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The structural performance of tall wood-frame walls under axial and transversal loads Leonard, Daniel 2004

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THE STRUCTURAL PERFORMANCE OF TALL WOOD-FRAME WALLS UNDER AXIAL AND TRANSVERSAL LOADS by DANIEL LEONARD B . A . S c , The U n i v e r s i t y o f B r i t i s h C o l u m b i a , 2002 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF M A S T E R S OF A P P L I E D SCIENCE  in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department o f C i v i l Engineering) W e accept this thesis as c o n f o r m i n g to the required standard  Dr. H.G.L. Prion  D r . T . Haukaas  Dr. M . Popovski  T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A October 2004 © D a n i e l E d w a r d L e o n a r d , 2004  THE  FACULTY OF G R A D U A T E STUDIES  U N I V E R S I T Y OF BRITISH C O L U M B I A  Library Authorization  In presenting this thesis in partial fulfillment of the requirements f o r an a d v a n c e d degree a t the University of British Columbia, I agree that the Library shall make it freely available for reference a n d study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by t h e head o f m y department o r by his o r her representatives. It is understood that copying o r publication of this thesis f o r financial gain shall n o t be allowed without my written permission.  ^X>r\^\et, N a m e of Author  Title of Thesis:  Degree:  e^^*^  Le^ofcE*  0*8/\o  (please print)  TH£  Date (dd/mm/yyyy)  ST•gOC-Toft^  M*7£jgS  /o<-|  &  A??LlGt>  f>6 lZ&>g.tJ>A<X£ o F  SCie^Oe'  Year:  T(\LL-  Q^O^Tj - r g A N \ €  ^ O C ^ j  Department o f The University o f British Columbia Vancouver, B C  Canada  grad.ubc.ca/forms/?formlD=THS  page 1 of 1  last updated:  20-Jul-04  Abstract  11  ABSTRACT T a l l w o o d - f r a m e w a l l s have emerged as a v i a b l e alternative to steel, concrete, and m a s o n r y i n the construction o f large industrial, c o m m e r c i a l , and institutional b u i l d i n g s i n N o r t h A m e r i c a . The construction o f t a l l w o o d - f r a m e w a l l s incorporates the advantages o f t y p i c a l residential wood-frame  p l a t f o r m construction, w h i c h  include  fast construction times and the use  of  r e l a t i v e l y u n s k i l l e d labour to deliver l i g h t w e i g h t b u i l d i n g s p r o v e n to be durable over m a n y years o f usage. Some o f the restrictions placed on the construction o f residential w o o d - f r a m e w a l l s b y applicable b u i l d i n g codes are also c u r r e n t l y placed o n the construction o f tall w o o d - f r a m e w a l l s . T h i s study focused on the response o f t a l l w o o d - f r a m e w a l l s under axial and transversal, or outof-plane, l o a d i n g w i t h particular emphasis on addressing the appropriateness o f certain current code restrictions o n this type o f construction.  The axial loads represented the loads applied to  the w a l l s f r o m the r o o f structure i n c l u d i n g the loads f r o m snow, r a i n , and w i n d . The loads i n the transversal d i r e c t i o n represented either compression or suction to the face o f the w a l l due to w i n d pressure.  Because o f the inherent v a r i a b i l i t y and non-linear behaviour o f w o o d , m a n y o f the components o f tall w o o d - f r a m e w a l l s were tested separately p r i o r to testing the full-scale w a l l specimens. These c o m p o n e n t tests were used to determine the b e n d i n g stiffness o f each material c o m p o n e n t individually.  I n a d d i t i o n to the lateral and w i t h d r a w a l stiffness o f nailed connections, the  b e n d i n g stiffness o f composite studs w i t h sheathing, and the response o f sheathing panels under r a c k i n g loads w i t h varied stud spacing was investigated.  T h e tests o f the sheathing panels  showed that the current l i m i t on stud spacing i n the Canadian W o o d D e s i g n Code is not  Table o f Contents  111  appropriate f o r this type o f w a l l construction. Because these types o f w a l l s are designed using an equivalent static w i n d pressure rather than a true representation o f the d y n a m i c characteristics o f w i n d , m o n o t o n i c tests were p r i m a r i l y conducted on all o f the components and the full-scale walls.  The experimental results f r o m the component tests were used to v e r i f y linear analytical  models representing the l o a d - d e f o r m a t i o n b e h a v i o u r o f composite T - b e a m s , consisting o f a stud connected to a t r i b u t a r y w i d t h o f sheathing, under transversal loads.  These models were then  used to v e r i f y m o r e sophisticated linear models representing the l o a d - d e f o r m a t i o n behaviour o f full-scale w a l l s under a x i a l and transversal loads. N o n - l i n e a r f i n i t e element models o f full-scale w a l l s were also v e r i f i e d using the results f r o m the c o m p o n e n t tests.  D e s i g n equations were  presented that accurately account f o r the composite action that exists between the sheathing and the studs.  F i n a l l y , some design and construction recommendations are discussed regarding  several aspects o f t a l l w o o d - f r a m e w a l l s based on the results o f the full-scale w a l l tests.  Table o f Contents  iv  t  T A B L E  O F  C O N T E N T S  ABSTRACT  ii  LIST OF TABLES  xi  LIST OF FIGURES  xiii  ACKNOWLEDGEMENTS  xxii  CHAPTER 1 INTRODUCTION  1  1.1 P R O B L E M O V E R V I E W  1  1.2 R E S E A R C H O B J E C T I V E S  5  1.3 S C O P E  6  '.  1.4 T H E S I S O U T L I N E  8  CHAPTER 2 LITERATURE REVIEW  10  2.1  WOOD-FRAME CONSTRUCTION IN NORTH AMERICA  10  2.2  PAST P E R F O R M A N C E OF W O O D - F R A M E B U I L D I N G S  13  2.3  W O O D AS A STRUCTURAL M A T E R I A L 2.3.1  Tall Wood-Frame Walls  !  16 16  2.3.1.1 Advantages of Tall Wood-frame Walls  16  2.3.1.2 Disadvantages of Tall Wood-frame walls  19  2.3.2  Concrete T i l t - U p C o n s t r u c t i o n  19  2.3.2.1 Description and Development  19  2.3.2.2 Advantages of Concrete Tilt-Up Construction  22  2.3.2.3 Disadvantages of Concrete Tilt-Up Construction  24  2.3.3  Masonry Construction  26  Table o f Contents  2.5  v  2.3.3.1 Advantages of Masonry Construction  27  2.3.3.2 Disadvantages of Masonry Construction  29  2.3.4  2.4  .  Steel C o n s t r u c t i o n  30  2.3.4.1 Advantages of Steel Construction  32  2.3.4.2 Disadvantages of Steel Construction  33  T A L L W O O D - F R A M E W A L L CASE STUDIES 2.4.1  Tembec M i l l i n Cranbrook, B.C  2.4.2  Trus Joist Research Center i n Boise, Idaho  PARTIAL COMPOSITE ACTION A N D EFFECTIVE FLANGE W I D T H  34 ...34 37 39  2.5.1  Partial C o m p o s i t e A c t i o n ( N e w m a r k , Seiss, and V i e s t )  40  2.5.2  Partial C o m p o s i t e A c t i o n ( G o o d m a n and P o p o v )  42  2.5.3  Partial C o m p o s i t e A c t i o n and E f f e c t i v e Flange W i d t h ( A m a n a and B o o t h ) . . . . 4 4  2.5.4  Partial C o m p o s i t e A c t i o n and E f f e c t i v e Flange W i d t h (Polensek and Kazic)  ,  47  2.5.5  Partial C o m p o s i t e A c t i o n ( K u e n z i and W i l k i n s o n )  51  2.5.6  Partial C o m p o s i t e A c t i o n ( M c C u t c h e o n )  52  2.5.6.1 Influence of Gaps  53  2.5.6.2 Beam-Spring Analog  53  2.5.6.3 Generalized Model for Partial Composite Action 2.5.7  Partial C o m p o s i t e A c t i o n ( I t a n i and B r i t o )  2.5.8  Partial C o m p o s i t e A c t i o n ( G i r h a m m a r and G o p u )  55 :...57 60  2.5.8.1 First-Order Solution  60  2.5.8.2 Second-Order Solution  60  2.5.8.3 Critical Buckling Load  62  2.5.9  Partial C o m p o s i t e A c t i o n ( K r e u t z i n g e r )  63  Table o f Contents  vi  2.5.10 Partial C o m p o s i t e A c t i o n (Ceccotti)  64  2.5.11 Effective Flange W i d t h ( M o h l e r )  66  2.5.12 E f f e c t i v e Flange W i d t h (Eurocode 5)  67  2.5.13 E f f e c t i v e Flange W i d t h ( K i k u c h i )  68  2.6  SHEATHING BUCKLING  71  2.7  NAILED CONNECTION LOAD-SLIP MODELS  74  2.8  LATERAL TORSIONAL BUCKLING  77  2.9  ROTATIONAL RESTRAINT A N D END CONNECTIONS  80  2.10 W O O D D I A P H R A G M M O D E L S  83  2.10.1 F I N W A L L (Polensek)  83  2.10.2 F E A F L O and N O N F L O ( T h o m p s o n , V a n d e r b i l t , and G o o d m a n )  85  2.10.3 F A P and P A N E L (Foschi)  87  2.10.4 B S A F ( L u i and B u l l e i t )  89  2.10.5 E q u i v a l e n t F i n i t e E l e m e n t M o d e l ( K a s a l and L e i c h t i )  90  2.11 P R E V I O U S F U L L - S C A L E W A L L T E S T I N G  C  H  A  P  92  2.11.1 Polensek  93  2.11.2 G r o m a l a  94  2.11.3 Stefanescu et. al  96  T  E  R  3  C  O  N  N  E  C  T  I  O  N  L O A D - S L I P  99  T E S T S  3.1  O B J E C T I V E S A N D SCOPE  100  3.2  METHODS A N D MATERIALS  100  3.3  3.2.1  C o n n e c t i o n Specimens  100  3.2.2  T e s t i n g Apparatus and Instrumentation  3.2.3  M a t e r i a l Properties  107  RESULTS A N D DISCUSSION  Ill  :  104  Table o f Contents  3.4  vii  3.3.1  C o n n e c t i o n Properties  •.  3.3.2  E f f e c t o f Sheathing O r i e n t a t i o n  117  3.3.3  Failure M o d e s  119  SUMMARY  CHAPTER 4 NAIL WITHDRAWAL TESTS  111  120  122  4.1  O B J E C T I V E S A N D SCOPE  122  4.2  METHODS AND MATERIALS  123  4.3  4.4  4.2.1  W i t h d r a w a l Specimens  123  4.2.2  T e s t i n g Apparatus and I n s t r u m e n t a t i o n  124  4.2.3  M a t e r i a l Properties  127  RESULTS A N D DISCUSSION  127  4.3.1  C o n n e c t i o n Properties  127  4.3.2  Failure M o d e s  131  SUMMARY  CHAPTER 5 COMPOSITE T-BEAM TESTS  131  132  5.1  O B J E C T I V E S A N D SCOPE  132  5.2  METHODS AND MATERIALS  133  5.3  5.2.1  T - B e a m Specimens  133  5.2.2  Testing Apparatus and I n s t r u m e n t a t i o n  137  5.2.3  Testing Procedures  140  5.2.4  M a t e r i a l Properties  143  RESULTS A N D DISCUSSION  148  5.3.1  M o n o t o n i c Tests.  149  5.3.2  A n a l y t i c a l P r e d i c t i o n o f C o m p o s i t e T - B e a m Tests  157  5.3.2.1 Partial Composite Action  158  Table o f Contents  5.4  viii  5.3.2.2 Effective Flange Width  162  5.3.2.3 Connection Stiffness  170  5.3.3  C y c l i c Tests  177  5.3.4  Failure M o d e s  181  SUMMARY  CHAPTER 6 SHEARWALL TESTS  184  186  6.1  O B J E C T I V E S A N D SCOPE  186  6.2  METHODS AND MATERIALS  188  6.3  6.4  6.2.1  Shearwall Specimens  188  6.2.2  T e s t i n g Apparatus and I n s t r u m e n t a t i o n  191  6.2.3  T e s t i n g Procedures  194  6.2.4  M a t e r i a l Properties  195  RESULTS A N D DISCUSSION  196  6.3.1  Pushover Results  196  6.3.2  Failure M o d e s  202  SUMMARY  CHAPTER 7 FULL-SCALE W A L L TESTS  204  206  7.1  O B J E C T I V E S A N D SCOPE  206  7.2  METHODS AND MATERIALS  208  7.3  7.2.1  Full-Scale W a l l Specimens  .208  7.2.2  T e s t i n g Apparatus and I n s t r u m e n t a t i o n  216  7.2.3  T e s t i n g Procedures  224  7.2.4  M a t e r i a l Properties  228  RESULTS A N D DISCUSSION  230  7.3.1  L o a d - D i s p l a c e m e n t Results  230  Table o f Contents  ix  7.3.2  L o a d Interaction  240  7.3.3  D i r e c t i o n o f L o a d i n g and C o n t r i b u t i o n s f r o m G y p s u m W a l l b o a r d  246  7.3.3.1 Direction of Loading  246 249  7.3.3.2 Gypsum Wallboard Sheathing.  251  7.3.3.3 Transversal Displacement Criteria 7.3.4  Transverse L o a d D i s t r i b u t i o n Effects  253  7.3.5  Stud Connections and E n d Rotational Restraint  262  262  7.3.5.1 Axially Loaded Stud Connections  271  7.3.5.2 End Rotational Restraint 7.3.6 7.4  U l t i m a t e Strength and M o d e s o f Failure  SUMMARY  CHPATER 8 ANALYTICAL PREDICTION OF FULL-SCALE WALLS 8.1  ANALYTICAL MODELS  277 284  287 288  8.1.1  P A N E L Finite Element M o d e l  288  8.1.2  Beam-Spring Analog Method  293  8.2  RESULTS A N D DISCUSSION  295  8.3  SUMMARY  303  CHAPTER 9 SUMMARY, CONCLUSIONS, AND RECOMMENDATIONS FOR FUTURE RESEARCH  304  9.1  SUMMARY  304  9.2  CONCLUSIONS A N D DESIGN RECOMMENDATIONS  308  9.3  R E C O M M E N D A T I O N S FOR FUTURE RESEARCH  317  CHAPTER 10 BIBLIOGRAPHY  323  APPENDIX A: CONNECTION TEST RESULTS  329  A.l  C O N N E C T I O N L O A D - S L I P TESTS  330  Table o f Contents  x  A. 2 W I T H D R A W A L TESTS  ;  384  394  APPENDIX B: T A L L W A L L EXAMPLE B. l  T A L L W A L L S WORKBOOK DESIGN EXAMPLE  B. 2  REVISED EXAMPLE INCORPORATING RESEARCH FINDINGS B.2.1  .....394 417  Wall Design  417  B.2.1.1 L o a d I n f o r m a t i o n . B.2.1.2Composite  418  Stud Resistance  419  B.2.1.3 Stud C o n n e c t i o n Design  427  429  APPENDIX C: ANALYTICAL MODELS C. 1 P A N E L F I N I T E E L E M E N T M O D E L C.2  BEAM-SPRING A N A L O G  „.... !  429 437  L i s t o f Tables  xi  L I S T O F  T A B L E S  Table 2 . 1 .  C o m p a r i s o n o f approximate and exact values o f f  Table 2.2.  C o m p a r i s o n o f approximate and exact second-order results ( G i r h a m m a r and  A  ( M c C u t c h e o n , 1977)  G o p u , 1991) Table 2.3.  61  R a t i o o f the m i d - s p a n d e f l e c t i o n f o r different l o a d i n g c o n f i g u r a t i o n s ( C e c c o t t i , 2003)  Table 2.4.  52  66  E f f e c t i v e flange w i d t h factors f r o m Eurocode 5 (Raadscelders and Blass, 1995)  68  Table 2.5.  Values f o r coefficients a and b f o u n d i n E q u a t i o n (2.83) ( K i k u c h i , 2 0 0 0 )  71  Table 2.6.  E f f e c t o f stud spacing on shearwalls f r o m ( T i s s e l l , 1993)  72  Table 3 . 1 .  C o n n e c t i o n load-slip test m a t r i x  103  Table 3.2.  A v e r a g e nail b e n d i n g properties obtained f r o m testing  110  Table 3.3.  A v e r a g e connection properties obtained f r o m tests  112  Table 4 . 1 .  N a i l w i t h d r a w a l connection test m a t r i x  124  Table 4.2.  A v e r a g e c o n n e c t i o n properties obtained f r o m tests  128  Table 5 . 1 .  T - b e a m test m a t r i x  134  Table 5.2.  Sheathing m o d u l u s o f elasticity i n b e n d i n g results  147  Table 5.3.  A v e r a g e T - b e a m stiffness values obtained f r o m m o n o t o n i c b e n d i n g tests  150  Table 5.4.  M i n i m u m sheathing thickness for a g i v e n stud spacing and factored w i n d load  155  Table 5.5.  Sheathing properties based o n sheathing b e n d i n g test results  157  Table 5.6.  L e n g t h factor as a f u n c t i o n o f the ratio o f gap spacing to total span length  170  Table 5.7.  A v e r a g e T - b e a m stiffness values compared w i t h analytical predictions  174  Table 5.8.  A v e r a g e T - b e a m slippage values compared w i t h analytical predictions  176  Table 6 . 1 .  Shearwall test m a t r i x  190  L i s t o f Tables  xii  Table 6.2.  Shearwall response parameters obtained f r o m tests  198  Table 7 . 1 .  Full-scale w a l l test m a t r i x  209  Table 7.2.  Test schedule f o r each full-scale w a l l specimen  226  Table 7.3.  Full-scale w a l l b e n d i n g stiffness values f r o m tests w i t h m o n o t o n i c transverse loads and constant axial loads  232  Table 7.4.  Transverse b e n d i n g stiffness o f sheathing alone and sheathing and b l o c k i n g  259  Table 7.5.  M a x i m u m axial load a p p l i e d or p o i n t o f axial failure  264  Table 7.6.  M a x i m u m transversal load applied or p o i n t o f failure i n b e n d i n g  278  Table 8 . 1 .  Full-scale w a l l stiffness test values compared w i t h linear b e a m - s p r i n g analog predictions  300  Table B. 1.  S u m m a r y o f axial loads  418  Table B.2.  S u m m a r y o f w i n d loads  418  L i s t o f Figures  xiii  L I S T O F  F I G U R E S  Figure 1.1.  Regular residential w o o d - f r a m e construction i n N o r t h A m e r i c a  2  Figure 1.2.  T a l l w o o d - f r a m e w a l l construction  3  Figure 1.3.  Tests conducted over the course o f this study  8  Figure 2 . 1 . D i s t r i b u t i o n o f w i n d pressure o n an enclosed b u i l d i n g ( F E M A , 1997)  15  Figure 2.2.  15  Figure 2.3.  Figure 2.4.  Figure 2.5.  Figure 2.6.  D i s t r i b u t i o n o f w i n d pressure o n a b u i l d i n g w i t h an opening ( F E M A , 1997) The largest t i l t - u p b u i l d i n g to date, a 160,000 square metre d i s t r i b u t i o n centre near C o l u m b u s , O h i o  22  a-b) Earthquake damage o n older t i l t - u p structures d u r i n g the 1994 N o r t h r i d g e earthquake  25  Earthquake damage o n t i l t - u p construction site d u r i n g the 1994 N o r t h r i d g e earthquake  26  E x a m p l e o f a concrete m a s o n r y b u i l d i n g : L a M i r a d a C o m m u n i t y G y m n a s i u m that is 2,000 square metres  27  Figure 2.7.  Damage to a m a s o n r y structure d u r i n g the N o r t h r i d g e earthquake  30  Figure 2.8.  T y p i c a l example o f a warehouse designed i n prefabricated steel  31  Figure 2.9.  T y p i c a l example o f the interior o f a warehouse designed i n prefabricated steel  ;  31  Figure 2.10. C o n s t r u c t i o n o f the Tembec Cresbrook M i l l i n C r a n b r o o k B.C  35  Figure 2 . 