315

039

5746

730

3187

717

7.8

152.

418

.26

4.28

9346

6.78

557

11.0

7492

-0.2

2762

80.

9999

75-1

.441

0.98

6504

4880

267

Pon

LinS

-400

8.8

1855

.17

-422

.315

039

9501

713

8230

726

6.7

152.

418

.26

1.95

5606

11.2

1935

13.1

7495

-0.2

2762

80.

9999

75-1

.441

0.98

6504

4880

267

Pon

LinS

-400

8.8

2433

.44

298.

3115

039

9501

713

8230

726

6.7

152.

418

.26

1.95

5606

11.2

1935

13.1

7495

0.16

0795

1.31

1675

-1.4

410.

9865

0448

8035

6Po

nLi

nS-4

008.

824

33.4

429

8.31

1503

968

492

-781

467

355.

615

2.4

18.2

6-1

.105

577

8.08

7323

6.98

1746

0.16

0795

1.31

1675

-1.4

410.

9865

0448

8035

6Po

nLi

nS-4

008.

829

67.2

297

4.44

1503

968

492

-781

517

355.

615

2.4

18.2

6-1

.105

644

8.08

7323

6.98

1679

0.52

5243

1.59

9393

-1.4

410.

9865

0448

8044

4Po

nLi

nS-4

008.

829

67.2

297

4.44

1503

9-1

8101

-341

832

744

4.5

152.

418

.26

-4.8

3607

4-2

.137

338

-6.9

7341

0.52

5243

1.59

9393

-1.4

410.

9865

0448

8044

4Po

nLi

nS-4

008.

832

34.1

215

17.1

1503

9-1

8096

-341

829

744

4.5

152.

418

.26

-4.8

3604

-2.1

3676

8-6

.972

810.

8177

651.

7432

58-1

.441

0.98

6504

48

Page 262: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

244

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

amSt

atio

nput

CaseT

yP

V2V3

TM

2M

3m

eEem

Stat

ion

6M33

/(bh2

)6M

22/(h

b2)s

umfle

xion

3V33

/(2bh

)3V

22/(2

bh)P

/(bh)

T/(a

lfa*d

l*dc2

)Te

xtm

mTe

xtTe

xtN

NN

N-m

mN

-mm

N-m

mTe

xm

mh

bN

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

3N

/mm

2

8053

3Po

nLi

nS-4

008.

832

34.1

215

17.1

1503

9-1

5299

6-6

2940

07

533.

415

2.4

18.2

6-8

.904

452

-18.

0652

7-2

6.96

970.

8177

651.

7432

58-1

.441

0.98

6504

4887

0Po

nLi

nS29

.41

-320

9.1

-155

415

234

-164

790

1415

618

015

2.4

18.2

62.

0027

33-1

9.45

793

-17.

4552

-0.8

3790

2-1

.729

745

0.01

060.

9993

2697

8788

.9Po

nLi

nS29

.41

-320

9.1

-155

415

234

-265

9642

6845

888

.915

2.4

18.2

66.

0388

07-3

.140

412

2.89

8395

-0.8

3790

2-1

.729

745

0.01

060.

9993

2697

8788

.9Po

nLi

nS29

.41

-294

2.2

-101

215

234

-265

9642

6845

888

.915

2.4

18.2

66.

0388

07-3

.140

412

2.89

8395

-0.5

4538

7-1

.585

885

0.01

060.

9993

2697

8717

8Po

nLi

nS29

.41

-294

2.2

-101

215

234

6335

368

8403

817

7.8

152.

418

.26

9.73

9205

7.48

0545

17.2

1975

-0.5

4538

7-1

.585

885

0.01

060.

9993

2697

8717

8Po

nLi

nS29

.41

-240

8.4

-335

.715

234

6334

768

8403

817

7.8

152.

418

.26

9.73

9205

7.47

9835

17.2

1904

-0.1

8093

8-1

.298

162

0.01

060.

9993

2697

8726

7Po

nLi

nS29

.41

-240

8.4

-335

.715

234

9318

990

2508

826

6.7

152.

418

.26

12.7

6825

11.0

0344

23.7

7169

-0.1

8093

8-1

.298

162

0.01

060.