1 1 . Connections between the studs and the b o t t o m plate ( C W C , 2 0 0 0 )  36  Figure 2.12. L i f t i n g o f a c o m p l e t e d section o f the w a l l i n place at Trus Joist T e c h n o l o g y Center i n Boisie ( T a y l o r , 2000) Figure 2.13. C o m p a r i s o n between (a) a b e a m w i t h o u t composite action and (b) a f u l l y composite b e a m (Ceccotti, 2 0 0 3 )  38 39  Figure 2.14. Stress d i s t r i b u t i o n i n the flange o f a composite m e m b e r (Raadscelders and Blass, 1995)  40  L i s t o f Figures  xiv  Figure 2.15. C o m p o s i t e T - b e a m w i t h imperfect interaction ( N e w m a r k et. al., 1951) (a) cross section, (b) internal forces, and (c) strain d i s t r i b u t i o n  41  Figure 2.16. L a y e r e d b e a m system layout ( G o o d m a n , 1969)  43  Figure 2.17. Three-layered b e a m internal forces and strains ( G o o d m a n , 1969)  43  Figure 2.18. D i f f e r e n t d i a p h r a g m c o n f i g u r a t i o n s considered b y A m a n a and B o o t h ( 1 9 6 7 ) (a) single rib or T - b e a m type, (b) double s k i n , double r i b type, and (c) m u l t i p l e r i b , double s k i n type  46  Figure 2.19. B e n d i n g and compression system w i t h nonlinear components (Polensek and K a z i c , 1991)  48  Figure 2.20. Cross-section o f an I-shaped composite b e a m  49  Figure 2 . 2 1 . Progression o f the b e a m - s p r i n g analog m e t h o d (a) composite w o o d - f r a m e floor, (b) transverse stiffness represented as an equivalent b e a m perpendicular to the j o i s t s , and (c) composite j o i s t s represented as springs supporting the equivalent transverse b e a m ( M c C u t c h e o n , 1984)  54  Figure 2.22. (a) cross-section and (b) side v i e w o f the revised m o d e l b y M c C u t c h e o n (1986)  56  Figure 2.23. B e a m w i t h gaps at the f o u r t h points ( I t a n i , 1983)  58 \  Figure 2.24. A n a l y s i s o f the beam w i t h gaps at the f o u r t h points ( I t a n i , 1983)  59  Figure 2.25. Cross-section o f an I-shaped composite b e a m  64  Figure 2.26. Cross-section o f a t h i n - f l a n g e d d i a p h r a g m (Raadscelders and Blass, 1995)  67  Figure 2.27. E f f e c t i v e flange w i d t h according to M o h l e r and E C 5 . (a) particleboard M o h l e r , (b) particleboard E C 5 , (c) p l y w o o d M o h l e r , and (d) p l y w o o d EC5 (Raadscelders and Blass, 1995)  68  Figure 2.28. The basic panel that is the basis f o r the f o r m u l a t i o n b y K i k u c h i ( K i k u c h i , 2000)  69  Figure 2.29. Sheathing panel loaded w i t h a constant shear stress a l o n g the edges (Kallsner, 1995)  73  Figure 2.30. D e f i n i t i o n o f the parameters o f the C E N procedure ( C E N , 1995)  75  Figure 2 . 3 1 . D e f i n i t i o n o f the parameters o f the f u n c t i o n b y Foschi (Foschi, 1974)  76  Figure 2.32. L o a d - s l i p curve m o d e l l e d b y a 5-parameter equaltion ( G i r h a m m a r et. al., 2004)  76  Figure 2.33. (a) to (c) (Lateral-torsional b u c k l i n g o f a s i m p l y supported b e a m ( H o o l e y and M a d s e n , 1964)  77  L i s t o f Figures  *  xv  Figure 2.34. T y p i c a l intercomponent c o n n e c t i o n system b e t w e e n a w a l l , f l o o r , and f o u n d a t i o n (Polensek and S c h i m e l , 1986)  81  Figure 2.35. Finite element mesh f o r the F I N W A L L program. (Polensek, 1976b)  84  Figure 2.36. A s s e m b l y o f I-beam c o l u m n and plate elements (Polensek, 1976b)  85  F i g u r e 2.37. Idealization o f a w o o d - j o i s t f l o o r system i n F E A F L O (Pellicane and R o b i n s o n , 1997)  86  Figure 2.38. (a) w o o d f l o o r assembly and (b) T - b e a m element strip (Foschi, 1989)  88  Figure 2.39. S p r i n g l o a d - d e f o r m a t i o n curve ( L u i and B u l l e i t , 1995)  90  Figure 2.40. Finite element mesh o f a (a) sheathed w a l l and (b) w a l l frame (Kasal and L e i c h t i , 1992)  91  Figure 2 . 4 1 . Finite element mesh o f equivalent w a l l m o d e l ( K a s a l and L e i c h t i , 1992)  92  Figure 2.42. W a l l test arrangement f o r tests b y Polensek (Polensek and A t h e r t o n , 1976)  93  Figure 2.43. Photo o f the overall test set-up ( G r o m a l a , 1983).  94  Figure 2.44. Schematic o f the test set-up ( G r o m a l a , 1983)  95  Figure 2.45. Schematic o f the w a l l test set-up (Stefanescu et. al., 2000)  96  Figure 2.46. Photo o f the w a l l test set-up described b y Stefanescu et. al. (2000)  97  Figure 3 . 1 . T y p i c a l detail o f a stud-to-sheathing c o n n e c t i o n  102  Figure 3.2.  102  Figure 3.3.  Spiral nail lengths used i n connection testing Photo o f the test set-up f o r d e t e r m i n i n g the load-slip properties o f stud-tosheathing connections  105  Figure 3.4.  Schematic o f load-slip test set-up  106  Figure 3.5.  Relative w o o d densities o f specimen materials  107  Figure 3.6.  Proprietary products used i n testing: (a) L V L , (b), L S L , (c) G l u l a m  108  Figure 3.7.  Fastener b e n d i n g (a) test apparatus and (b) test set-up  109  Figure 3.8.  (a) L o a d - d e f o r m a t i o n curves and (b) failure modes o f spiral nails i n b e n d i n g  110  F i g u r e 3.9.  T y p i c a l connection load-slip results  Ill  Figure 3.10. Load-slip curves obtained f r o m testing, (a) 18.5 m m CSP sheathing, (b) 18.5 m m O S B sheathing, (c) CSP sheathing w i t h SPF studs, (d) O S B sheathing w i t h SPF studs, (e) CSP sheathing w i t h L S L studs, and ( f ) O S B sheathing w i t h L S L studs  115  L i s t o f Figures  xvi  Figure 3 . 1 1 . L o a d - s l i p curves w i t h sheathing parallel and perpendicular, (a) CSP sheathing w i t h SPF studs, (b) O S B sheathing w i t h SPF studs, (c) CSP sheathing w i t h L S L studs, and (d) O S B sheathing w i t h L S L studs  118  Figure 3.12. P u l l o u t failure mode  119  Figure 3.13. P u l l - t h r o u g h the sheathing failure mode  120  Figure 4 . 1 . T y p i c a l details o f a nailed connection prepared f o r w i t h d r a w a l testing  123  Figure 4.2.  Photo o f the test set-up f o r d e t e r m i n i n g the w i t h d r a w a l characteristics o f nails  125  Figure 4.3.  Schematic o f w i t h d r a w a l test set-up  126  Figure 4.4.  T y p i c a l w i t h d r a w a l connection results  127  Figure 4.5.  L o a d - d e f l e c t i o n curves obtained f r o m w i t h d r a w a l testing, (a) 65 m m spiral  Figure 4.6.  n a i l , (b) 76 m m spiral n a i l , (c) 102 m m spiral n a i l , and (d) L S L studs  130  T y p i c a l nail w i t h d r a w a l failure mode  131  Figure 5 . 1 . T y p i c a l details o f a T - b e a m composite specimen  135  Figure 5.2.  T - b e a m specimens prepared f o r testing (stacked t w o h i g h )  135  Figure 5.3.  Photo o f the T - b e a m test set-up  137  Figure 5.4.  Schematic o f beam test set-up  138  Figure 5.5.  M o n o t o n i c loading programs (a) f o r stiffness i n the linear and nonlinear range and (b) f o r stiffness i n the linear range w i t h d i f f e r i n g sheathing lengths R e d u c i n g the gap spacing b y c u t t i n g the sheathing o f an already tested T -  141  b e a m specimen  142  Figure 5.7.  C y c l i c l o a d i n g properties used f o r testing o f composite T-beams  143  Figure 5.8.  L o a d e d stud under t h i r d - p o i n t b e n d i n g to o b t a i n m o d u l u s o f elasticity  144  Figure 5.9.  C u m u l a t i v e d i s t r i b u t i o n o f m o d u l u s o f elasticity f o r SPF and L S L studs  144  Figure 5.6.  Figure 5.10. The test set-up f o r d e t e r m i n i n g the stiffness and strength characteristics o f O S B sheathing used i n the testing p r o g r a m  145  Figure 5 . 1 1 . Schematic o f sheathing b e n d i n g test set-up  146  Figure 5.12. Relative densities o f O S B sheathing specimens  148  Figure 5.13. Load-displacement relationships obtained f r o m testing, (a) sheathing orientation, (b) stud m o d u l u s o f elasticity, (c) c o n n e c t i o n stiffness, (d)  L i s t o f Figures  xvii  sheathing thickness, (e) nailed c o n n e c t i o n w i t h gaps, and ( f ) g l u e d connection w i t h gaps  151  Figure 5.14. V a r i a t i o n o f the increase i n stiffness f o r several different f o r m u l a t i o n s  159  Figure 5.15. Cross-section o f a T-shaped composite b e a m  160  Figure 5.16. Stress d i s t r i b u t i o n i n the flange o f a composite m e m b e r  162  Figure 5.17. V a r i a t i o n o f effective flange w i d t h f o r several different f o r m u l a t i o n s  163  Figure 5.18. Increase i n composite m e m b e r b e n d i n g stiffness w i t h effective flange w i d t h  163  Figure 5.19. Increase i n composite m e m b e r b e n d i n g stiffness w i t h gap spacing  165  Figure 5.20. C o m p a r i s o n o f the increase i n stiffness o f p a r t i a l l y composite members over the bare stud stiffness w i t h test results f o r a g l u e d specimen w i t h gaps.  167  Figure 5 . 2 1 . D i s t r i b u t i o n o f axial stress i n the flange f r o m f i n i t e element models  168  Figure 5.22. A p p r o x i m a t e distributions o f a x i a l stress i n the flange u s i n g gap length  168  Figure 5.23. L e n g t h factor for use i n effective w i d t h calculations  169  Figure 5.24. Load-displacement response o f a T - b e a m loaded b e y o n d the linear range. (a) m i d - s p a n displacement and (b) slippage between the sheathing and the stud Figure 5.25. Percentage difference between test and a n a l y t i c a l l y predicted results at different load levels  172  173  Figure 5.26. H i s t o g r a m o f analytical predictions versus test results f o r b e n d i n g stiffness  175  Figure 5.27. L o a d versus displacement f o r a t y p i c a l c y c l i c test specimen  178  Figure 5.28. (Inset o f Figure 5.27). D e g r a d i n g stiffness w i t h increasing load levels  179  Figure 5.29. D e g r a d i n g stiffness values under c y c l i c l o a d i n g w i t h increasing load levels  179  Figure 5.30. Slippage between sheathing and stud d u r i n g c y c l i c l o a d i n g  180  Figure 5 . 3 1 . T - b e a m failure due to stud failure  182  Figure 5.32. T - b e a m failure due to stud failure  182  Figure 5.33. D i s t r i b u t i o n o f stress f o r a composite T - b e a m  183  Figure 6 . 1 . T y p i c a l details o f a shearwall specimen  188  Figure 6.2.  189  (a) and (b) Shearwall specimens prepared f o r testing  L i s t o f Figures  Figure 6.3.  xviii  Photo o f the test set-up f o r d e t e r m i n i n g the response o f sheathing panels to r a c k i n g loads  192  Figure 6.4.  Schematic o f shearwall test set-up  193  F i g u r e 6.5.  C u m u l a t i v e d i s t r i b u t i o n o f m o d u l u s o f elasticity f o r SPF studs and plates  195  Figure 6.6.  Load-displacement response o f the shearwalls tested  197  Figure 6.7.  D i a g o n a l d e f o r m a t i o n response o f shearwalls tested  199  Figure 6.8.  B u c k l i n g o f the sheathing o f w a l l specimen 2 0 2 A  199  Figure 6.9.  (a) and (b) B u c k l i n g o f the sheathing o f w a l l specimen 2 0 2 A  200  Figure 6.10. (a) and (b) Failure o f the double central stud and top plate i n w a l l 2 0 I B  203  Figure 6 . 1 1 . (a) and (b) Failure o f the b o t t o m plate i n w a l l 2 0 4 A  204  Figure 7 . 1 . Details o f full-scale w a l l specimen types (a) W I and (b) W 2  210  Figure 7.2.  Details o f full-scale w a l l specimen types (a) W 4 and (b) W 5  211  Figure 7.3.  Full-scale w a l l specimen (a) w i t h o u t sheathing and (b) w i t h sheathing b e i n g prepared f o r testing  212  Tape and spackle b e i n g applied to g y p s u m w a l l b o a r d on a full-scale w a l l specimen  212  Figure 7.4.  Figure 7.5.  Full-scale w a l l stud connection types: (a) SPF j o i s t hanger w i t h tension  ,- ' v  strap; (b) L S L j o i s t hanger w i t h tension strap; (c) specially fabricated stucl connector; and (d) L S L j o i s t hanger connected to the end plate w i t h screws  214  Figure 7.6.  Schematic o f connector type C. (a) face v i e w and (b) side v i e w  215  Figure 7.7.  Photo o f the test set-up f o r d e t e r m i n i n g the response o f full-scale' w a l l s under axial and transversal loads  Figure 7.8.  Idealization o f the test set-up f o r d e t e r m i n i n g the response o f full-scale w a l l s under axial and transversal loads  Figure 7.9.  217  218  Full-scale w a l l test set-up details: (a) displacement and r o t a t i o n transducers at roller-supported end; (b) r a c k i n g stop and transversal displacement transducer at m i d - s p a n ; ( c ) transversal displacement transducer at m i d - s p a n o f the centre stud; and (d) slippage p o t at the end o f the centre stud  220  Figure 7.10. Schematic o f full-scale w a l l test set-up  222  Figure 7 . 1 1 . Schematic o f full-scale w a l l test set-up  223  Figure 7.12. Transversal and axial loads as a f u n c t i o n o f t i m e f o r test protocols: (a) T I ; (b) T 2 ; ( c ) T 3 ; a n d (d) T 4  225  L i s t o f Figures  xix  Figure 7.13. W a l l specimen b e i n g prepared f o r second test on internal side: (a) i n v e r t i n g a w a l l using an overhead crane; and (b) an inverted w a l l i n test frame  227  Figure 7.14. Full-scale w a l l studs tested under t h i r d p o i n t l o a d i n g to determine m o d u l u s o f elasticity  229  Figure 7.15. C u m u l a t i v e d i s t r i b u t i o n o f m o d u l u s o f elasticity f o r full-scale w a l l studs, plates and b l o c k i n g F i g u r e 7.16. Load-displacement relationships obtained f r o m testing, (a) stud m o d u l u s o f elasticity, (b) connection stiffness, (c) sheathing thickness, (d) stud spacing, (e) SPF w i t h gaps i n the sheathing, and ( f ) L S L w i t h gaps i n the sheathing  229  236  Figure 7.17. R e d u c t i o n i n b e n d i n g stiffness due to axial load f o r w a l l specimens w i t h SPF studs spaced at 610 m m o n centre Figure 7.18. R e d u c t i o n i n b e n d i n g stiffness due to "axial load f o r w a l l specimens w i t h L S L studs spaced at 610 m m o n centre  242  243  Figure 7.19. R e d u c t i o n i n b e n d i n g stiffness due to axial load f o r w a l l specimens w i t h L S L studs spaced at 1,220 m m on centre  244  Figure 7.20. Load-displacement response o f w a l l specimens loaded i n the transversal d i r e c t i o n o n the sheathed and un-sheathed faces, (a) W a l l 508, (b) W a l l 509, a n d ( c ) W a l l 512 Figure 7 . 2 1 . Lateral-torsional b u c k l i n g o f the studs i n a tall w o o d - f r a m e w a l l  247 248  Figure 7.22. Load-displacement response o f w a l l s loaded i n the axial and transversal directions w i t h and w i t h o u t g y p s u m w a l l b o a r d on the interior face  250  Figure 7.23. L o a d - s l i p response o f the pots located nearest to the roller-supported end o f the w a l l s w i t h and w i t h o u t g y p s u m w a l l b o a r d o n the interior face  251  Figure 7.24. Load-displacement response o f the w a l l w i t h g y p s u m w a l l b o a r d loaded b e y o n d the linear-elastic range  ^.253  Figure 7.25. Transversal p o i n t load applied to the m i d d l e o f the central stud o f a w a l l specimen  257  Figure 7.26. A n a l y t i c a l l y predicted m i d - h e i g h t d e f l e c t i o n o f the central stud o f a w a l l w i t h an increasing n u m b e r o f studs  260  Figure 7.27. A n a l y t i c a l l y predicted m i d - h e i g h t d e f l e c t i o n o f each stud i n a w a l l w i t h an increasing n u m b e r o f studs  261  Figure 7.28. Load-displacement response o f w a l l specimens under a x i a l load o n l y f o r (a) w a l l W l w i t h L S L studs, (b.) connection type B, and (c) tension connectors on three studs and (d) load-rotation response o f w a l l specimens under a x i a l load o n l y  265  L i s t o f Figures  xx  Figure 7.29. Failure modes o f the full-scale w a l l stud c o n n e c t i o n types under a x i a l load: (a) SPF j o i s t hanger w i t h tension strap; (b) L S L j o i s t hanger w i t h tension strap; (c) manufactured j o i s t hanger; and (d) L S L j o i s t hanger screwed to plate  267  Figure 7.30. Calculated end restraint rotational stiffness based o n the results o f testing. (a) stud spacing and connector type, (b) sheathing c o n n e c t i o n stiffness, and (c) stud material and sheathing type Figure 7 . 3 1 . E n d restraint rotational stiffness o f w a l l 504 w i t h varied applied a x i a l load  273 274  Figure 7.32. Calculated end restraint rotational stiffness based o n the results o f testing. (a) stud spacing and connector type, (b) sheathing c o n n e c t i o n stiffness, (c) stud material and sheathing type, and (d) w a l l height Figure 7.33. Load-displacement relationships obtained f r o m testing, (a) w a l l w i t h SPF studs, (b) effect o f connection stiffness, (c) effect o f connector type, and (d) effect o f sheathing type  276  279  Figure 7.34. Failure modes, o f the full-scale w a l l s w i t h SPF studs under transversal loads: (a) and (b) tension failure i n w a l l studs; and (c) deformations i n stud connection  280  Figure 7.35. Failure modes o f full-scale w a l l 505 under transversal loads: (a) s p l i t t i n g o f the end plate at the roller-supported end;(b) deformations i n stud c o n n e c t i o n ; and (c) failure o f an outside stud  282  Figure 8 . 