9993

2697

8726

7Po

nLi

nS29

.41

-183

0.1

384.

9415

234

9318

990

2508

826

6.7

152.

418

.26

12.7

6825

11.0

0344

23.7

7169

0.20

7491

-0.9

8646

20.

0106

0.99

9326

9787

356

Pon

LinS

29.4

1-1

830.

138

4.94

1523

458

968

1065

204

835

5.6

152.

418

.26

15.0

76.

9627

5322

.032

750.

2074

91-0

.986

462

0.01

060.

9993

2697

8735

6Po

nLi

nS29

.41

-129

6.3

1061

.115

234

5897

410

6520

48

355.

615

2.4

18.2

615

.07

6.96

3463

22.0

3346

0.57

1939

-0.6

9874

30.

0106

0.99

9326

9787

445

Pon

LinS

29.4

1-1

296.

310

61.1

1523

4-3

5355

1180

446

844

4.5

152.

418

.26

16.7

004

-4.1

7457

712

.525

820.

5719

39-0

.698

743

0.01

060.

9993

2697

8744

5Po

nLi

nS29

.41

-102

9.4

1603

.815

234

-353

5511

8044

68

444.

515

2.4

18.2

616

.700

4-4

.174

577

12.5

2582

0.86

4455

-0.5

5487

90.

0106

0.99

9326

9787

533

Pon

LinS

29.4

1-1

029.

416

03.8

1523

4-1

7792

812

7196

28

533.

415

2.4

18.2

617

.995

12-2

1.00

918

-3.0

1406

0.86

4455

-0.5

5487

90.

0106

0.99

9326

9794

0Po

nLi

nS20

.35

-108

9.8

-157

9-0

.11

-185

760

1263

376

90

152.

418

.26

17.8

7365

-21.

934

-4.0

6035

-0.8

5114

6-0

.587

409

0.00

73-7

.216

E-06

9410

2Po

nLi

nS20

.35

-108

9.8

-157

9-0

.11

-253

2813

7409

69

101.

615

2.4

18.2

619

.440

07-2

.990

657

16.4

4941

-0.8

5114

6-0

.587

409

0.00

73-7

.216

E-06

9410

2Po

nLi

nS20

.35

-822

.87

-103

6-0

.11

-253

2813

7409

69

101.

615

2.4

18.2

619

.440

07-2

.990

657

16.4

4941

-0.5

5862

5-0

.443

544

0.00

73-7

.216

E-06

9420

3Po

nLi

nS20

.35

-822

.87

-103

6-0

.11

7996

814

5770

09

203.

215

2.4

18.2

620

.622

869.

4423

2530

.065

18-0

.558

625

-0.4

4354

40.

0073

-7.2

16E-

0694

203

Pon

LinS

20.3

5-2

89.0

9-3

60.3

-0.1

179

961

1457

700

920

3.2

152.

418

.26

20.6

2286

9.44

1514

30.0

6437

-0.1

9418

2-0

.155

826

0.00

73-7

.216

E-06

9430

5Po

nLi

nS20

.35

-289

.09

-360

.3-0

.11

1165

6214

8707

29

304.

815

2.4

18.2

621

.038

3913

.763

2334

.801

62-0

.194

182

-0.1

5582

60.

0073

-7.2

16E-

0694

305

Pon

LinS

20.3

528

9.18

360.

37-0

.11

1165

6214

8707

29

304.

815

2.4

18.2

621

.038

3913

.763

2334

.801

620.

1942

470.

1558

740.

0073

-7.2

16E-

0694

406

Pon

LinS

20.3

528

9.18

360.

37-0

.11

7994

814

5769

19

406.

415

2.4

18.2

620

.622

729.

4400

5630

.062

780.

1942

470.

1558

740.

0073

-7.2

16E-

0694

406

Pon

LinS

20.3

582

2.97

1036

.5-0

.11

7995

514

5769

19

406.

415

2.4

18.2

620

.622

729.

4408

6730

.063

590.

5586

950.

4435

980.

0073

-7.2

16E-

0694

508

Pon

LinS

20.3

582

2.97

1036

.5-0

.11

-253

5313

7407

79

508

152.

418

.26

19.4

3979

-2.9

9357

516

.446

220.