1 . (a) w o o d f l o o r assembly and (b) T - b e a m element strip (Foschi, 1989)  289  Figure 8.2.  Schematic o f w a l l type W 2 in P A N E L p r o g r a m  291  Figure 8.3.  D e f i n i t i o n o f the parameters i n the load-slip f u n c t i o n b y Foschi (1974)  293  Figure 8.4.  Progression o f the b e a m - s p r i n g analog m e t h o d , (a) composite w o o d - f r a m e system, (b) transverse stiffness represented as an equivalent beam perpendicular to the load resisting elements, and (c) composite load resisting elements represented as springs supporting the equivalent transverse b e a m ( M c C u t c h e o n , 1984)  294  Figure 8.5.  Load-displacement response c o m p a r i s o n f o r w a l l 502  296  Figure 8.6.  Load-displacement response c o m p a r i s o n f o r three different studs i n w a l l 502  297  Figure 8.7.  Load-displacement response comparison f o r w a l l 504  298  Figure 8.8.  Load-displacement response c o m p a r i s o n f o r w a l l 509  299  Figure 8.9.  H i s t o g r a m o f analytical predictions versus test results f o r b e n d i n g stiffness assuming p i n ended supports  302  L i s t o f Figures  xxi  Figure 8.10. H i s t o g r a m o f analytical predictions versus test results f o r b e n d i n g stiffness assuming one end o f s i m p l y supported w a l l has a rotational spring Figure A . l . T y p i c a l load-displacement results  302 329  Acknowledgements  xxii  A C K N O W L E D G E M E N T S  T h i s project was conducted w i t h the f i n a n c i a l and i n - k i n d support f r o m N a t u r a l Resources Canada (Canadian Forest Service), the N a t u r a l Sciences and E n g i n e e r i n g Research C o u n c i l o f Canada, the Department o f C i v i l E n g i n e e r i n g at the U n i v e r s i t y o f B r i t i s h C o l u m b i a , and F o r i n t e k Canada C o r p . and its industry members.  The support o f all o f these institutions is g r a t e f u l l y  acknowledged.  I w o u l d l i k e to thank m y t w o supervisors, D r . M a r j a n P o p o v s k i at F o r i n t e k and D r . H e l m u t P r i o n at U B C , f o r their guidance, technical advice, and financial support.  T h e y b o t h gave m e a great  deal o f f r e e d o m i n p u r s u i n g this research topic but were always available w h e n I needed assistance.  I w o u l d also like to thank D r . Ricardo Foschi at U B C and D r . E r o l K a r a c a b e y l i at  F o r i n t e k f o r their professional advice d u r i n g the research project.  The extensive experimental p o r t i o n o f this thesis w o u l d not have been possible w i t h o u t the assistance o f the engineers, technologists, and technicians at Forintek.  I w o u l d like to thank  H e n l e y Fraser, Paul S y m o n s , T o n y T h o m a s , L e n Stroh, Jules G a r d y , R o y A b b o t t , and B i l l Deacon f o r their i n v o l v e m e n t i n this research. I a m especially grateful to H e n l e y Fraser and Paul Symons f o r their advice and guidance o n the experimental test p r o g r a m and their k n o w l e d g e o f w o o d construction.  I w o u l d like to thank m y parents, Frank and Elaine, w h o have supported me i m m e a s u r a b l y and have inspired me to strive to produce the best w o r k that I a m capable of.  Introduction  1  1.  I N T R O D U C T I O N  1.1  PROBLEM OVERVIEW  I n N o r t h A m e r i c a , w o o d - f r a m e construction u t i l i z i n g d i m e n s i o n l u m b e r has been i n use since the early 1 9  th  century. There are m a n y examples o f houses b u i l t w i t h this system that are m o r e than  100 years o l d and still continue to p e r f o r m their o r i g i n a l f u n c t i o n . A l t h o u g h the system has e v o l v e d and changed over t i m e , w o o d - f r a m e construction still remains s i m p l e i n concept and w e l l w i t h i n the scope o f the average builder. W o o d - f r a m e construction w i t h  its  comfort,  e c o n o m y , energy e f f i c i e n c y and use o f renewable resources, is so practical and effective that m o r e than n i n e t y percent o f N o r t h A m e r i c a n homes are still constructed u s i n g this b u i l d i n g method.  A  wall  system  utilizing  regular  residential  wood-frame  construction  methods  c o m m o n l y f o u n d i n N o r t h A m e r i c a is s h o w n i n Figure 1.1.  Efforts have been made to extend the use o f this m e t h o d to non-residential  applications.  D e v e l o p m e n t s such as hotels, motels, l o w - r i s e c o m m e r c i a l properties, c o m m u n i t y centres and other b u i l d i n g applications are a l l b e n e f i t i n g f r o m the advantages that w o o d - f r a m e construction has to offer. I n spite o f this market expansion, the p r o p o r t i o n o f non-residential b u i l d i n g s constructed w i t h w o o d remains relatively l o w c o m p a r e d to other construction materials such as steel, concrete  or masonry.  F o r applications  such as hotels and motels, the  wood-frame  construction concept can be used w i t h little m o d i f i c a t i o n f r o m its residential v e r s i o n . T h a t is n o t the case, h o w e v e r , f o r m o s t industrial or c o m m e r c i a l buildings. These b u i l d i n g s usually require larger open spaces and greater heights than other non-residential b u i l d i n g s .  Introduction  2  R e l a t i v e l y small r o o f and f l o o r spans  T h i n sheathing  Repetitive, sawn lumber framing closely spaced  Studs end nailed to plates  Concrete f o u n d a t i o n w i t h anchor bolt  Figure 1.1. Regular residential w o o d - f r a m e construction i n N o r t h A m e r i c a .  T o assist the specifiers o f larger c o m m e r c i a l and industrial structures, the Canadian W o o d C o u n c i l has issued t w o publications d u r i n g the last f o u r years. The " D e s i g n and C o s t i n g W o r k b o o k " gives detailed design and costing i n f o r m a t i o n on single storey b u i l d i n g s w i t h a f l o o r area o f up to 14,400 square metres ( C W C , 1999). The f o l l o w up p u b l i c a t i o n " T a l l  Walls  W o r k b o o k " ( C W C , 2000) provides i n f o r m a t i o n on tall w a l l design f o r c o m m e r c i a l and industrial structures. T a l l w a l l s are an extension o f p l a t f o r m w o o d - f r a m e construction into non-residential applications, where w a l l heights are usually f r o m 4.8 m (16 ft) to 10.7 m (35 f t ) . The T a l l W a l l s W o r k b o o k provides stud tables f o r lumber studs and studs made f r o m selected engineered w o o d  Introduction  3  products up to 10.7  m (35 ft) i n height. The engineered w o o d products considered include  S e l e c T e m ™ ( L V L ) , TimberStrand® ( L S L ) and W e s t l a m ® ( G l u l a m ) . A t y p i c a l t a l l w o o d - f r a m e w a l l system is s h o w n i n Figure  1.2.  L i g h t , long-span r o o f structure  T h i c k sheathing  Engineered lumber framing widely spaced  Studs connected to plates for h i g h shear and u p l i f t forces  Short masonry w a l l w i t h anchor b o l t  Figure 1.2.  T a l l w o o d - f r a m e w a l l construction.  The publications m e n t i o n e d above p r o v i d e an excellent foundation for the use o f tall w a l l s i n c o m m e r c i a l structures. T h e y are b u i l t on the l o n g - t e r m positive experience o f u s i n g w o o d - f r a m e construction i n residential applications. Incremental research contributions, however, are needed i f tall walls are to make further inroads into the non-residential construction market. Some o f the current restrictions on w o o d - f r a m e construction i n the Canadian W o o d D e s i g n Code seem o v e r l y conservative and m a y not be appropriate f o r tall w o o d - f r a m e walls. B y u s i n g t h i c k e r sheathing  Introduction  4  on the w a l l s , f o r example, d e f l e c t i o n criteria under design w i n d loads c o u l d easily be met b y accounting f o r the composite action that exists between the sheathing and the stud. i n c l u s i o n o f composite action is c u r r e n t l y not p e r m i t t e d i n the code.  The most  The  important  parameter that affects the amount o f composite action i n a w a l l system is the stiffness o f the connection between the sheathing and the studs, w h i c h t y p i c a l l y consists o f nails alone or nails c o m b i n e d w i t h adhesive.  There is currently v e r y little test data available o n the  load-  displacement response o f these types o f connections w h e n t h i c k sheathing or engineered w o o d products are used, and the degree o f composite action that can be achieved.  O f the test programs that have investigated composite action between w a l l sheathing and studs i n w o o d - f r a m e w a l l s over the past t h i r t y years, none have i n c l u d e d components and connections that s i g n i f i c a n t l y increased the b e n d i n g stiffness o f the w a l l s . These tests were m o s t l y concerned w i t h d e t e r m i n i n g the amount o f composite action i n e x i s t i n g structures that were b u i l t w i t h regular w o o d - f r a m e construction techniques.  For larger w a l l s , an increase i n the stud spacing  w o u l d certainly be an o p t i o n w o r t h investigating, as it w o u l d l i k e l y result i n a m o r e efficient b u i l d i n g system. The m a x i m u m spacing currently a l l o w e d b y the code seems o v e r l y restrictive as it is based o n research conducted o n regular w o o d - f r a m e shearwalls w i t h t h i n sheathing. U s i n g thicker sheathing as required to span the longer distance between studs w i l l also m o s t l i k e l y increase the composite action i n the w a l l system and a l l o w f o r greater stud spacing.  The studs i n regular w o o d - f r a m e w a l l s are t y p i c a l l y o n l y connected to the top and b o t t o m w a l l plates w i t h t w o or three nails.  D u e to the increased w a l l heights and r o o f spans f o u n d i n  b u i l d i n g s w i t h t a l l w a l l s , the stud connections are subjected to m u c h higher loads necessitating the use o f special connectors. These connectors, and the labour i n v o l v e d i n their installation, can increase the total cost o f construction s i g n i f i c a n t l y .  M o r e e c o n o m i c a l connection solutions are  needed w h i l e m a i n t a i n i n g the overall performance o f the tall w o o d - f r a m e w a l l s under axial and  5  Introduction  transversal, or out-of-plane, loads.  For larger b u i l d i n g s w i t h large free-standing w a l l s the a x i a l  loads f r o m show, r a i n , and w i n d o n the roof, c o m b i n e d w i t h the transversal w i n d loads on the w a l l surface, w i l l require construction d e t a i l i n g that is b e y o n d the r e a l m o f regular w o o d - f r a m e construction.  To  achieve  economically  competitive  solutions, m o r e  sophisticated  design  methods and analysis models are required.  Sophisticated mathematical models f o r the analysis o f tall w o o d - f r a m e w a l l s under axial and transversal loads are an essential t o o l to extend the a p p l i c a t i o n o f experimental results, predict the l o a d - d e f l e c t i o n response, and p e r f o r m parametric studies on their performance.  Once  analytical m o d e l s have been v e r i f i e d against test results, the m o d e l s can then be used to determine factors f o r use i n design, and to validate s i m p l e r , a n d u s e r - f r i e n d l y analysis tools f o r use i n design offices.  1.2 RESEARCH OBJECTIVES For the reasons m e n t i o n e d above, F o r i n t e k Canada C o r p . initiated a research p r o g r a m on the structural performance o f tall w a l l s i n Canada i n 2003. The objective o f this p r o g r a m is to assist the forest products industry i n e x p a n d i n g its share o f the market i n the construction o f b o x - t y p e b u i l d i n g s i n the c o m m e r c i a l and industrial sectors using tall w o o d - f r a m e w a l l s .  T h i s thesis  focuses on the structural performance o f t a l l w a l l s under axial and transversal loads.  A  subsequent study w i l l focus on the performance o f these w a l l s under in-plane lateral loads due to w i n d and earthquakes.  The m a i n objectives o f this thesis o n t a l l w o o d - f r a m e w a l l s can be  s u m m a r i z e d as f o l l o w s : •  Increase the b o d y o f k n o w l e d g e on the performance o f w o o d - f r a m e w a l l s under axial and transversal loads and their component properties w i t h special attention to the use o f engineered w o o d product studs and t h i c k , oversized sheathing;  Introduction  •  6  D e t e r m i n e the factors that influence the response o f t a l l w o o d - f r a m e w a l l s under a x i a l and transversal loads;  •  Investigate the appropriateness o f the l i m i t on stud spacing c u r r e n t l y f o u n d i n the Canadian W o o d D e s i g n Code for w o o d - f r a m e w a l l s ;  •  D e t e r m i n e e c o n o m i c a l stud connections for tall w o o d - f r a m e w a l l s to resist axial and shear loads and study the influence o f these connections on the o v e r a l l performance o f tall w a l l s under axial and transversal loads;  •  V e r i f y linear equations to predict composite action f o r use i n design and v e r i f y non-linear f i n i t e element m o d e l s f o r use i n future research;  •  1.3  Propose a simple analysis m o d e l f o r tall w a l l s that can be used i n engineering practice  SCOPE  T o meet the objectives o u t l i n e d above, a research p r o g r a m was devised, w h i c h consists o f  five  parts: 1.  A  literature  review  on  wood-frame  construction  including  previous  research  on  composite construction and full-scale w a l l testing; 2.  M o n o t o n i c testing on the i n d i v i d u a l material components, i n d i v i d u a l connections, and composite stud elements o f a full-scale tall w o o d - f r a m e w a l l ;  3.  M o n o t o n i c testing to determine the b u c k l i n g characteristics o f sheathing panels under r a c k i n g loads to determine the v a l i d i t y o f the restriction o n stud spacing;  4.  M o n o t o n i c testing o f full-scale t a l l w o o d - f r a m e w a l l s under axial and transversal loads;  5.  A n analytical study to v e r i f y mathematical models to expand the test results to different design c o n d i t i o n s and establish appropriate design factors.  Introduction  7  There have been numerous f o r m u l a t i o n s and c o m p u t e r models developed over the past f i f t y years to analyze the response o f composite w o o d - f r a m e diaphragms.  A r e v i e w o f these studies  was needed to determine accurate and s t r a i g h t f o r w a r d methods f o r p r e d i c t i n g the response o f the tests conducted i n this study, and that c o u l d also be easily incorporated into standard design practice.  Because o f the inherent v a r i a b i l i t y and n o n - l i n e a r i t y o f w o o d , m a n y o f the components o f tall w o o d - f r a m e w a l l s were tested separately p r i o r to testing full-scale w a l l specimens. properties obtained f r o m these component tests are required input values i n the  The  analytical  models. A chart s h o w i n g the organization o f the tests conducted i n this study is s h o w n i n Figure 1.3. Because the n o n - l i n e a r i t y o f the i n d i v i d u a l connections between the sheathing and the studs were greater than that o f the larger composite components and full-scale w a l l s , m a n y more connections types were tested i n order to b u i l d a database that c o u l d be incorporated into future analytical studies.  Tests were subsequently conducted on composite T-beams, c o m p r i s i n g a stud and a tributary w i d t h o f sheathing, i n b e n d i n g to study the sensitivity o f composite action to specific properties such as connection stiffness, m o d u l u s o f elasticity, sheathing thickness, and the presence o f gaps i n the sheathing.  Shearwall tests were conducted to determine the out-of-plane  buckling  characteristics o f sheathing panels subjected to lateral loads. The shearwall tests w e r e conducted to validate the use o f large stud spacing i n the full-scale w a l l tests. A d d i t i o n a l properties o f t a l l w o o d - f r a m e w a l l s were also investigated t h r o u g h o u t the course o f the full-scale tests.  These  i n c l u d e d : the interaction o f a x i a l and transversal l o a d ; the presence o f non-structural sheathing; the effect o f load reversal o n b e n d i n g stiffness; in-plane load d i s t r i b u t i o n effects; the effect o f end support conditions on m i d - h e i g h t deflections; and response o f several stud connection types to a x i a l and transversal loads. The stud materials used f o r b o t h the composite T - b e a m and f u l l -  8  Introduction  scale w a l l tests were spruce-pine-fir sawn lumber and laminated strand lumber. T h e nails used to connect the sheathing to the studs f o r a l l tests were spiral nails, as these are c o m m o n l y used i n the construction o f w o o d - f r a m e w a l l s .  Full-Scale Wall Test  1  I Shearwall Test  I Stud MOE Bending Test  T-Beam Test  I Sheathing MOE Bending Test  I  Stud Connection Test 1  Load-Slip Connection Test  Nail Bending Test  Figure 1.3.  I Nail Withdrawal Test Material Density Test  Tests conducted over the course o f this study.  1.4 THESIS OUTLINE The thesis presents the different steps f o l l o w e d i n the study to achieve the research objectives. A n o v e r v i e w o f w o o d - f r a m e construction i n N o r t h A m e r i c a , past performance o f w o o d - f r a m e b u i l d i n g s , the advantages and disadvantages o f w o o d , concrete, steel, a n d m a s o n r y materials w h e n used i n non-residential construction, and the corresponding literature r e v i e w o n issues concerning tall w o o d - f r a m e w a l l s are g i v e n i n the second chapter. Chapters 3 and 4 describe the m o n o t o n i c tests conducted o n a n u m b e r o f different nailed connections under lateral a n d w i t h d r a w a l loads, respectively.  I n Chapter 5 the m o n o t o n i c and c y c l i c tests o n composite T -  beams under transversal loads are described, i n a d d i t i o n to analytical predictions u s i n g linear approximations. chapter.  A discussion o f issues regarding composite action is also presented i n this  Chapter 6 describes the m o n o t o n i c lateral load tests conducted o n the shearwalls. T h e  Introduction  9  m o n o t o n i c tests that were conducted on full-scale t a l l w o o d - f r a m e w a l l s under axial transversal loads are presented i n Chapter 7.  Several issues a f f e c t i n g the p e r f o r m a n c e o f tall  w o o d - f r a m e w a l l s are also addressed i n this chapter.  Results and discussion o n the test results  f r o m all chapters include l o a d - d e f o r m a t i o n characteristics and m a x i m u m loads. predictions o f the full-scale tall w a l l tests are presented i n Chapter 8. s u m m a r y o f the results o f the study is g i v e n .  and  Analytical  F i n a l l y , i n Chapter 9 a  The chapter also provides recommendations f o r  changes that c o u l d be made to current design practice and recommendations f o r further research. A list o f references is g i v e n i n Chapter 10 i n the thesis.  10  Literature R e v i e w  2. L I T E R A T U R E  R E V I E W  2.1 WOOD-FRAME CONSTRUCTION IN NORTH AMERICA The research investment into the engineering properties o f Canadian w o o d species i n the 1970's and 1980's y i e l d e d enormous returns f o r the Canadian l u m b e r industry and paved the w a y f o r its current d o m i n a t i o n i n the residential market i n N o r t h A m e r i c a . I n the construction market most o f the Canadian w o o d products exported are used i n residential construction, w h i l e o n l y a small percentage is used i n non-residential construction.  The N o r t h A m e r i c a n non-residential market  is vast and comparable i n size to the residential market.  It is c u r r e n t l y v a l u e d at about U S $ 3 0 0  b i l l i o n a year, and as such it should be a m a j o r target f o r the w o o d products industry. The total value o f non-residential construction i n the U n i t e d States alone i n 1999 was U S $ 2 7 3 . 5 b i l l i o n , w h i c h is nearly 8 0 % o f the value o f n e w residential homes i n the same year ( U S B C , 2000).  I n the past, w o o d and engineered w o o d products have made o n l y modest inroads into this steel and concrete d o m i n a t e d market. T h i s is especially surprising g i v e n the fact that about 90 percent o f all non-residential construction a c t i v i t y is. f o u r stories or less and c o u l d incorporate w o o d products i n structural applications according to most b u i l d i n g codes.  Y e t , the non-residential  construction m a r k e t used less than 1 1 % o f the amount o f w o o d products used i n residential construction i n 1995, and this figure is i n decline f r o m a previous study conducted i n 1985 (McKeever  and A d a i r ,  1998).  It is d i f f i c u l t  to estimate the exact value o f this  missed  o p p o r t u n i t y , but a r o u g h estimate t a k i n g into account b u i l d i n g code restrictions, is that an additional 9.9 m i l l i o n cubic metres (7.5 b i l l i o n b o a r d feet) o f l u m b e r and 560 m i l l i o n square  Literature R e v i e w  11  metres (6 b i l l i o n square feet) o f panels c o u l d have been used i n the U n i t e d States f o r n o n residential construction i n 1995 alone.  The need to examine n e w w o o d markets becomes even m o r e urgent as steel and concrete s l o w l y continue to erode w o o d ' s dominance i n the residential sector.  It is estimated that c a p t u r i n g an  additional 2 % o f the non-residential market share w o u l d result i n an increase o f the i n d u s t r y income o f U S $ 5 . 4 b i l l i o n per year ( U S B C , 2000).  Furthermore, this value does not take into  account the fact that the greater the use o f w o o d i n structural applications, the greater its use becomes f o r non-structural and f i n i s h i n g purposes as w e l l .  For all these reasons, a successful  penetration o f the forest products industry into the non-residential market is critical at this time.  T h e direct m a r k e t i m p a c t o f a tall w o o d - f r a m e w a l l s o l u t i o n is d i f f i c u l t t o estimate at this point. The most recent non-residential w o o d usage data available does not contain sufficient detail to accurately make such an estimate ( M c K e e v e r and A d a i r , 1998).  The details required f o r an  accurate estimate w o u l d include specific usage and b u i l d i n g code i n f o r m a t i o n f o r the aggregate data reported b y M c K e e v e r and A d a i r .  N e w non-residential b u i l d i n g s constructed i n 1995  totalled a p p r o x i m a t e l y 2 6 0 m i l l i o n square metres (2.8 b i l l i o n square feet) o f area, contained 140 m i l l i o n square metres (1.5 b i l l i o n square feet) o f exterior w a l l s , and had a total construction value o f U S $ 1 8 5 b i l l i o n . W o o d was used i n o n l y 1 0 % o f exterior w a l l s . W h e n w o o d is used at all in non-residential b u i l d i n g s , it is preferred f o r roofs ( 1 9 % o f non-residential roofs use w o o d ) , upper-story floors ( 1 4 % ) , and interior w a l l s ( 1 3 % ) .  A  2001 study e x p l o r e d the reasons w h y w o o d is not used m o r e often i n  construction (Gaston et. al., 2001).  non-residential  Code l i m i t a t i o n s , w h i c h restrict the use o f w o o d to smaller  b u i l d i n g s and m a y f o r b i d it entirely f o r some b u i l d i n g types, were cited as a p r i m a r y reason. W o o d is least restricted as a r o o f material, w h i c h m a y e x p l a i n w h y its non-residential usage is  Literature R e v i e w  12  greatest i n r o o f applications.  A n o t h e r k e y h u r d l e f o r w o o d is total design and installed costs:  w o o d was cited as not c o s t - c o m p e t i t i v e w i t h other materials, p a r t i c u l a r l y pre-engineered steel. Steel is q u i c k l y and i n e x p e n s i v e l y erected f o r simple warehouse-style structures, w h i c h is w h y it is a strongly preferred material i n this market.  I n other tall w a l l cases, concrete has a m a j o r  advantage over w o o d f o r its impact and vandal resistance i n , f o r example, prisons, schools, and warehouses w i t h m o v i n g f o r k l i f t s and m a c h i n e r y .  A s s u m i n g that a tall w o o d - f r a m e w a l l is cost-competitive w i t h steel, masonry, and t i l t - u p concrete and can meet all the performance expectations o f these materials f o r a g i v e n b u i l d i n g application, then the market potential can be e x a m i n e d i n a r o u g h manner b y considering o n l y the size o f the m a r k e t f o r b u i l d i n g types w h i c h m i g h t include t a l l w a l l s . I n other w o r d s , i g n o r i n g the segment o f the m a r k e t that w o u l d not choose w o o d due to cost or specific usage issues. The segments o f the market w i t h p a r t i c u l a r l y stringent code restrictions on w o o d , f o r example, b u i l d i n g s that w o u l d be classified under code as "hazardous" categories w i l l also be ignored. Some tall w a l l b u i l d i n g applications, such as m a n y factories, w o u l d f a l l into those occupancies. I g n o r i n g current b u i l d i n g code restrictions is a reasonable assumption f o r a l o n g - t e r m forecast, as it is expected that the objective-based codes to be adopted i n near future w i l l p r o b a b l y place no such l i m i t a t i o n s on material as a f u n c t i o n o f c o m b u s t i b i l i t y .  I f a t a l l w a l l is defined as one w i t h a height somewhere i n the range o f 3.6 m to 10.7 m ( 1 2 ' to 3 5 ' ) , then the m a j o r i t y o f non-residential b u i l d i n g s w o u l d q u a l i f y as the target market, as a 3.6 m or larger f l o o r - t o - f l o o r height is t y p i c a l f o r non-residential b u i l d i n g s .  A m o r e realistic estimate  f o r market potential can be d e r i v e d b y considering w h i c h types o f b u i l d i n g s have tall w a l l s , perhaps  5 m  (16.5')  and higher, where w o o d - f r a m e  c o m p e t i t i v e w i t h other materials.  structures are expected to be  more  Factories, warehouses and b i g b o x retail stores are the m o s t  Literature R e v i e w  13  obvious examples o f these b u i l d i n g types, w h i c h actually represent the m a j o r i t y o f n o n residential construction.  I n 1995, the categories o f "stores" and "industrial b u i l d i n g s " together  accounted f o r 5 8 % o f all non-residential f l o o r area built.  The potential incremental v o l u m e f o r  w o o d i n these categories is 2.0 m i l l i o n cubic metres (1.5 b i l l i o n b o a r d feet) o f l u m b e r and 140 m i l l i o n square metres (1.5 b i l l i o n square feet) o f panels f o r stores, and 340,000 cubic metres (255 m i l l i o n b o a r d feet) o f l u m b e r and 130 m i l l i o n square metres (1.4 b i l l i o n square feet) o f panels f o r industrial b u i l d i n g s .  C o m b i n e d , this is 2.2 m i l l i o n cubic metres (1.7 b i l l i o n b o a r d  feet) o f l u m b e r and 270 m i l l i o n square metres (2.9 b i l l i o n square feet) o f panels, f o r a total value i n 2002 dollars o f C A D S 1.94 b i l l i o n . T h i s represents the m a x i m u m potential incremental m a r k e t f o r w o o d i n the retail and industrial categories o f b u i l d i n g s , and assumes that a l l  other  appropriate elements o f the b u i l d i n g are also made o f w o o d a l o n g w i t h the tall exterior w a l l s . U n d e r present code scenarios, some o f these b u i l d i n g s w o u l d be precluded f r o m w o o d due to a hazardous occupancy class and/or a f l o o r area above the m a x i m u m f o r combustible construction. H o w e v e r , other b u i l d i n g categories h o l d strong potential f o r a p p l i c a t i o n o f a tall w o o d - f r a m e w a l l s o l u t i o n : schools, offices, p u b l i c b u i l d i n g s and health care facilities.  It is d i f f i c u l t to  estimate w h a t f r a c t i o n o f these w o u l d convert to w o o d i f a set o f w o o d - b a s e d tall w a l l structural solutions were offered to designers.  2.2 PAST PERFORMANCE OF WOOD-FRAME BUILDINGS E v e n t h o u g h w o o d - f r a m e structures represent a significant p o r t i o n o f the existing b u i l d i n g stock i n N o r t h A m e r i c a , r e l a t i v e l y little is k n o w n about h o w these structures p e r f o r m under h i g h w i n d forces f r o m the standpoint o f engineering b e h a v i o u r ( R o s o w s k y et. al., 2000).  The need f o r  further research is warranted, as w i n d forces are the most c o m m o n source o f damage to l i g h t w o o d - f r a m e construction ( F E M A , 1997). Despite that fact, it has been documented that w o o d -  Literature R e v i e w  14  frame construction has p e r f o r m e d w e l l under h i g h w i n d forces and that a lot has been done to better understand these forces and h o w they affect b u i l d i n g s .  Recent w o r k has led to increased  design w i n d speeds i n b u i l d i n g codes f o r m a n y areas. A n d advances like h o l d - d o w n s , b r a c i n g , and fastening systems have resulted i n a b u i l d i n g system that can resist even the most extreme forces o f hurricanes ( C W C , 2002).  D e t e r m i n i n g h o w actual w i n d forces are applied t o a structure is v e r y c o m p l i c a t e d and depends on several variables. Factors such as geographic l o c a t i o n , variations i n topography, b u i l d i n g size and c o n f i g u r a t i o n , openings i n the b u i l d i n g , and b u i l d i n g stiffness all effect w i n d b e h a v i o u r and velocity.  W i n d near the earth's surface is a d y n a m i c p h e n o m e n o n , causing an erratic and  unpredictable c o n d i t i o n called gusting. t o t a l l y reversing its m o t i o n . building.  T h i s occurs w h e n w i n d suddenly changes d i r e c t i o n ,  The d i s t r i b u t i o n o f w i n d v e l o c i t y varies over the height o f a  Roughness elements on the earth's surface, w h i c h can range f r o m grass to other  b u i l d i n g s , s l o w d o w n the w i n d v e l o c i t y near the ground.  It is clear, therefore, that l o w - r i s e  b u i l d i n g s are m o r e greatly affected b y the presence o f these elements than are larger structures.  The presence o f large openings i n a b u i l d i n g can have a significant i m p a c t o n the m a g n i t u d e o f w i n d forces o n a structure.  B u i l d i n g s that have m a n y large openings such as warehouses and  industrial facilities are especially prone to h i g h w i n d forces f o r this reason. Figure 2.1 shows the d i s t r i b u t i o n o f w i n d forces o n a l o w - r i s e b u i l d i n g that is enclosed.  Because a different  atmospheric pressure exists inside the b u i l d i n g than exists outside, b o t h internal and external pressures act simultaneously o n the surfaces o f the b u i l d i n g . The internal pressures are smaller than the external but they are always added.  I n contrast, i f the b u i l d i n g has a large o p e n i n g  (Figure 2.2) then the internal pressures are a p p r o x i m a t e l y the same magnitudes as the external pressures creating significant w i n d forces o n the surfaces o f the b u i l d i n g .  Literature R e v i e w  15  Figure 2 . 1 . D i s t r i b u t i o n o f w i n d pressure o n an enclosed b u i l d i n g ( F E M A , 1997).  Figure 2.2. D i s t r i b u t i o n o f w i n d pressure o n a b u i l d i n g w i t h an o p e n i n g ( F E M A , 1997).  Because the d i s t r i b u t i o n and magnitude o f w i n d forces o n a b u i l d i n g is d i f f i c u l t to predict, b u i l d i n g codes have s i m p l i f i e d this p h e n o m e n o n so that it can be easily incorporated into design. Forces are determined f r o m w i n d velocities f o r specific geographic locations m u l t i p l i e d b y internal pressure, external pressure, and gust coefficients based on the b u i l d i n g type particular b u i l d i n g surface o f interest. static load case i n b u i l d i n g codes.  and  Despite its d y n a m i c nature, w i n d forces are treated as a  For w o o d design, this assumption is offset b y a d u r a t i o n o f  load factor that increases the strength o f w o o d f o r short-term loading. The load-duration effect is applied to b o t h w o o d members and connections.  Such a p h e n o m e n o n , h o w e v e r , has never been  d o c u m e n t e d i n connections and it has recently been s h o w n that an increase i n strength m a y not exist at a l l i n some types o f w o o d connections ( R o s o w s k y Reed, and T y n e r , 1998).  Literature R e v i e w  16  2.3 WOOD AS A STRUCTURAL MATERIAL I f the t a l l w o o d - f r a m e w a l l system is to make significant expansion i n the non-residential market, it has to take market share a w a y f r o m its competitors i n the market. T h e biggest competitors i n the market c u r r e n t l y are t i l t - u p concrete structures, m a s o n r y structures, and steel structures. Some o f the most i m p o r t a n t characteristics, advantages, and disadvantages o f t i l t - u p concrete, masonry, and steel construction are presented i n this section, f o l l o w i n g a s i m i l a r analysis o f t a l l wood-frame walls.  