5586

950.

4435

980.

0073

-7.2

16E-

0694

508

Pon

LinS

20.3

510

89.8

615

79.2

-0.1

1-2

5353

1374

077

950

815

2.4

18.2

619

.439

79-2

.993

575

16.4

4622

0.85

1211

0.58

7457

0.00

73-7

.216

E-06

9461

0Po

nLi

nS20

.35

1089

.86

1579

.2-0

.11

-185

797

1263

347

960

9.6

152.

418

.26

17.8

7324

-21.

9383

7-4

.065

130.

8512

110.

5874

570.

0073

-7.2

16E-

0610

20

Pon

LinS

29.5

410

29.5

2-1

604

-152

34-1

7790

712

7193

310

015

2.4

18.2

617

.994

71-2

1.00

675

-3.0

1204

-0.8

6438

50.

5549

330.

0106

-0.9

9929

5510

288

.9Po

nLi

nS29

.54

1029

.52

-160

4-1

5234

-353

4511

8040

910

88.9

152.

418

.26

16.6

9987

-4.1

7345

12.5

2642

-0.8

6438

50.

5549

330.

0106

-0.9

9929

5510

288

.9Po

nLi

nS29

.54

1296

.41

-106

1-1

5234

-353

4511

8040

910

88.9

152.

418

.26

16.6

9987

-4.1

7345

12.5

2642

-0.5

7186

90.

6987

920.

0106

-0.9

9929

5510

217

8Po

nLi

nS29

.54

1296

.41

-106

1-1

5234

5897

310

6515

910

177.

815

2.4

18.2

615

.069

366.

9632

8722

.032

65-0

.571

869

0.69

8792

0.01

06-0

.999

2955

102

178

Pon

LinS

29.5

418

30.2

-384

.8-1

5234

5896

610

6515

910

177.

815

2.4

18.2

615

.069

366.

9625

7722

.031

94-0

.207

421

0.98

6516

0.01

06-0

.999

2955

102

267

Pon

LinS

29.5

418

30.2

-384

.8-1

5234

9317

690

2454

1026

6.7

152.

418

.26

12.7

675

11.0

0196

23.7

6946

-0.2

0742

10.

9865

160.

0106

-0.9

9929

5510

226

7Po

nLi

nS29

.54

2408

.46

335.

8-1

5234

9317

690

2454

1026

6.7

152.

418

.26

12.7

675

11.0

0196

23.7

6946

0.18

1003

1.29

821

0.01

06-0

.999

2955

102

356

Pon

LinS

29.5

424

08.4

633

5.8

-152

3463

324

6883

4210

355.

615

2.4

18.2

69.

7383

357.

4770

5317

.215

390.

1810

031.

2982

10.

0106

-0.9

9929

5510

235

6Po

nLi

nS29

.54

2942

.25

1011

.9-1

5234

6333

068

8342

1035

5.6

152.

418

.26

9.73

8335

7.47

7764

17.2

161

0.54

5451

1.58

5934

0.01

06-0

.999

2955

102

445

Pon

LinS

29.5

429

42.2

510

11.9

-152

34-2

6631

4267

7610

444.

515

2.4

18.2

66.

0378

21-3

.144

496

2.89

3325

0.54

5451

1.58

5934

0.01

06-0

.999

2955

102

445

Pon

LinS

29.5

432

09.1

415

54.6

-152

34-2

6631

4267

7610

444.

515

2.4

18.2

66.

0378

21-3

.144

496

2.89

3325

0.83

7967

1.72

9793

0.01

06-0

.999

2955

102

533

Pon

LinS

29.5

432

09.1

415

54.6

-152

34-1

6483

614

1483

1053

3.4

152.

418

.26

2.00

1632

-19.

4633

2-1

7.46

170.

8379

671.

7297

930.

0106

-0.9

9929

5511

20

Pon

LinS

-247

4.2

17.2

562

.16

-188

2511

0741

6946

.66

110

18.2

615

2.4

0.82

024

1.56

6715

2.38

6955

0.03

3506

0.00

9298

-0.8

89-1

.234

8581

112

406

Pon

LinS

-247

4.2

17.2

562

.16

-188

2585

481

-65.

1311

406.