2.3.1 Tall Wood-Frame Walls 2.3.1.1 Advantages of Tall Wood-frame Walls  The expansion o f the use o f tall w o o d - f r a m e w a l l s as a structural system i n non-residential applications can benefit f r o m the experience and the success o f t i l t - u p concrete and prefabricated steel construction. T h e u l t i m a t e wood-based s o l u t i o n has to include a fast construction sequence, s i m p l i c i t y , and f l e x i b i l i t y , w h i l e a p p l y i n g the advantages o f the w o o d - b a s e d materials and their properties. These advantages are p r i m a r i l y realized b y the f o l l o w i n g :  •  W a l l fabrication is faster than i n concrete t i l t - u p and m a s o n r y construction.  I n the case o f  t i l t - u p concrete, the construction process includes the f a b r i c a t i o n o f perimeter installation o f reinforcement  steel and l i f t i n g  openings, and p l a c i n g the concrete.  forms,  inserts, b l o c k i n g the d o o r a n d w i n d o w  W i t h a t a l l w o o d - f r a m e w a l l system the f r a m i n g c r e w  can fabricate the entire w a l l assembly at one t i m e ; •  W o o d - f r a m e construction does n o t require c u r i n g t i m e f o r the w a l l panels, w h i c h i n the case o f concrete t i l t - u p construction is t y p i c a l l y ten days before the panels can be l i f t e d ;  Literature R e v i e w  •  17  W h e n using w o o d - f r a m e w a l l s there is no concern about delays due to c o l d and f r e e z i n g weather conditions.  W h e n u s i n g concrete t i l t - u p i n c o l d weather situations, the contractor  must p r o v i d e tenting, supplemental heat, and insulation blankets f o r c u r i n g o f the concrete. I f the temperature drops b e l o w - 5 ° C the concrete should not be placed at a l l ; •  Smaller, m o r e r e a d i l y available and less expensive m o b i l e cranes can be e m p l o y e d to l i f t the w o o d - f r a m e panels.  W o o d - f r a m e panels t y p i c a l l y w e i g h around 1 0 % o f comparable size  concrete w a l l panels; •  L a b o u r costs f o r w o o d - f r a m e construction are usually l o w e r due to reduced n u m b e r o f s k i l l e d trades necessary to frame the w a l l s . M a s o n r y construction requires h i g h l y trained labour that is m o r e expensive. which  increases  subcontractor  Concrete t i l t - u p construction requires the use o f several subcontractors,  the  building  cost.  For  example,  in  tilt-up  construction  a  framing  is needed to construct perimeter f o r m s , f o l l o w e d b y a r e i n f o r c i n g  steel  subcontractor, concrete subcontractor f o r p l a c i n g and f i n i s h i n g o f the concrete, structural steel subcontractor, l i f t i n g accessories supplier, crane and r i g g i n g subcontractor, w e l d i n g subcontractor, and sealant subcontractor; •  Concrete t i l t - u p is further l i m i t e d i n f l e x i b i l i t y b y l i m i t e d casting space.  I f the ratio o f  b u i l d i n g w a l l to f l o o r area is h i g h , it becomes d i f f i c u l t to lay out and cast a l l o f the w a l l panels at once. W o o d - f r a m e t i l t - u p w a l l s , however, can be placed on top o f each other after assembly, thus conserving space and a l l o w i n g greater f r e e d o m o f m o v e m e n t f o r materials and equipment o n the construction site; •  Because the mass o f w o o d - b a s e d w a l l s is m u c h l o w e r than that o f concrete w a l l s , the connections between the w a l l s and the r o o f become r e l a t i v e l y inexpensive. Such connections are massive and expensive i n concrete t i l t - u p construction.  18  Literature R e v i e w  •  Foundations f o r w o o d - f r a m e w a l l s are expected to be smaller than f o r t i l t - u p  concrete  because they do not need to support the h i g h dead loads associated w i t h concrete or m a s o n r y walls; •  The most important benefit o f u s i n g lighter tall w o o d - f r a m e w a l l s w i l l be i n the regions w i t h h i g h seismic a c t i v i t y , where large seismic forces are generated i n b u i l d i n g s that use concrete or masonry w a l l s . This is a significant issue since the proposed peak accelerations o f g r o u n d m o t i o n s (and seismic loads) f o r most cities i n Canada and the U n i t e d States w i l l increase according to proposed codes.  •  W o o d - b a s e d w a l l systems are expected to have a l o w e r cost o f interior w a l l  finishing  necessary f o r o f f i c e applications c o m p a r e d to that o f concrete t i l t - u p or m a s o n r y solutions. •  L i g h t industrial and c o m m e r c i a l b u i l d i n g s w i t h tall w o o d - f r a m e w a l l s are perceived as m o r e w a r m and aesthetic than other types o f b u i l d i n g s ;  •  W o o d b u i l d i n g s usually do not have the problems w i t h isolation and  air-conditioning  associated w i t h b u i l d i n g s i n other c o m p e t i t i v e materials; •  W o o d is a renewable material and w o o d - b a s e d solutions f o r structural systems are better choices f r o m an e n v i r o n m e n t a l p o i n t o f v i e w ;  •  General contractors m a y prefer w o o d - f r a m e solutions because they give t h e m m o r e c o n t r o l over the k e y components o f the b u i l d i n g . W i t h other systems they m a y depend on sub-trades to keep up w i t h the schedule.  W o o d is also a f l e x i b l e and f o r g i v i n g material o n the  construction site a l l o w i n g easier adjustments and alterations than other materials; •  It is easier to achieve the required insulation values i n w o o d - f r a m e construction than i n concrete t i l t - u p , masonry, or steel construction. extreme climates.  T i l t - u p concrete is not a g o o d system f o r  Steel studs, o n the other hand, have no insulating properties and thus  conduct c o l d t h r o u g h an insulated w a l l , r e d u c i n g the o v e r a l l i n s u l a t i o n value. I n such cases  Literature R e v i e w  19  insulation has to be installed o n the outside face o f the b u i l d i n g , w h i c h adds costs not incurred w i t h w o o d - f r a m e w a l l s .  2.3.1.2 Disadvantages of Tall Wood-frame Walls  Disadvantages o f w o o d - f r a m e construction used i n tall w a l l solutions include the f o l l o w i n g :  •  L a c k o f technical solutions f o r t a l l w a l l s w i t h various wood-based materials used f o r the studs and the sheathing;  •  L a c k o f design capacities f o r such technical solutions f o r tall w a l l s w i t h various stud spacing and sheathing thickness, subjected to g r a v i t y , w i n d and seismic l o a d i n g ;  •  L a c k o f technical-solutions and design values f o r connections used i n t a l l w a l l s ;  •  External d u r a b i l i t y concerns related to water penetration;  •  Internal d u r a b i l i t y concerns related to b u i l d i n g damage caused b y m o v i n g e q u i p m e n t or machinery;  •  Concerns related to b u i l d i n g b r e a k - i n and v a n d a l i s m ;  •  H i g h e r insurance p r e m i u m s .  Disadvantages related to the use o f w o o d as a structural material include shrinkage, w a r p i n g , s w e l l i n g , decay, d i s c o l o r a t i o n , m i l d e w , and termite problems.  2.3.2  Concrete Tilt-Up Construction  2.3.2.1 Description and Development  T i l t - u p concrete construction, w h i c h began i n southern C a l i f o r n i a i n the late 1950's as an economical and fast w a y to construct concrete w a l l s f o r warehouses, has become a m u l t i - b i l l i o n d o l l a r industry today, a c c o u n t i n g f o r over 10,000 b u i l d i n g s annually. It is n o w used f o r s h o p p i n g  Literature R e v i e w  20  centres, d i s t r i b u t i o n facilities, warehouses, m a n u f a c t u r i n g plants, o f f i c e b u i l d i n g s , schools churches, or i n other w o r d s , i n nearly every type o f one to f o u r - s t o r y  prisons, building.  A c c o r d i n g to a survey b y the T i l t - U p Concrete A s s o c i a t i o n ( T C A ) , over 60 m i l l i o n square metres (600 m i l l i o n square feet) o f t i l t - u p b u i l d i n g s were constructed i n 2001 alone ( T C A , 2 0 0 3 ) . That area equates to an estimated 12,000 b u i l d i n g s , r a n g i n g i n size f r o m 400 square metres (4,000 square feet) t o over 100,000 square metres (one m i l l i o n square feet).  Those f i g u r e s  conservatively place the area o f t i l t - u p w a l l s at 40 m i l l i o n square metres (400 m i l l i o n square feet), w h i c h at an average in-place cost o f U S $ 7 0 . 0 0 per square metre translates into an annual w a l l market o f U S $ 2 . 8 b i l l i o n .  Clearly, this is a huge market w i t h r o o m f o r n e w entries, not  necessarily u s i n g concrete as the construction material.  The t e r m " t i l t - u p " was coined i n the late 1940's to describe a" m e t h o d f o r constructing concrete w a l l s r a p i d l y and e c o n o m i c a l l y w i t h o u t the f o r m w o r k necessary for poured-in-place w a l l s . It is a two-step process: First, slabs o f concrete, w h i c h w i l l comprise sections o f w a l l , are cast h o r i z o n t a l l y o n the b u i l d i n g f l o o r slab, or separate casting slab.  T h e n , after attaining proper  strength, they are l i f t e d (tilted) w i t h a crane and set on prepared foundations to f o r m the exterior walls.  These large slabs o f concrete u s u a l l y w e i g h 40 tonnes or m o r e , and have an average  thickness o f 152 m m to 200 m m ( 6 " to 8"). There is little f o r m w o r k , since o n l y perimeter f o r m s are required to contain the concrete.  W h e n they have attained sufficient strength, u s u a l l y i n  seven t o ten days, a m o b i l e t r u c k crane is b r o u g h t to the j o b site t o l i f t t h e m and set t h e m o n prepared foundations. between t h e m caulked.  The erected panels are t e m p o r a r i l y braced, connected, and the j o i n t s The r o o f structure is then constructed and attached to the w a l l s to  complete the b u i l d i n g shell.  C o n s t r u c t i o n time for a t i l t - u p b u i l d i n g , f r o m c o m p l e t i o n o f the  f l o o r slab to c o m p l e t i o n o f the b u i l d i n g shell is often less than four weeks ( R u h n k e Schexnayder, 2002).  and  Literature R e v i e w  21  Over the years the investment i n research o f t i l t - u p concrete construction made b y the concrete industry resulted i n numerous refinements i n design and construction methods. The refinements resulted i n construction methods able to t i l t panels higher than 12 metres (40 feet), faster erection t i m e , w i t h l i f t i n g , setting, and b r a c i n g o f 20 to 30 panels per day, achieved t h r o u g h w e l l - t r a i n e d crews and i n n o v a t i v e ground-release l i f t attachments, as w e l l as a w i d e choice o f finishes available f o r architectural attractiveness. D e s i g n and construction o f t i l t - u p concrete structures is constantly b e i n g fine-tuned b y researchers, and h i g h l y s k i l l e d w o r k e r s , u s i n g state-of-the-art techniques. T o assure that q u a l i f i e d f i e l d personal are available, a c e r t i f i c a t i o n p r o g r a m is b e i n g developed j o i n t l y b y the T i l t - U p Concrete A s s o c i a t i o n and the A m e r i c a n Concrete Institute.  I n the sun-belt states today, an estimated 7 5 % o f all n e w one-story industrial b u i l d i n g s are o f t i l t u p construction, w i t h C a l i f o r n i a leading the w a y w i t h nearly 9 0 % . The geographical d i s t r i b u t i o n o f t i l t - u p construction across the U n i t e d States is the f o l l o w i n g : C a l i f o r n i a 3 6 % , Texas and the Southwest 2 0 % , O r e g o n and W a s h i n g t o n States 2 0 % , F l o r i d a 1 1 % , Southeast and Southern States 9%, Great Lakes States and the M i d w e s t 3%, and Northeast States 1 % ( B r o o k s , 1999). A n n u a l g r o w t h i n recent years has averaged nearly 2 0 % , w i t h an increasing n u m b e r contractors, developers and b u i l d i n g owners b e c o m i n g aware o f its m a n y advantages.  of  Recently  there has also been considerable t i l t - u p concrete construction i n M e x i c o , Canada, A u s t r a l i a , and N e w Zealand. The largest u n d e r - o n e - r o o f t i l t - u p b u i l d i n g , to date, is a 160,000 square metre (1.7 m i l l i o n square f o o t ) d i s t r i b u t i o n centre near C o l u m b u s , O h i o (Figure 2.3). panel erected is a 28 m ( 9 1 ' ) h i g h panel f o r a H o u s t o n , Texas church.  T h e tallest t i l t - u p The record f o r the  heaviest single panel goes to a 16 m ( 5 1 ' ) w i d e b y 13 m ( 4 2 ' ) h i g h , 300 m m ( 1 2 " ) t h i c k w a l l panel f o r a d i s t r i b u t i o n centre i n O n t a r i o , C a l i f o r n i a , w e i g h i n g 150 tonnes.  Although tilt-up  construction has been introduced i n every state o f the U n i t e d States, it still remains u n f a m i l i a r  Literature R e v i e w  22  construction m e t h o d i n m a n y geographical areas ( t y p i c a l l y i n the East and Northeast U n i t e d States).  Figure 2.3.  T h e largest t i l t - u p b u i l d i n g to date, a 160,000 square metre d i s t r i b u t i o n centre near C o l u m b u s , O h i o .  2.3.2.2 Advantages of Concrete Tilt-Up Construction  The non-residential construction market i n N o r t h A m e r i c a is h i g h l y c o m p e t i t i v e , and t i l t - u p construction is chosen o n l y w h e n its advantages, g i v e n the site and circumstances o f a project, clearly f a v o u r it. T h e N o r t h A m e r i c a n forest products industry, u s i n g tall w a l l solutions, should be able to capitalize o n the opportunities  where t i l t - u p construction is n o t the preferred  construction o p t i o n o f choice.  T o use t i l t - u p e f f e c t i v e l y and e c o n o m i c a l l y some basic criteria should be met. T h e b u i l d i n g s h o u l d be at least 6 0 0 square metres (6,000 square feet) i n f l o o r size.  U s u a l l y the larger the  b u i l d i n g , the more e c o n o m i c a l it is, a l l o w i n g enough r o o m to cast the panels and use the crane  Literature R e v i e w  23  and r i g g i n g c r e w i n an effective w a y . T i l t - u p construction requires the existence o f extensive w a l l surfaces, so that it can be d i v i d e d into liftable panels.  T h e panels should not w e i g h more  than 4 0 t o 6 0 tonnes each, and there should not be over 5 0 % o f surface area i n openings i n the panels. W h i l e one and t w o - s t o r y b u i l d i n g s are the most e c o n o m i c a l , m a n y t i l t - u p structures have three or four stories. W h e n basic conditions o f b u i l d i n g size are m e t , t i l t - u p construction offers the f o l l o w i n g advantages over other construction types ( B r o o k s 1999):  •  Economy - I n areas where t i l t - u p design and construction expertise are available, p a r t i c u l a r l y a trained crane and r i g g i n g crew, t i l t - u p can be m o r e e c o n o m i c a l than c o m p e t i n g c o n s t r u c t i o n methods f o r s i m i l a r types o f b u i l d i n g s ;  •  Speed of Construction - T h e g r o w t h o f concrete t i l t - u p construction can be attributed i n large part to the desire o f b u i l d i n g owners t o shorten the construction process, i n other w o r d s to condense the t i m e it takes to go f r o m b r e a k i n g g r o u n d t o tenant occupancy. F r o m the t i m e the f l o o r slab is placed, the t y p i c a l elapsed t i m e f r o m starting t o f o r m the panels u n t i l the b u i l d i n g shell is c o m p l e t e d is f o u r t o f i v e weeks ( T C A , 2003). T h i s a l l o w s b u i l d i n g owners to m i n i m i z e their construction f i n a n c i n g costs and m a x i m i z e their revenue stream;  •  Durability - T i l t - u p b u i l d i n g s usually show less v i s i b l e signs o f aging, a l t h o u g h architectural s t y l i n g is an issue i n older b u i l d i n g s .  •  Fire Resistance - Concrete offers h i g h fire protection. A 180 m m t h i c k m o n o l i t h i c w a l l , f o r example, has a f o u r - h o u r fire resistive r a t i n g ( N B C C , 1995);  •  Low Maintenance Costs - Sometimes the o n l y t h i n g that t i l t - u p structures need is a coat o f paint every six to eight years;  Literature R e v i e w  •  24  Lower Insurance Rates - T h e h i g h fire resistance o f t i l t - u p concrete w a l l s results i n l o w insurance p r e m i u m s , although this m i g h t not be the decisive argument f o r the selection o f the structural system;  •  Architectural Attractiveness - T h e architect has relative f r e e d o m to arrange and assemble the panels, a n d a w i d e choice o f surface finishes;  •  Expandability - B y p l a n n i n g f o r the p o s s i b i l i t y o f expansion, panel connections can be designed so that the panels can be detached and relocated;  •  Security - U n l i k e steel and w o o d - f r a m e b u i l d i n g s , f o r c e d entry t h r o u g h w a l l s can o n l y be made t h r o u g h door and w i n d o w openings;  •  Value Appreciation - L o w insurance costs, a l o n g w i t h b u i l d i n g d u r a b i l i t y a n d security, assure a desirable investment f o r the buyer;  •  Sound Insulation - Concrete construction i n general provides better sound insulation than w o o d - f r a m e construction.  2.3.2.3 Disadvantages of Concrete Tilt-Up Construction  The disadvantages o f the concrete t i l t - u p construction can be s u m m a r i z e d as f o l l o w s :  •  Poor Seismic Performance - T h e seismic performance o f concrete t i l t - u p b u i l d i n g s is one o f the biggest concerns a m o n g the engineering c o m m u n i t y .  Because the t i l t - u p w a l l s are h e l d  v e r t i c a l l y i n place b y a precarious c o n n e c t i o n to the roof, structures b u i l t i n the t i l t - u p style are a m o n g the most dangerous to occupants i n the event o f an earthquake. T h e first w a r n i n g about the seismic deficiencies o f t i l t - u p buildings came d u r i n g the 1964 A l a s k a n earthquake ( M a g n i t u d e o f 8.4), i n w h i c h three o f the five bays o f an E l m e n d o r f A i r Force Base warehouse f e l l to the g r o u n d .  A c c o r d i n g to a C i t y o f L o s Angeles report, quoted i n the  Literature R e v i e w  25  October 1 4 , 1999 issue o f " M e t r o " , the C a l i f o r n i a S i l i c o n V a l l e y ' s w e e k l y newspaper, the th  1994 N o r t h r i d g e C a l i f o r n i a Earthquake left m o r e than 4 0 0 t i l t - u p b u i l d i n g s w i t h a partial r o o f or exterior w a l l collapse in the San Fernando V a l l e y , out o f 1,200 existing i n the area ( F i g u r e 2.4 and 2.5). Fortunately no one was k i l l e d b y f a l l i n g debris largely because the earthquake took place before n o r m a l w o r k i n g hours. •  E x p e n s i v e C o n n e c t i o n s - Connections i n t i l t - u p structures have to be designed to sustain large loads, sometimes i n excess o f 250 k N (50,000 lbs.), w h i c h make t h e m expensive.  •  H i g h H e a t i n g a n d C o o l i n g Costs - Costs associated w i t h heating and c o o l i n g i n t i l t - u p structures are usually higher than those i n other types o f structures;  •  Skilled L a b o u r  - T i l t - u p construction requires the use o f s k i l l e d labour that  increase  construction costs; •  H i g h W e i g h t - The heavy w e i g h t o f t i l t - u p structures requires that large cranes be used to lift the panels.  T h i s process is v e r y expensive and cannot be e c o n o m i c a l l y feasible f o r smaller  buildings.  (a)  Figure 2.4.  Earthquake damage on older t i l t - u p structures d u r i n g the 1994 N o r t h r i d g e earthquake.  Literature R e v i e w  26  in I  Figure 2.5.  Earthquake damage o n a t i l t - u p construction site d u r i n g the 1994 N o r t h r i d g e earthquake.  Some o f the advantages and disadvantages presented above represent general trends.  The  b u i l d i n g size, location, occupancy type, design and performance criteria requested b y the o w n e r can change some o f the general advantages into disadvantages and vice versa. A detailed cost analysis o f the design solutions f o r a particular b u i l d i n g w i t h various construction materials is needed to determine the exact construction costs o f each solution.  2.3.3  Masonry Construction  M a s o n r y is one o f the oldest f o r m s o f construction k n o w n to man. T h r o u g h c i v i l i z a t i o n , builders have chosen m a s o n r y f o r its d u r a b i l i t y , p r o v i d i n g structures that can w i t h s t a n d the n o r m a l wear and tear f o r centuries.  The methods f o r p r o d u c i n g b r i c k have c o n t i n u e d to evolve t h r o u g h the time.  C u r r e n t l y , the  standard U n i t e d States b r i c k size is 64 m m b y 95 m m b y 203 m m ( 2 . 5 " x 3.75" x 8 " ) . T h e e v o l u t i o n o f b r i c k construction also led to the development o f the concrete masonry b l o c k .  Literature R e v i e w  Figure 2.6.  27  E x a m p l e o f a concrete masonry b u i l d i n g : L a M i r a d a C o m m u n i t y G y m n a s i u m that is 2,000 square metres.  Today's m u l t i - c o l o u r e d , m u l t i - t e x t u r e d concrete products give designers the chance t o create single a n d m u l t i - f a m i l y residences, o f f i c e b u i l d i n g s , warehouses, m u n i c i p a l b u i l d i n g s , religious b u i l d i n g s , m a n u f a c t u r i n g facilities, correctional facilities, learning institutions, and hospitals. A n example o f m o d e r n masonry structure is s h o w n i n Figure 2.6. Concrete M a s o n r y A s s o c i a t i o n ( N C M A ,  A c c o r d i n g to the N a t i o n a l  2003), the market f o r masonry b u i l d i n g i n N o r t h  A m e r i c a today is valued t o be 15 times larger than that o f concrete t i l t - u p , or a p p r o x i m a t e l y U S $ 4 0 b i l l i o n annually.  W h i l e concrete t i l t - u p construction is the most prevalent type o f  construction i n the western part o f the U n i t e d States, concrete masonry prevails i n the Northeast U n i t e d States.  2.3.3.1 Advantages of Masonry Construction  The advantages o f masonry construction over other construction types are listed b e l o w .  As for  the concrete t i l t - u p examples, some o f the advantages a n d disadvantages presented represent general trends. Advantages o f using masonry construction include:  Literature R e v i e w  •  28  Economy - M a s o n r y construction w i l l compete f a v o u r a b l y w i t h concrete t i l t - u p and w o o d frame  construction  f o r smaller  buildings  (under  about  inexpensive masonry materials and labour are available.  6 0 0 square  metres)  or  where  Crane t i m e is u n e c o n o m i c a l f o r  such small b u i l d i n g s i n the case o f t i l t - u p concrete;  •  Low Maintenance - Ease o f maintenance p l a y e d a m a j o r role i n the use o f concrete m a s o n r y t a l l slender w a l l s over t i l t - u p technologies.  U s u a l l y c o l o u r e d concrete masonry retains its  o r i g i n a l appearance w i t h m o r e consistency than the painted f i n i s h o n t i l t - u p w a l l s ;  •  Durability - Concrete masonry has a p r o v e n record o f d u r a b i l i t y and resistance to "abuse" that is required f o r some types o f b u i l d i n g s such as industrial or correctional facilities;  •  Fire Resistance - M a s o n r y construction has h i g h fire resistant properties. A solid b r i c k unit o f 178 m m thickness has a four h o u r fire p r o t e c t i o n r a t i n g ( N B C C 1995);  •  Low Maintenance - S i m i l a r l y to t i l t - u p structures, masonry structures have l o w maintenance costs;  •  Lower Insurance Rates - T h e fire resistance and d u r a b i l i t y o f m a s o n r y structures results i n l o w insurance p r e m i u m s ;  •  Insulation and Energy Efficiency - T h e energy e f f i c i e n c y o f concrete m a s o n r y can be i m p r o v e d b y isolating the h o l l o w - c o r e units. W h e n u s i n g t i l t - u p t e c h n o l o g y , i n s u l a t i o n is required o n the inside o f the w a l l where it is visible and unattractive, or requires that panels be pre-cast w i t h insulation sandwiched between t h e m ;  •  Bed Casting - N o f l o o r or large w o r k i n g space is needed p r i o r to w a l l construction;  •  Sound Insulation - M a s o n r y construction provides better sound insulation than m o s t construction types;  Literature R e v i e w  •  29  Life Cycle Cost Analysis - M a s o n r y structures can have higher i n i t i a l costs i n some cases but the l i f e cycle costs are usually l o w e r ;  •  Finishing - F r o m an architectural p o i n t o f v i e w , a w i d e v a r i e t y o f f i n i s h i n g textures and patterns exist f o r concrete m a s o n r y applications.  2.3.3.2 Disadvantages of Masonry Construction  Disadvantages o f m a s o n r y construction include the f o l l o w i n g :  •  Expensive Buildings - T h e i n i t i a l construction cost o f m a s o n r y b u i l d i n g s is u s u a l l y higher than that o f t i l t - u p concrete or steel b u i l d i n g s ;  •  Expensive and Highly Trained Labour - One o f the reasons w h y the i n i t i a l costs are so h i g h is because masonry construction is a labour intensive process.  D e p e n d i n g o n the  location, labour can be v e r y expensive i n N o r t h A m e r i c a ;  •  Low Earthquake Resistance. - U n r e i n f o r c e d m a s o n r y construction has the lowest resistance to earthquake loads o f any type o f construction.  A c o m b i n a t i o n o f h i g h stiffness, large  w e i g h t , and l o w d u c t i l i t y o f the material used, make this construction v e r y vulnerable even to moderate earthquakes.  There have been numerous examples o f w i d e spread damage to  m a s o n r y structures d u r i n g the past earthquakes (Figure 2.7). T o i m p r o v e the earthquake resistance o f m a s o n r y structures, they need to be reinforced w i t h vertical steel r e i n f o r c i n g bars d u r i n g construction, w h i c h further increases the cost;  •  Water Absorption - M a s o n r y blocks are water absorbent a n d to a v o i d water penetration they must be isolated (weather-proofed) to p r o v i d e a better p a i n t i n g ( f i n i s h i n g ) surface;  •  Modular Construction - Concrete m a s o n r y construction is a m o d u l a r construction u s i n g m a i n l y 203 m m b y 203 m m b y 4 0 6 m m ( 8 " x 8" x 16") n o m i n a l dimensions f o r the m a s o n r y b l o c k unit.  I t is thus d i f f i c u l t to have w a l l s w i t h o d d dimensions, s m o o t h curves, or s m o o t h  Literature R e v i e w  30  thickness transitions. T h i s is especially true for b u i l d i n g s w i t h a clear height greater than 7.3 m ( 2 4 ' ) where t i l t - u p w a l l s can vary more incrementally than the large j u m p s f r o m 203 m m ( 8 " ) to 305 m m ( 1 2 " ) required f o r masonry b l o c k units; •  I n s u l a t i o n - Concrete masonry blocks have l o w insulation values and generally w a l l s must be insulated, w h i c h is usually not an easy and inexpensive task;  •  D u r a t i o n o f C o n s t r u c t i o n - M a s o n r y construction usually requires the longest p e r i o d o f construction o f all c o m p e t i t i v e construction materials.  Figure 2.7. Damage to a masonry structure d u r i n g the N o r t h r i d g e earthquake.  2.3.4 Steel Construction Steel construction has one o f the largest shares o f the non-residential market i n N o r t h A m e r i c a ( A I S I , 2003).  T h e value o f the steel non-residential market is conservatively estimated to be  around U S $ 9 0 b i l l i o n a year. high-rise o f f i c e towers.  T h i s includes all non-residential applications o f steel, i n c l u d i n g  The p o r t i o n that corresponds to the low-rise steel structures, where  Literature R e v i e w  31  wood-based solutions can compete f o r the structural system, is expected to be more than 5 0 % o f this market.  Figure 2.9.  T y p i c a l example o f the interior o f a warehouse designed i n prefabricated steel.  Steel structures in non-residential applications can be categorized i n t w o types: c o n v e n t i o n a l and pre-engineered steel structures. C o n v e n t i o n a l steel structures are b u i l t w i t h hot r o l l e d structural steel members, and an engineering consultant designs each structure separately.  T h e y require  Literature R e v i e w  32  engineering design calculations a n d connection detailing f o r each separate b u i l d i n g .  Pre-  engineered steel b u i l d i n g s , on other hand, use c o l d - f o r m e d steel structural elements. I n this case the b u i l d i n g s  are m a i n l y  constructed using standard pre-designed  connections, w h i c h are manufactured i n a plant setting.  structural  sections a n d  Such elements are then shipped to the  construction site f o r b u i l d i n g assembly. Examples o f steel construction f o r warehouses are s h o w n i n Figure 2.8 and 2.9.  2.3.4.1 Advantages of Steel Construction  Steel construction i n non-residential applications offers the f o l l o w i n g advantages over other construction materials:  •  Strength - Steel offers the highest strength-to-weight ratio (matched b y that o f clear w o o d ) o f any w i d e l y used structural m a t e r i a l ;  •  Light structure - Steel structures, like w o o d structures, are m u c h lighter than r e i n f o r c e d concrete or m a s o n r y structures, attracting l o w e r h o r i z o n t a l forces due t o earthquakes;  •  Foundations - A s lighter structures, steel b u i l d i n g s also require smaller f o u n d a t i o n s ;  •  Material Efficiency - Pre-engineered b u i l d i n g s can be an additional 3 0 % lighter than c o n v e n t i o n a l steel b u i l d i n g s , w i t h even greater material efficiency.  Primary  structural  members are usually tapered ( v a r y i n g depth) w i t h larger depths i n areas o f h i g h stress;  •  Inexpensive Design - C o n s t r u c t i o n design, shop details and erection d r a w i n g s f o r prefabricated  (off-the-shelf  designs)  are usually  supplied  free  o f charge  from  the  manufacturer;  •  Construction Cost - M a t e r i a l and erection costs are exactly k n o w n based o n extensive experience w i t h other s i m i l a r b u i l d i n g s ;  Literature R e v i e w  •  33  Delivery Time - D e l i v e r y t i m e f o r prefabricated structures is u s u a l l y short, b e t w e e n six to eight weeks;  •  Design Accuracy and Quality Control - Steel structures offer h i g h accuracy o f dimensions and u n i f o r m material q u a l i t y due to close c o n t r o l o f the pre-fabrication process i n the plant. This s i g n i f i c a n t l y reduces the labour requirements at the construction site, w h i c h can be an important consideration i n the face o f g r o w i n g shortages o f s k i l l e d labour;  •  Combustibility - Steel buildings are rated as n o n - c o m b u s t i b l e structures i n b u i l d i n g s codes;  •  Expandability - Manufacturers o f pre-fabricated steel b u i l d i n g s u s u a l l y keep a l l c o m p l e t e d projects i n electronic f o r m a t f o r a l o n g t i m e , so that future expansions can be made easily and inexpensively;  •  Recycling - Steel is a recyclable m a t e r i a l ;  •  Durability - Steel is i m p e r v i o u s to termites a n d other w o o d b o r i n g insects, thus e l i m i n a t i n g the structural damage that can be caused b y these insects i n w o o d ;  2.3.4.2 Disadvantages of Steel Construction  Disadvantages o f steel structures can be s u m m a r i z e d as f o l l o w s :  •  Fire Resistance - A l t h o u g h steel structures are rated as n o n - c o m b u s t i b l e , steel members m a y y i e l d and subsequently loose strength and stability w h e n subjected to h i g h temperatures e x h i b i t e d d u r i n g a fire. Fire p r o t e c t i o n o f a l l structural members is required, w h i c h increases the material and labour costs. I n a d d i t i o n , the fire rating f o r steel structures is l o w e r than that o f concrete or masonry structures;  •  Material Costs - Steel is an expensive material and m u c h m o r e expensive than m a s o n r y or concrete;  Literature R e v i e w  •  Environmental - T h e m a j o r  34  environmental  concerns  include  the energy  used  in  m a n u f a c t u r i n g , d i s r u p t i o n o f the affected area, a n d air and water q u a l i t y degradation as a result o f m i n i n g and m a n u f a c t u r i n g activities.  Steel is one o f the most energy-intensive  industrial materials, generating p o l l u t i o n and waste d u r i n g a l l stages o f the m a n u f a c t u r i n g process, i n c l u d i n g c o k i n g coal, p u r i f y i n g i r o n , and g a l v a n i z i n g .  •  Insulation Properties - Steel structures have l o w e r insulation properties than other types o f structures.  I n a d d i t i o n , steel is h i g h l y c o n d u c t i v e , w h i c h increases the potential f o r t h e r m a l  bridging;  •  Labour Costs - I n some areas i t is d i f f i c u l t to f i n d crews that are trained i n constructing steel structures. This disadvantage usually raises the o v e r a l l project cost;  •  Corrosion - Steel components rust i f they are left exposed i n marine climates or i n internal climates w i t h h i g h h u m i d i t y and acidity.  2.4 T A L L WOOD-FRAME WALL CASE STUDIES O n l y a h a n d f u l o f b u i l d i n g s have been designed and constructed t o date w i t h tall w o o d - f r a m e w a l l s as the load-resisting system.  B r i e f case studies o n t w o b u i l d i n g s that are o f significant  importance f o r the topic are presented b e l o w .  2.4.1 Tembec Mill in Cranbrook, B.C. A s a manufacturer o f w o o d products, Tembec Industries Inc. a i m e d t o use w o o d f o r the m a j o r expansion o f its Crestbrook plant i n C r a n b r o o k , B r i t i s h C o l u m b i a .  T h e design s o l u t i o n ,  h o w e v e r , still had t o make g o o d business sense. The plant expansion was to house 2,024 square metres (22,000 square feet) o f value-added m a n u f a c t u r i n g area f o r the p r o d u c t i o n o f f i n g e r j o i n e d l u m b e r ( W o o d w o r k s , 2003).  