418

.26

152.

4-0

.007

691.

2093

491.

2016

590.

0335

060.

0092

98-0

.889

-1.2

3485

8111

281

3Po

nLi

nS-2

474.

217

.25

62.1

6-1

8825

6022

1-7

076.

911

812.

818

.26

152.

4-0

.835

622

0.85

1983

0.01

6361

0.03

3506

0.00

9298

-0.8

89-1

.234

8581

146

0Po

nLi

nS-2

474.

517

.25

-62.

218

824

-110

774

6945

.73

120

18.2

615

2.4

0.82

013

-1.5

6717

8-0

.747

05-0

.033

527

0.00

9298

-0.8

891.

2348

2271

146

406

Pon

LinS

-247

4.5

17.2

5-6

2.2

1882

4-8

5497

-65.

2712

406.

418

.26

152.

4-0

.007

707

-1.2

0957

-1.2

1728

-0.0

3352

70.

0092

98-0

.889

1.23

4822

7114

681

3Po

nLi

nS-2

474.

517

.25

-62.

218

824

-602

20-7

076.

312

812.

818

.26

152.

4-0

.835

542

-0.8

5196

2-1

.687

5-0

.033

527

0.00

9298

-0.8

891.

2348

2271

180

0Po

nLi

nS89

1.16

65.1

60.

99-1

8825

-825

.17

2194

3.6

130

152.

418

.26

0.31

0448

-0.0

9743

30.

2130

140.

0005

340.

0351

230.

3202

-1.2

3485

8118

040

6Po

nLi

nS89

1.16

65.1

60.

99-1

8825

-122

6.8

-453

8.3

1340

6.4

152.

418

.26

-0.0

6420

5-0

.144

86-0

.209

070.

0005

340.

0351

230.

3202

-1.2

3485

8118

081

3Po

nLi

nS89

1.16

65.1

60.

99-1

8825

-162

8.5

-310

2013

812.

815

2.4

18.2

6-0

.438

858

-0.1

9228

8-0

.631

150.

0005

340.

0351

230.

3202

-1.2

3485

8121

40

Pon

LinS

891.

5-6

5.25

-0.9

918

824

-162

9-3

1067

140

152.

418

.26

-0.4

3951

4-0

.192

346

-0.6

3186

-0.0

0053

4-0

.035

171

0.32

041.

2348

2271

Page 263: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

245

TAB

LE:

Elem

ent F

orce

s - F

ram

esFr

amSt

atio

nput

CaseT

yP

V2V3

TM

2M

3m

eEem

Stat

ion

6M33

/(bh2

)6M

22/(h

b2)s

umfle

xion

3V33

/(2bh

)3V

22/(2

bh)P

/(bh)

T/(a

lfa*d

l*dc2

)Te

xtm

mTe

xtTe

xtN

NN

N-m

mN

-mm

N-m

mTe

xm

mh

bN

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

2N

/mm

3N

/mm

2

214

406

Pon

LinS

891.

5-6

5.25

-0.9

918

824

-122

7.1

-454

7.7

1440

6.4

152.

418

.26

-0.0

6433

8-0

.144

887

-0.2

0923

-0.0

0053

4-0

.035

171

0.32

041.

2348

2271

214

813

Pon

LinS

891.

5-6

5.25

-0.9

918

824

-825

.12

2197

1.2

1481

2.8

152.

418

.26

0.31

0838

-0.0

9742

80.

2134

1-0

.000

534

-0.0

3517

10.

3204

1.23

4822

7124

70

Pon

LinS

-12.

34-9

2.55

-23.

6119

268

-607

8.7

-640

0515

015

2.4

18.2

6-0

.905

516

-0.7

1775

5-1

.623

27-0

.012

726

-0.0

4988

6-0

.004

1.26

3976

5424

721

6Po

nLi

nS-1

2.34

-92.

55-2

3.61

1926

8-9

81.3

9-4

4023

1521

5.9

152.

418

.26

-0.6

2282

2-0

.115

879

-0.7

387

-0.0

1272

6-0

.049

886

-0.0

041.

2639

7654

247

432

Pon

LinS

-12.

34-9

2.55

-23.

6119

268

4115

.9-2

4041

1543

1.8

152.