Literature Review  35  Figure 2.10. Construction of the Tembec Cresbrook Mill in Cranbrook, BC.  The production area of the new facility needed to have a large roof span of nearly 42.5 m (140') across, with no interior columns (Figure 2.10). For this type of structure, off-the-shelf steel and tilt-up concrete buildings have often proven to be most cost effective.  Preliminary cost  comparisons for this project, however, favoured a tall wood-frame wall solution. Moreover, with the natural insulating properties of wood, the insulating value of a wood-frame building is higher than that of steel. It was also recognized that using wood would benefit the local economy, whereas a steel alternative would likely be factory-built outside the province of British Columbia.  The building has a conventional concrete foundation and ground floor slab. Wall and roof components were assembled on the ground, and then lifted into place. Tall walls were framed with continuous Laminated Veneer Lumber (LVL) studs 7.6 m (25') in length, with horizontal LVL top and bottom plates. The studs were spaced at 610 mm (24") on centre. They were fastened to the top and bottom plates with specially manufactured steel brackets, using two lag  Literature Review  36  screws and a thru-bolt in the stud (Figure 2.11). Information from building contractors suggests that those connections were actually the most time-consuming aspect of the construction process. They also suggested that having standardized connection details for such buildings would increase their competitiveness. The walls also had horizontal L V L blocking every 1,220 mm (48") to provide the strength necessary to carry the imposed lateral loads. On the exterior of the walls, 38 mm by 140 mm (2" x 6") rough-sawn, horizontal tongue and groove cladding was applied. The walls were built in 9 m (30') sections and tilted up by crane.  Figure 2.11. Connections between the studs and the bottom plate (CWC, 2000). The roof consisted of pitched open web trusses spaced 610 mm (24") on centre. The trusses, which taper from 3,048 mm to 1,270 mm (120" to 50"), were manufactured in two pieces to facilitate transportation and then assembled on site.  Four bays of trusses were connected  together with bracing and oriented strandboard (OSB) sheathing to provide the rigidity necessary to avoid damage when lifting them by crane into place.  Literature R e v i e w  37  2.4.2 Trus Joist Research Center in Boise, Idaho A n o t h e r example o f the successful use o f tall w o o d - f r a m e w a l l s is the Trus Joist T e c h n o l o g y Center i n Boise, Idaho, c o m p l e t e d i n J u l y 2000. T h i s 16,350 square metre (176,000 square f o o t ) f a c i l i t y was designed w i t h the goal o f p r o v i d i n g an e n v i r o n m e n t that w o u l d foster i n f o r m a t i o n and idea sharing b e t w e e n m u l t i p l e groups focused o n the research, development, engineering, m a r k e t i n g , sales, and m a n u f a c t u r i n g support o f T r u s Joist engineered w o o d products. T h e w a l l s , roofs and floors were constructed p r i m a r i l y w i t h engineered w o o d products. T o t a l quantities o f w o o d products included 3 0 0 cubic metres o f Parallam® P S L , 800 cubic metres o f TimberStrand® L S L , 10 cubic metres o f M i c r o l l a m ® L V L , 1,250 m o f TJI® F l o o r Joists, and 15,600 m o f open web trusses ( T a y l o r , 2000).  The m a n u f a c t u r i n g , research, and development functions o f the b u i l d i n g required a 30.5 m ( 1 0 0 ' ) clear r o o f span and a 12.2 m ( 4 0 ' ) b u i l d i n g height constructed w i t h exposed engineered w o o d products. T h e p r i m a r y objective was t o construct a f u n c t i o n a l and s t i m u l a t i n g workspace w h i l e showcasing  efficient,  innovative  structural  framing  systems  with  typical  materials  and  connections f o r v i e w i n g b y potential Trus Joist customers.  T a l l w a l l s were used as the p r i m a r y structural system f o r resisting the v e r t i c a l and h o r i z o n t a l loads i n the b u i l d i n g .  T a l l w a l l s consisted o f L S L studs, plates, a n d f u l l b i l l e t sheathing (large  uncut sheets o f laminated strandboard).  T h e lateral and v e r t i c a l loads o n the w a l l dictated the  stud spacing as w e l l as the stud and plate size. T h e stud system was f r a m e d using c o n v e n t i o n a l carpentry methods a n d t i l t e d i n place b y a crane i n 21.9 m ( 7 2 ' ) l o n g sections to reduce labour t i m e (Figure 2.12). T h e f u l l b i l l e t L S L panellized w a l l s reduced the mass o f the b u i l d i n g w h e n compared w i t h m a s o n r y and concrete systems.  Therefore, the t i l t - u p wood-based  system  38  Literature R e v i e w  s i g n i f i c a n t l y reduced the lateral shear requirements f o r the connections.  The strength and  integrity o f the L S L a l l o w e d f o r the nails to be fastened at 38 m m o n centre resulting i n an allowable lateral load capacity o f up to 12,690 N / m (9,360 lb./ft.) ( T a y l o r , 2000).  Figure 2.12. L i f t i n g o f a completed section o f the w a l l i n place at the Trus Joist T e c h n o l o g y Center i n Boisie, Idaho ( T a y l o r , 2000). T w o configurations were used f o r the l o n g span r o o f systems o f the b u i l d i n g .  The first system  was made o f P a r a l l a m * P S L heavy t i m b e r trusses assembled on the g r o u n d and raised into place as three truss sections spanning 30.5 m ( 1 0 0 ' ) . Microllanr  The second system was constructed  of  L V L flanged open w e b trusses delivered in continuous 30.5 m spans. The r o o f  trusses were assembled o n the g r o u n d i n m u l t i p l e truss sections before b e i n g put i n place b y a crane and fastened to the beam supports and tilt up w a l l systems.  Literature R e v i e w  39  2.5 PARTIAL COMPOSITE ACTION AND EFFECTIVE FLANGE WIDTH Partial composite action is used to describe the interaction o f t w o or more components o f a structural m e m b e r w h e n interlayer slip can occur between the components.  A beam without  composite action and a f u l l y composite b e a m are s h o w n i n Figure 2.13. W h i l e this p h e n o m e n o n has been analyzed and c o d i f i e d f o r use w i t h several structural materials, this section w i l l focus  Figure 2.13. C o m p a r i s o n between (a) a b e a m w i t h o u t composite action and (b) a f u l l y composite b e a m ( C e c c o t t i , 2003).  o n applications f o r w o o d construction. T-shape and I-shape sections are the m o s t c o m m o n w h e n dealing w i t h p a r t i a l l y composite members i n w o o d construction. Since the d i s t r i b u t i o n o f stress i n the flanges o f these members is not u n i f o r m , several methods have been developed to determine an equivalent flange w i d t h o f u n i f o r m stress f o r use i n the analysis o f composite members (Figure 2.14). w i l l also be discussed.  M e t h o d s f o r d e t e r m i n i n g effective flange w i d t h i n w o o d c o n s t r u c t i o n  Literature Review  40  Figure 2.14. Stress distribution in the flange o f a composite member (Raadschelders and Blass, 1995).  2.5.1 Partial Composite Action (Newmark, Seiss, and Viest) The concept of partial composite action has been studied extensively over the past half century. Granholm (1949), reporting in Swedish, and Pleskov (1952), reporting in Russian, investigated composite timber members with Pleshkov also considering interlayer slip. Newmark, Seiss, and Viest (1951) investigated the incomplete interaction o f composite steel and concrete T-beams (Figure 2.15).  Their theoretical analysis incorporated the load-slip characteristics o f steel  channel shear connectors.  Comparisons between test results and theoretical analyses were  difficult because minimal slip occurred in the concrete and steel connections.  Even though  theoretical results were only compared with testing on these composite steel and concrete members with minimal measurable slippage, it was concluded that the theorem for composite beams with incomplete interaction was generally accurate and was not limited to that type o f member as long as the basic assumptions were satisfied to a reasonable degree.  Those  assumptions were: •  The shear connection between elements was assumed to be continuous along the length of the member;  Literature R e v i e w  •  41  T h e amount o f slip p e r m i t t e d b y the shear connection was d i r e c t l y p r o p o r t i o n a l to the load transmitted;  •  T h e d i s t r i b u t i o n o f strain t h r o u g h o u t the depth o f each element was linear; a n d  •  T h e elements were assumed to deflect equal amounts at each cross section a l o n g the length o f the m e m b e r at a l l times.  Notts A negative sign Indicates compreslve •train  Neutral Axis of Slab  Neutral Axis of Beam)  (a) C r o s s - S e c t i o n  (b) I n t e r n a l F o r c e s (c) S t r a i n  Distribution  Figure 2.15. C o m p o s i t e T - b e a m w i t h imperfect interaction ( N e w m a r k et. a l . , 1951).  The d e f l e c t i o n o f a s i m p l y supported T - b e a m under a single p o i n t load was g i v e n b y :  ( EI V  1-  1, L, L  1 6  2 2-H--  + •  L  EAr  2  2  C F  L  (2.1)  E I rc  2  where the force acting at the centroids o f the t w o elements was  f  EI  u^ 1 - -  y_Vc_ L  7t  sinh  K  f  Vc~ f  sinh  u^ 1 - sinh  n  A  V  VC L  (2.2) y  vVCy  F  L  =F  L  a t C = 0,  1 7t EA^EI 2  C =  k  L  2  EI  (2.3)  Literature R e v i e w  42  EI = ^ E I + E A r 1 EA  1 E,A,  ,and  2  (2.4)  1  +E  2  A  (2.5) 2  The parameter k is called the slip m o d u l u s . It was g i v e n b y the equation:  (2.6)  Subscript 1 denotes the flange element and subscript 2 denotes the w e b element o f the T - b e a m . I n the previous f o r m u l a t i o n the symbols are d e f i n e d as f o l l o w s : P = concentrated p o i n t load u = the distance o f the concentrated p o i n t load f r o m the left support L = length o f the composite m e m b e r y = distance o f the cross section f r o m the left support r = distance between the centroidal axis o f the w e b and the flange E; = m o d u l u s o f elasticity o f the i Ii = m o m e n t o f inertia o f the i A j = area o f the i K  n  t h  t h  t h  component  component  component that is equal to w i d t h , bi, m u l t i p l i e d b y height, hj  = stiffness o f an i n d i v i d u a l connector  S = spacing o f the connectors.  2.5.2 Partial Composite Action (Goodman and Popov) G o o d m a n a n d P o p o v later applied the theory developed b y N e w m a r k , Siess, and V i e s t to nailed, layered t i m b e r beams ( G o o d m a n and P o p o v , 1968; G o o d m a n , 1969).  The deflection o f a simply  supported b e a m m e m b e r consisting o f three identical layers connected b y nails under a single p o i n t load was g i v e n b y :  Literature R e v i e w  A = A  43  + — — — F , , where 9kh  (2.7)  L  p  C  =  ^  L  C, = 1  c  2  =  P  2  n  ~  sirm[Vc7(L-u)jsinh[Vc7 yj sinhf^/cY L^  r  |  C  '  2  C,  u  (2.8)  L  v  ^ ^ , and bhE  (2.9)  hk  (2.10)  3 El'  T h e parameters b and h, the w i d t h and height o f each layer o f the composite beam, are s h o w n i n Figures 2.16 and 2.17.  A^  is the d e f l e c t i o n o f a perfectly r i g i d composite beam.  symbols have been d e f i n e d p r e v i o u s l y .  J n t e r l o y e r Connections ( j o i n t s )  1  i ! 1 I  - I1 1  1 — A1-  s  ! -'t T  i T— lr—  1  joint spacing  Figure 2.16. L a y e r e d b e a m system layout ( G o o d m a n , 1969). b  t h n  h  /  2  h/2  . ft  h h  h/2  4  -  k  1  2 I  /  3/  Figure 2.17. Three-layered b e a m internal forces and strains ( G o o d m a n , 1969).  T h e other  Literature R e v i e w  44  Excellent agreement was f o u n d w i t h the experimental tests that were p e r f o r m e d to v e r i f y the developed theory. Theoretical equations to determine the d e f l e c t i o n o f a nailed b e a m w i t h g l u e d ends were also developed.  It was f o u n d that the restraining effect o f u s i n g a small a m o u n t o f  glue at the ends o f nailed beams o n d e f l e c t i o n was significant. It was c o n c l u d e d that this scheme w o u l d p r o v i d e an e c o n o m i c a l m e t h o d o f i m p r o v i n g stiffness.  2.5.3 Partial Composite Action and Effective Width (Amana and Booth) A m a n a and B o o t h developed a mathematical f o r m u l a t i o n to predict the response o f g l u e d p l y w o o d stressed-skin components ( A m a n a & B o o t h , 1967).  Equations were d e r i v e d f o r three  configurations,  solutions  shown  i n Figure  2.18.  T h e theoretical  experimental testing that was conducted o n several specimens.  compared  well  with  T h i s m e t h o d i n c l u d e d an  allowance f o r an effective flange w i d t h that was embedded w i t h i n the c a l c u l a t i o n f o r d e f l e c t i o n . A s w e l l , the m e t h o d c o u l d easily be applied to several l o a d i n g c o n f i g u r a t i o n s because it contained a Fourier series coefficient as an input parameter.  The deflection o f a partially  composite T - b e a m was g i v e n b y :  (2.11)  (EI)  G(b')  0  s(b') ^ ( E I )  h,E, f ( b ' )  2 '  s(x) = ( p  +e  n  (p  E A 2  0  (2.12)  2  was denoted as the n o n - d i m e n s i o n a l positive j o i n t constant,  (2.13)  2  (2.14) 2  f ( x ) = 2 ( p - s i n h ( p x ) - q - s i n h ( q x ) ) + 0 (p • cosh(p x ) - q - c o s h ( q x ) ) , n  (2.15)  Literature R e v i e w  45  (X\ + v  e„ =  x y  )sinh(p b ' ) - ^  (l] + v  x y  )sinh(q b')  (A + v ) c o s h ( p b ' ) - K + v ) c o s h ( q b')  (2.16)  2  2  x y  x y  I n the previous f o r m u l a t i o n , the symbols are d e f i n e d as f o l l o w s : p = A,© q = A- co 2  A, = ->Ja--Jaf^$ 2  E.  a = 2G  x y  xy  ( E l ) = the stiffness o f a l l b e a m parts as i f u n g l u e d 0  • b ' = one h a l f the stud spacing For a s i m p l y supported b e a m w i t h a u n i f o r m l y distributed load:  n7t  F„ =  4w  Lu7  n = 1,3,5,...  It was determined that v e r y f e w terms were required to achieve accurate  results w i t h i n one percent.  Literature R e v i e w  46  (o) SINGLE T-6EAM  (c)  (b)  RIB OR TYPE  DOUBLE SKIN, DOUBLE RIB TYPE  MULTIPLE RI&, OOU&LE SKIN TYPE  Figure 2.18.  Different  d i a p h r a g m configurations  considered b y A m a n a and  Booth  (1967). A m a n a and B o o t h c o m p u t e d a s t i f f e n i n g factor, i, that was obtained b y c o m p a r i n g the d e f l e c t i o n o f a composite b e a m w i t h that o f a bare stud as f o l l o w s :  i = — - , where A  (2.17)  F sin(co y ) n  = 2  n=l  co E I  (2.18)  2  2  2  The s t i f f e n i n g factor c o u l d also be used to calculate an effective b e n d i n g stiffness, w h i c h c o u l d be used i n s i m p l i f i e d b e a m equations. T h i s was g i v e n by:  Literature R e v i e w  (El)  e f f  47  =i-E I . 2  (2.19)  2  W h i l e the determination o f effective flange w i d t h is included i n the c a l c u l a t i o n o f d e f l e c t i o n , it c o u l d also be calculated separately:  Z A f ( b ' ) s i n ( c o y) n  b  = — ^  e f f  , where  (2.20)  ^f> s(b')sin(a>y) n  Ei  A  "  =  n  =l  f ( b ' ) [ o ( b V c / „  j  r  a  2  1  )  It can be seen that b o t h d e f l e c t i o n a n d effective flange w i d t h are a f u n c t i o n o f the type o f loading. T h e influence o f the type o f l o a d i n g o n these values w i l l be discussed i n detail later i n this chapter.  2.5.4 Partial Composite Action and Effective Width (Polensek and Kazic) Polensek a n d K a z i c m o d i f i e d the s o l u t i o n b y A m a n a and B o o t h i n order to m o d e l a m o r e c o m p l e x system, s h o w n i n Figure 2.19, u s i n g r e l i a b i l i t y analysis (Polensek & K a z i c , 1991).  It  was recognized that the solution b y A m a n a and B o o t h o n l y w o r k s w h e n a > ( 3 , w h i c h is not 1/2  v a l i d f o r systems w i t h g y p s u m w a l l b o a r d .  I n a d d i t i o n , the t w o flanges and flange c o n n e c t i o n  types o f a composite I-section t y p i c a l l y have different properties w h e n used i n w a l l construction but the solution b y A m a n a and B o o t h assumed that the composite I-section was s y m m e t r i c . Therefore, the f o l l o w i n g solution was developed f o r a composite I-section, based u p o n the o r i g i n a l w o r k b y A m a n a and B o o t h b u t w i t h a n e w f u n c t i o n that satisfies a > p (El)  e f f  = E •I 2  e f f  , where the effective m o m e n t o f inertia,  ' [l,+A (r, K,E K;|+r, K E K;;)]. I  J  2  J  1  !  l / 2  : (2.22)  ( 2  2 3  )  Literature R e v i e w  48  K = l+ K E K- +K E K;;+K 3E (K |  l  /  \  2  2  3  2  l  K, =  E A - ^  f  2  S A,(A +A ) I  2  E  K = 3  ^  S A (A +A,); 3  3  \  4  f  S S A A A I  I  e  3  — A ^ i+A a 2  ^  2  V  /  Ki = K, with A  I  2  =0  2  (2.25)  2y  E  f  2  -  (2.24)  n  '  v  3  v  K 3)- , 1  n l  K  3  = K  3  with A  =0  2  (2.26)  2J  E  E E  3  F  A  (2.27)  2  + A a ,  2  3  (2.28)  3  \*—bo—*\  f il  JOINT INTERLAYERS STUD (joist)  Q O  _j  W  •CC '< LU  s  o1 S 1 t  Sc2  St2  SLIP MOR  y +  STRAIN  XfNSION - J " . COMPRESSION COVERING J F COVERING  Figure 2.19.  