418

.26

-0.3

4012

70.

4859

970.

1458

7-0

.012

726

-0.0

4988

6-0

.004

1.26

3976

5426

50

Pon

LinS

-12.

4492

.73

-23.

8-1

9268

-612

964

091.

416

015

2.4

18.2

60.

9067

35-0

.723

693

0.18

3042

-0.0

1282

90.

0499

83-0

.004

-1.2

6397

9226

521

6Po

nLi

nS-1

2.44

92.7

3-2

3.8

-192

68-9

90.8

244

071.

316

215.

915

2.4

18.2

60.

6234

99-0

.116

993

0.50

6506

-0.0

1282

90.

0499

83-0

.004

-1.2

6397

9226

543

2Po

nLi

nS-1

2.44

92.7

3-2

3.8

-192

6841

47.4

2405

1.1

1643

1.8

152.

418

.26

0.34

0263

0.48

9707

0.82

9971

-0.0

1282

90.

0499

83-0

.004

-1.2

6397

9228

30

Pon

LinS

95.7

159

9.97

37.4

9-2

623

2184

338

1166

170

152.

418

.26

5.39

256

2.57

9206

7.97

1766

0.02

0208

0.32

3396

0.03

44-0

.172

0858

283

330

Pon

LinS

95.7

159

9.97

37.4

9-2

623

9463

.418

3058

1733

0.2

152.

418

.26

2.58

9812

1.11

7407

3.70

722

0.02

0208

0.32

3396

0.03

44-0

.172

0858

283

660

Pon

LinS

95.7

159

9.97

37.4

9-2

623

-291

6.7

-150

5117

660.

415

2.4

18.2

6-0

.212

935

-0.3

4439

1-0

.557

330.

0202

080.

3233

960.

0344

-0.1

7208

5831

10

Pon

LinS

95.7

160

0.05

37.4

826

1729

11.5

1505

518

015

2.4

18.2

60.

2129

90.

3437

830.

5567

730.

0202

020.

3234

390.

0344

0.17

1675

8631

133

0Po

nLi

nS95

.71

600.

0537

.48

2617

-946

4.1

-183

082

1833

0.2

152.

418

.26

-2.5

9015

3-1

.117

495

-3.7

0765

0.02

0202

0.32

3439

0.03

440.

1716

7586

311

660

Pon

LinS

95.7

160

0.05

37.4

826

17-2

1840

-381

218

1866

0.4

152.

418

.26

-5.3

9329

6-2

.578

772

-7.9

7207

0.02

0202

0.32

3439

0.03

440.

1716

7586

337

0Po

nLi

nS-9

25.5

9-9

5.72

37.3

6-3

863

4003

8-2

9718

190

18.2

615

2.4

-3.5

0899

80.

5664

42-2

.942

560.

0201

38-0

.051

595

-0.3

33-0

.253

3739

337

610

Pon

LinS

-925

.59

-95.

7237

.36

-386

317

261

2863

1.1

1960

9.6

18.2

615

2.4

3.38

0669

0.24

4207

3.62

4876

0.02

0138

-0.0

5159

5-0

.333

-0.2

5337

3933

80

Pon

LinS

-152

5.6

-0.0

044

-0.1

20.

9814

644

-166

5.1

200

18.2

615

2.4

-0.1

9661

40.

2071

820.

0105

68-6

.47E

-05

-2.3

8E-0

6-0

.548

6.42

86E-

0533

861

0Po

nLi

nS-1

525.

6-0

.004

4-0

.12

0.98

1471

5-1

662.

520

609.

618

.26

152.

4-0

.196

297

0.20

8181

0.01

1884

-6.4

7E-0

5-2

.38E

-06

-0.5

486.

4286

E-05

339

0Po

nLi

nS-9

25.6

795

.7-3

7.61

3870

1733

828

627.

721

018

.26

152.

43.

3802

710.

2452

953.

6255

66-0

.020

273

0.05

1584

-0.3

330.

2538

6325

339

610

Pon

LinS

-925

.67

95.7

-37.

6138

7040

264

-297

1421

609.

618

.26

152.

4-3

.508

522

0.56

9643

-2.9

3888

-0.0

2027

30.

0515

84-0

.333

0.25

3863

2534

00

Pon

LinS

-23.

61-1

2.34

-92.

55-2

1691

-192

68-4

715.

622

018

.26

152.

4-0

.556

807

-0.2

7260

1-0

.829

41-0

.049

886

-0.0

0665

2-0

.008

-1.4

2286

9934

041

9Po

nLi

nS-2

3.61

-12.

34-9

2.55

-216

9119

520

457.

6122

419.

118

.26

152.

40.

0540

330.

2761

590.

3301

92-0

.049

886

-0.0

0665

2-0

.008

-1.4

2286

9934

083

8Po

nLi

nS-2

3.61

-12.

34-9

2.55

-216

9158

308

5630

.85

2283

8.2

18.2

615

2.4

0.66

4873

0.82

4919

1.48

9792

-0.0

4988

6-0

.006

652

-0.0

08-1

.422

8699

374

0Po

nLi

nS-2

3.8

-12.

4492

.73

2169

619

268

-475

1.9

230

18.2

615

2.4

-0.5

6108

30.

2726

01-0

.288

480.

0499

83-0

.006

705

-0.0

091.

4232

0513

374

419

Pon

LinS

-23.

8-1

2.44

92.7

321

696

-195

9446

0.03

2341

9.1

18.2

615

2.4

0.05

4319

-0.2

7720

9-0

.222

890.

0499

83-0

.006

705

-0.0

091.

4232

0513

374

838

Pon

LinS

-23.

8-1

2.44

92.7

321

696

-584

5756

71.9

123

838.

218

.26

152.

40.

6697

21-0

.827

02-0

.157

30.

0499

83-0

.006

705

-0.0

091.

4232

0513

408

0Po

nLi

nS-8

3.37

-833

.03

-13.

7520

621

-502

2.6

-541

043

240

152.

418

.26

-7.6

5442

7-0

.593

052

-8.2

4748

-0.0

0741

2-0

.449

02-0

.03

1.35

2696

240

833

0Po

nLi

nS-8

3.37

-833

.03

-13.

7520

621

-481

.11

-265

976

2433

0.2

152.

418

.26

-3.7

6289

8-0

.056

808

-3.8

1971

-0.0

0741

2-0

.449

02-0

.03

1.35

2696

240

845

6Po

nLi

nS-8

3.37

-833

.03

-13.

7520

621

1250

-161

127

2445

6.1

152.

418

.26

-2.2

7955

40.

1475

94-2

.131

96-0

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412

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4902

-0.0

31.

3526

962

408

456

Pon

LinS

-95.

72-9

25.5

9-3

7.36

-400

38-4

721.

3-1

8292

325

015

2.4

18.2

6-2

.587

912

-0.5

5747

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4538

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2013

8-0

.498

912

-0.0

34-2

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4377

408

660

Pon

LinS

-95.

72-9

25.5

9-3

7.36

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3829

13.5

6208

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2520

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152.

418

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0.08

7828

0.34

4015

0.43

1843

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2013

8-0

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912

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34-2

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4377

436

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nLi

nS-9

5.7

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6140

264

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4.7

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1.9

260

152.

418

.26

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8774

1-0

.344

16-0

.431

9-0

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273

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9895

5-0

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2.64

1278

6443

620

3Po

nLi

nS-9

5.7

-925

.67

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6140

264

4710

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1487

2620

2.8

152.

418

.26

2.56

759

0.55

6233

3.12

3823

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2027

3-0

.498

955

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342.

6412

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436

203

Pon

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27-8

32.9

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3.81

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515

9832

270

152.

418

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2.26

1226

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92.

1116

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444

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4897

2-0

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4789

1843

633

0Po

nLi

nS-8

3.27

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81-2

0548

493.

3626

5982

2712

7.4

152.

418

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3.76

299

0.05

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3.82

1245

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0744

4-0

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972

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3-1

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8918

436

660

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LinS

-83.

27-8

32.9

4-1

3.81

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4850

53.3

5410

1927

457.

615

2.4

18.2

67.

6540

880.

5966

758.

2507

63-0

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444

-0.4

4897

2-0

.03

-1.3

4789

1847

20

Pon

LinS

-318

2.8

-60.

35-9

.285

8618

0.94

-353

4928

015

2.4

18.2

6-0

.500

099

0.02

1365

-0.4

7873

-0.0

0495

9-0

.032

53-1

.144

0.56

3233

1147

240

6Po

nLi

nS-3

182.

8-6

0.35

-9.2

8586

3918

.7-1

0824

2840

6.4

152.

418

.26

-0.1

5313

40.

4627

030.

3095

69-0

.004

959

-0.0

3253

-1.1

440.

5632

3311

472

813

Pon

LinS

-318

2.8

-60.

35-9

.285

8676

56.4

1370

0.7

2881

2.8

152.

418

.26

0.19

383

0.90

4041

1.09

7872

-0.0

0495

9-0

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53-1

.144

0.56

3233

1150

60

Pon

LinS

-318

2.8

-60.

349.

06-8

586

-236

.04

-353

4629

015

2.4

18.2

6-0

.500

056

-0.0

2787

1-0

.527

930.

0048

84-0

.032

525

-1.1

44-0

.563

2259

506

406

Pon

LinS

-318

2.8

-60.

349.

06-8

586

-391

9.1

-108

2229

406.

415

2.4

18.2

6-0

.153

107

-0.4

6275

5-0

.615

860.

0048

84-0

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525

-1.1

44-0

.563

2259

506

813

Pon

LinS

-318

2.8

-60.

349.

06-8

586

-760

2.2

1370

1.4

2981

2.8

152.

418

.26

0.19

3841

-0.8

9763

8-0

.703

80.

0048

84-0

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525

-1.1

44-0

.563

2259

Max

891.

549

04.9

916

41.2

4026

411

6562

1487

072

152.

415

2.4

21.0

3839

13.7

6323

34.8

0162

0.88

4657

2.64

3892

0.32

042.

6412

7864

Min

-400

8.9

-490

5-1

641

-400

38-1

8868

6-6

2940

018

.26

18.2

6-8

.904

452

-22.

2794

5-2

6.96

97-0

.884

592

-2.6

4389

2-1

.441

-2.6

2643

7726

.50.

75.

310

.80.

7

Page 264: DESIGNING, MODELLING AND TESTING OF JOINTS AND … · panneaux MDF a moins varié, conférant une résistance plus homogène. On a également ... An increase in length of gusset-plate

246

Table II - 8. Element joint forces –Links for configuration (c) sofa frame under heavy-service acceptance level load TABLE: Element Joint Forces - LinksLink LinkElem Joint tputCaCaseType F1 F2 F3 M1 M2 M3Text Text Text Text Text N N N N-mm N-mm N-mm

1 5 405 PonctuLinStatic 713.46 2.03 7.95 -51.14 18121.38 -2.721 5 5 PonctuLinStatic -713.46 -2.03 -7.95 -0.33 0.43 2.723 6 346 PonctuLinStatic 0.00189 -37.91 0.04684 -40.81 0.88 3.533 6 9 PonctuLinStatic -0.00189 37.91 -0.04684 -1.1 -0.88 -3.584 7 286 PonctuLinStatic 504.69 -2.03 -7.95 51.34 12818.87 0.384 7 312 PonctuLinStatic -504.69 2.03 7.95 0.33 0.22 -0.385 8 285 PonctuLinStatic -504.69 -2.01 -7.95 50.72 -12818.87 -0.375 8 313 PonctuLinStatic 504.69 2.01 7.95 0.33 -0.22 0.376 9 406 PonctuLinStatic -713.46 2.02 7.95 -50.93 -18121.38 2.726 9 6 PonctuLinStatic 713.46 -2.02 -7.95 -0.34 -0.43 -2.727 10 379 PonctuLinStatic -0.001893 -37.95 -0.02239 17.23 -0.88 -3.537 10 8 PonctuLinStatic 0.001893 37.95 0.02239 -1.09 0.88 3.588 11 225 PonctuLinStatic 0.0003477 -256.51 -0.003284 1.58 -0.75 -2.638 11 4 PonctuLinStatic -0.000348 256.51 0.003284 -1.66 0.75 2.629 12 159 PonctuLinStatic 0.0003478 1798.73 -0.003609 1.71 -0.75 -2.639 12 36 PonctuLinStatic -0.000348 -1798.73 0.003609 -1.8 0.75 2.6210 1 2 PonctuLinStatic -6.13E-16 2.921E-12 -4.56E-13 -2.96E-12 -9.236E-11 2.848E-1010 1 21 PonctuLinStatic 6.132E-16 -2.921E-12 4.562E-13 2.964E-12 -7.987E-12 -2.594E-1211 2 1 PonctuLinStatic -6.63E-15 -3.466E-12 -1.49E-13 1.208E-11 -1.529E-11 -7.258E-1111 2 56 PonctuLinStatic 6.631E-15 3.466E-12 1.493E-13 -1.21E-11 2.75E-12 -2.68E-1212 3 35 PonctuLinStatic 6.377E-16 3.572E-12 6.172E-13 1.264E-11 7.414E-11 4.165E-1112 3 3 PonctuLinStatic -6.38E-16 -3.572E-12 -6.17E-13 -1.26E-11 -2.396E-11 2.251E-1213 4 36 PonctuLinStatic 1.014E-13 2.701E-13 -1E-13 3.993E-12 2.572E-11 -7.404E-1113 4 4 PonctuLinStatic -1.01E-13 -2.701E-13 1E-13 -3.99E-12 -6.278E-13 -1.219E-1216 13 160 PonctuLinStatic -0.000347 -256.92 -0.003289 1.58 0.75 2.6316 13 1 PonctuLinStatic 0.0003468 256.92 0.003289 -1.67 -0.75 -2.6217 14 126 PonctuLinStatic -0.000347 1798.54 -0.003614 1.71 0.75 2.6317 14 56 PonctuLinStatic 0.0003468 -1798.54 0.003614 -1.8 -0.75 -2.6218 15 464 PonctuLinStatic -4.25E-05 3460.85 -0.005328 2.42 0.33 -0.3718 15 10 PonctuLinStatic 4.253E-05 -3460.85 0.005328 -2.55 -0.33 0.3719 16 431 PonctuLinStatic 4.356E-05 3460.83 -0.005326 2.42 -0.33 0.3719 16 7 PonctuLinStatic -4.36E-05 -3460.83 0.005326 -2.55 0.33 -0.3720 17 2 PonctuLinStatic -0.000347 -256.92 -0.003289 -1.17 0.75 2.9220 17 192 PonctuLinStatic 0.0003468 256.92 0.003289 1.09 -0.75 -2.9121 18 21 PonctuLinStatic -0.000347 1798.54 -0.003614 -1.32 0.75 2.9221 18 94 PonctuLinStatic 0.0003468 -1798.54 0.003614 1.23 -0.75 -2.9122 19 35 PonctuLinStatic 0.0003478 1798.73 -0.003609 -1.32 -0.75 -2.9222 19 127 PonctuLinStatic -0.000348 -1798.73 0.003609 1.22 0.75 2.9123 20 3 PonctuLinStatic 0.0003477 -256.51 -0.003284 -1.17 -0.75 -2.9223 20 193 PonctuLinStatic -0.000348 256.51 0.003284 1.09 0.75 2.9124 21 11 PonctuLinStatic 4.356E-05 3460.83 -0.005326 -2.05 -0.33 0.3324 21 463 PonctuLinStatic -4.36E-05 -3460.83 0.005326 1.91 0.33 -0.3325 22 12 PonctuLinStatic -4.25E-05 3460.85 -0.005328 -2.05 0.33 -0.3325 22 496 PonctuLinStatic 4.253E-05 -3460.85 0.005328 1.91 -0.33 0.3326 23 242 PonctuLinStatic 0.00189 -37.91 0.04684 961.28 0.93 1.9526 23 13 PonctuLinStatic -0.00189 37.91 -0.04684 1.54 -0.88 -1.9527 24 259 PonctuLinStatic -0.001893 -37.95 -0.02239 962.31 -0.93 -1.9527 24 15 PonctuLinStatic 0.001893 37.95 0.02239 1.54 0.88 1.95

Max 713.46 3460.85 7.95 962.31 18121.38 3.58Min -713.46 -3460.85 -7.95 -51.14 -18121.38 -3.58