B e n d i n g and compression system w i t h non-linear components (Polensek & K a z i c , 1991).  I n the previous f o r m u l a t i o n , the symbols are defined as f o l l o w s (Figure 2.20): „  _{T A -T A ) 3  3  1  1  Literature R e v i e w  a, = r, + a  49  2  A, = b , h , | i -  A  A  =b h  2  3  2  = b  3  h  2  3  - ^ E 2  A =  A [ + A  2  + A  3  The other symbols have been defined p r e v i o u s l y .  A s can be seen, this s o l u t i o n f o r the effective  m e m b e r properties o f a p a r t i a l l y composite section is independent o f the type o f c o n f i g u r a t i o n . N o testing was conducted i n this study to v e r i f y the new s o l u t i o n . b,  ,1  |a  b —  2  r  ai 2  2  1  Figure 2.20. Cross-section o f an I-shaped composite beam.  a3  loading  Literature R e v i e w  50  A n e w s o l u t i o n f o r effective flange w i d t h was also introduced and was f o u n d b y appropriate b o u n d a r y conditions to the f u n c t i o n m e n t i o n e d p r e v i o u s l y .  applying  It can be seen i n the  above solution that effective flange w i d t h is n o w an input parameter and not e x p l i c i t l y contained i n the calculations f o r the composite properties o f the member.  T h e s o l u t i o n f o r effective flange  w i d t h was s i m p l i f i e d b y t a k i n g n equal to one and e x p a n d i n g the t r i g o n o m e t r i c and h y p e r b o l i c functions into exponential series. A s w e l l , it was s h o w n that i g n o r i n g terms c o n t a i n i n g Poisson's ratio affected the s o l u t i o n b y less than five percent.  T h e effective flange w i d t h was thus g i v e n  by:  b  = 2b[90(3 + 30a(3co + o3 ( 3 a p + (3 )J3 [30(3 + 30a(3co + c o ((3 + 5 a ( 3 ) J " ' , 4  e  2  2  2  4  2  2  (2.29)  where  co =  — . L  T h e r e l i a b i l i t y analysis that was conducted accounted f o r the non-linear properties o f the composite sections. T h i s was achieved b y c h a n g i n g the stiffness o f the j o i n t s and the studs w i t h increasing displacements (Figure 2.19).  The m e m b e r m o d e l consisted o f a composite b e a m -  c o l u m n w a l l section under a x i a l and transversal, or out-of-plane, l o a d i n g .  The d e f l e c t i o n at the  m i d - h e i g h t o f the w a l l was g i v e n b y :  A =  M  , where  48 ( E l ) ,  w L max  8  2  (2.30)  PL w 2  1+  4 (EI),  (2.31)  Literature R e v i e w  51  2.5.5 Partial Composite Action (Kuenzi and Wilkinson) K u e n z i and W i l k i n s o n  studied the response o f composite beams  o f various  construction  configurations w i t h fasteners o f f i n i t e r i g i d i t y ( K u e n z i & W i l k i n s o n , 1971). T h e i r solutions were based u p o n w o r k done at the Forest Products L a b o r a t o r y i n the 1950's ( N o r r i s et a l , 1952). Testing was conducted o n t w e n t y - f o u r beams i n c l u d i n g double T-beams, double rectangular beams, and b o x beams.  I-beams,  N a i l load-slip values were taken f r o m previous testing b y  W i l k i n s o n b u t shear load-slip data f o r construction mastic adhesives was d e t e r m i n e d f r o m testing f o r this study.  T h e m i d - s p a n deflection o f a s i m p l y supported b e a m under a u n i f o r m l y  distributed load, w , was g i v e n b y :  A = K„  5wL  +  2  K^A.,  384 ( E I ) .  1 H  a =  4  "(EI).  5 _(EI)  r k 2  (EIL-(EI)  0  ~( V  (Ell 0  (EI)  where  2 ] L  oc  2  y  1-2  (2.34)  r  2 ]  ^CCLJ  , and  1— cosh  'LcO v 2  (2.35)  j j  (2.36)  0  ( E l ) , is the stiffness o f the composite b e a m as i f the components were g l u e d together w i t h r i g i d adhesive.  Better agreement was f o u n d between the theoretical and experimental data f o r the l o a d d e f l e c t i o n results than f o r the load-slip results. T h e differences f o u n d f r o m the comparisons o f the load-slip results was thought to arise because o f the assumption o f constant shear stress t h r o u g h o u t the thickness o f a l l inner members.  Literature R e v i e w  52  2.5.6 Partial Composite Action (McCutcheon) McCutcheon  sought  to  simplify  the s o l u t i o n  provided  by  Kuenzi  and W i l k i n s o n  by  a p p r o x i m a t i n g the h y p e r b o l i c t r i g o n o m e t r i c functions used i n their calculations ( M c C u t c h e o n , 1977).  H i s s o l u t i o n f o r the m i d - s p a n deflection o f a s i m p l y supported b e a m under a n y type o f  l o a d i n g was g i v e n b y :  A = AJ1 + /  "(EI). A  (EI)  h  /  A  =  1 •, where  (2.37)  0  y_ • ( L a ) +10  (2.38)  h  is an a p p r o x i m a t i o n o f the factor c o n t a i n i n g h y p e r b o l i c t r i g o n o m e t r i c functions o f L a that  v a r y depending u p o n the type o f l o a d i n g .  B y u s i n g this factor it was then possible to c o m p u t e  the properties  o f a p a r t i a l l y composite  member  configuration.  Table 2.1 compares the a p p r o x i m a t i o n w i t h the exact solutions f o r the three  independently  different l o a d i n g configurations at the m i d - s p a n o f a beam.  f r o m the type  o f loading  T h e discrepancy between these  values is small. T h e effective b e n d i n g stiffness o f a p a r t i a l l y composite b e a m was then g i v e n b y :  Table 2 . 1 . C o m p a r i s o n o f approximate and exact values o f f  A  Exact /  La  Approximate  Quarter-  /A  point loading  ( M c C u t c h e o n , 1977).  A  Distributed  Mid-span  loading  loading  0.0  1.000  1.000  1.000  1.000  1.0  0.909  0.907  0.908  0.909  2.0  0.714  0.708  0.711  0.715  5.0  0.286  0.276  0.281  0.291  10.0  0.091  0.084  0.088  0.096  50.0  0.004  0.003  0.004  0.005  100.0  0.001  0.001  0.001  0.001  CO  0.000  0.000  0.000  0.000  Literature R e v i e w  53  (El)  O i U1 ^ '  ( e i L = 1 +  /  A  I  (EI)  '  (2 39)  0  2.5.6.1 Influence of Gaps  M c C u t c h e o n i d e n t i f i e d the influence o f gaps i n the flange as b e i n g significant a n d it was subsequently included i n the theorem.  T h e amount o f composite action was d e f i n e d b y  f. A  Since a is a property o f the cross section, it was determined that r e d u c i n g the length value i n the f  &  factor should account f o r the r e d u c t i o n i n stiffness due to the presence o f gaps.  Thus the  presence o f gaps was accounted f o r b y r e w r i t i n g equation (2.38) as:  A = (La) / , v +10 T  ( - °) 2  i n  4  where L ' is the distance between discontinuities (open gaps) i n the sheathing i n the d i r e c t i o n o f the span. It was assumed that the gaps were evenly spaced a l o n g the span.  D a t a f r o m seven floors that were tested f o r this 1977 study a l o n g w i t h data f r o m T - b e a m tests conducted at C o l o r a d o State U n i v e r s i t y and the N A H B Research F o u n d a t i o n p r o v i d e d sufficient information  to validate this theoretical m e t h o d .  T h e specimens  were  subjected t o b o t h  concentrated and u n i f o r m load tests. T h e computations p e r f o r m e d b y this m e t h o d were f o u n d to m a t c h w e l l w i t h results obtained e x p e r i m e n t a l l y , v a l i d a t i n g the s o l u t i o n f o r a p a r t i a l l y composite member w i t h gaps i n the flange.  2.5.6.2 Beam-Spring Analog  W h i l e M c C u t c h e o n i d e n t i f i e d the need t o determine the d i s t r i b u t i o n o f the load i n the transverse (in-plane) d i r e c t i o n to the composite members i n 1977, he d i d n o t p u b l i s h his s o l u t i o n t o this  Literature R e v i e w  54  p r o b l e m u n t i l 1984 ( M c C u t c h e o n , 1984).  U s i n g what he called a b e a m - s p r i n g analog, a f l o o r  was m o d e l e d as a b e a m supported b y elastic springs to account f o r t w o - w a y action due to the cross-member d i s t r i b u t i o n properties o f the sheathing. The progression o f this m o d e l is s h o w n i n Figure 2 . 2 1 . A s stated, each composite m e m b e r was represented b y an elastic spring that was a constant ratio o f m e m b e r load to j o i s t deflection.  For each member, j , the spring constant was  given by:  (2.41)  /lh  (c) Figure 2 . 2 1 . Progression o f the beam-spring analog m e t h o d (a) composite w o o d - f r a m e floor,  (b)  transverse  stiffness  represented  as  an  equivalent  beam  perpendicular to the j o i s t s , and (c) composite j o i s t s represented as springs supporting the equivalent transverse b e a m ( M c C u t c h e o n , 1984). The analog b e a m represents the aforementioned distributional properties o f the sheathing a l o n g the length o f the composite member. The b e n d i n g stiffness o f this b e a m is equal to the stiffness o f the sheathing i n the transverse d i r e c t i o n and was g i v e n b y :  Literature R e v i e w  55  (2.42)  E  s  is the bending m o d u l u s o f elasticity o f the sheathing i n the cross-joist d i r e c t i o n , s is the  composite m e m b e r spacing, and / ' is the length o f sheathing i n the cross-joist direction. A s c a n be seen, this equation also accounts f o r gaps i n the sheathing b u t i n the transverse d i r e c t i o n . I n a t y p i c a l f l o o r or w a l l system the gaps i n the sheathing i n the transverse d i r e c t i o n are staggered. T h i s equation approximates the reduced stiffness o f the analog beam b y averaging the effects o f these discontinuities.  The analog system can be solved u s i n g m a t r i x analysis as the i n d i v i d u a l spring stiffness values and the b e a m stiffness are k n o w n . T h i s m e t h o d o f analysis was compared w i t h the f i n i t e element p r o g r a m F E A F L O ( T h o m p s o n et a l , 1977), described i n Section 2.10.2, and w i t h the data f r o m the seven floors that were tested i n the 1977 study b y M c C u t c h e o n .  T h e results were v i r t u a l l y  identical to those obtained f r o m the finite element p r o g r a m and v e r y close t o the data obtained f r o m testing.  2.5.6.3 Generalized Model for Partial Composite Action  A l l o f the w o r k done b y M c C u t c h e o n described p r e v i o u s l y h a d been f o r composite members w i t h sheathing o n one face o n l y . H e later reinterpreted his solution f o r the effective properties o f a p a r t i a l l y composite m e m b e r t o include sheathing o n b o t h faces ( M c C u t c h e o n , 1986). The n e w solution was v a l i d f o r a m e m b e r w i t h t w o different sheathing a n d c o n n e c t i o n types.  The  effective b e n d i n g stiffness was g i v e n b y : (El)  = ( E l ) + E A , r, + E A 2  e f f  0  3  r  2  - A y  2  , where  (2.43)  Literature R e v i e w  56  i = 1,3. + 10  (2.44)  k.L]  k j is the interlayer slip f o r sheathing layer i, and h- is the distance between discontinuities (open gaps) i n sheathing layer i i n the d i r e c t i o n o f the span.  A d d i t i o n a l l y , the total area o f the  t r a n s f o r m e d section and the location o f the neutral axis were respectively g i v e n b y (Figure 2.22): A = E A 2  2  + EAi + EA3  (2.45)  r,EAi - r E A 3 3  (2.46)  EA,  hi EA?  y h  3  EA, (a)  Figure 2.22. (a) cross-section and (b) side v i e w o f the revised m o d e l b y M c C u t c h e o n (1986). N u m e r o u s tests were conducted to validate this f o r m u l a t i o n , i n c l u d i n g t w e l v e T-beams and t w e n t y - f o u r I-beams, under t h i r d - p o i n t loading.  Once again, the c o m p a r i s o n o f l o a d - d e f l e c t i o n  Literature R e v i e w  57  results w i t h test data p r o v e d to be m u c h closer than that o f load-slip results. however,  the difference  I n this case,  i n accuracy was attributed to the use o f a linear n a i l  load-slip  relationship. A c t u a l n a i l load-slip test data was s h o w n to be h i g h l y non-linear.  2.5.7 Partial Composite Action (Itani and Brito) A theoretical study f o r c o m p u t i n g stresses a n d deflections i n floors w i t h gaps was developed b y Itani and B r i t o (1978) concurrently w i t h the study done b y M c C u t c h e o n (1977). T h e theoretical results were v e r i f i e d against the experimental results o n T-beams connected w i t h elastomeric adhesive presented b y Bessette (1977).  U n l i k e the theoretical f o r m u l a t i o n developed b y  M c C u t c h e o n , the f o r m u l a t i o n b y Itani and B r i t o is not as easily a p p l i e d to different gap configurations as it is derived f r o m a basic d i f f e r e n t i a l equation f o r each separate c o n f i g u r a t i o n . A n example o f a T - b e a m w i t h gaps placed at the f o u r t h points is s h o w n i n Figure 2.23 and the analysis m e t h o d o l o g y is s h o w n g r a p h i c a l l y i n Figure 2.24.  T h e b e a m is m o d e l e d into f o u r  segments and the m i d - s p a n deflection is the s u m o f deflections at the ends o f the equivalent beams. T h e equation f o r m i d - s p a n d e f l e c t i o n o f a composite T - b e a m under a u n i f o r m l y distributed load, w , was g i v e n b y ( I t a n i , 1983):  13 V 3072 A =  w V  67LVw (E,I,+E I ) 2  2  3072 V R r L 4  4Vc7 where:  2  Q> ] r  ^  +  ^  T " / = l 3 tanh(Vc7L/%)-R ]..  4Vc7 r L  + 4Vc7  cosh(7c7L/4)  p  3  [3 P t a n h ( 7 c 7 L / 8 ) - 2 R J. 4  4  (2.47)  Literature R e v i e w  w C  R, =  58  2  3 w L  (2.49)  C-  2  32  ~C,  wL _C  •csch(7c7L/4)  ,/  2  R  =  32  4  Q, =  W  C  2  C,  (2.50)  csch(7c7L/4^  (2.51)  (2.52)  2  2C,  EI  C, = k  (2.53)  EA(E,I, + E I ) 2  C  k  2  r  (2.54)  (E,I,+E I )  2  2  2  The other terms i n the proceeding equations have been defined p r e v i o u s l y .  PLAN w Ibs./ft  TZI imr A L/4  L/4  L/4  L/4  f ELEVATION  Figure 2.23. B e a m w i t h gaps at the f o u r t h points ( I t a n i , 1983).  END  VIEW  Literature R e v i e w  59  Y  a) Free Body  b) Deflected  Y  *  Diagrams  Beam  c) Four "Equivalent" Beams  Figure 2.24. A n a l y s i s o f the b e a m w i t h gaps at the f o u r t h points ( I t a n i , 1983).  A parametric study was conducted u s i n g the same theory as the above example.  The beams  investigated v a r i e d w i t h respect to span, sheathing thickness, and j o i s t size. T h e sheathing w i d t h , u n i f o r m l y distributed load, m o d u l u s o f elasticity f o r the sheathing, m o d u l u s o f elasticity f o r the j o i s t , and connection stiffness were all held constant.  The f i n d i n g s s h o w e d that sheathing  discontinuities have a considerable effect o n the deflection o f a beam. The relationship between a discontinuous and a continuous f l o o r system was not affected b y j o i s t depth or flange thickness but it was s l i g h t l y affected b y the thickness o f the sheathing. It was c o n c l u d e d that the presence o f open gaps redistributed stresses i n the sheathing and joists causing a shift i n the neutral axis o f the composite beam.  Literature R e v i e w  60  2.5.8 Partial Composite Action (Girhammar and Gopu) 2.5.8.1 First-Order Solution  G i r h a m m a r and G o p u developed a s o l u t i o n f o r the response o f a p a r t i a l l y composite T - b e a m under axial and transversal l o a d i n g that i n c l u d e d the second order effects  o f axial  load  ( G i r h a m m a r & G o p u , 1 9 9 1 ; G i r h a m m a r & G o p u , 1993). T h e i r first-order solution f o r the m i d span displacement o f a s i m p l y supported T - b e a m under a u n i f o r m l y distributed load, w , w a s given by:  5 wL  4  384 ( E l )  • +a  (EI).  w 4  M  (ElXA(El)  0  1 22 r- + -CC L ^aL 8 1  -1  7  cosh  T  where  (2.55)  v ^ J  a  2  (EA)  - k  JEA)  0  r  +  2  ' (EI)  p  (2.56) 0  (EA) =E,A,-E A , p  (EA) (EI)  0  0  2  (2.57)  2  =E,A, +E A ,and 2  2  =E I +E I . 1  1  2  2  (2.58) (2.59)  2.5.8.2 Second-Order Solution  B o t h the first-order and second-order analyses include the assumption that axial load is shared b y the w e b and flange members i n p r o p o r t i o n to their a x i a l stiffness.  T h i s ensures that the a x i a l  load produces u n i f o r m strain over the cross section and does n o t contribute t o the b e n d i n g o f the member.  T h e second-order s o l u t i o n f o r the m i d - s p a n displacement o f a s i m p l y supported T -  b e a m under a u n i f o r m l y distributed load was g i v e n b y :  Literature R e v i e w  61  (2.60)  where  (2.61)  (2.62)  The second-order analysis was used to solve m a n y other section properties such as the shear force and b e n d i n g m o m e n t s i n each m e m b e r element as w e l l .  Results f r o m the first-order a n d  second-order f o r m u l a t i o n s were compared f o r an example T - b e a m .  The magnifications for  several different b e a m properties were presented (Table 2.2). Subscripts 1 and 2 denote a p p l i e d forces and b e n d i n g m o m e n t s i n the flange and the w e b members, respectively. Table 2.2 shows that the m a g n i f i c a t i o n o f displacements, forces, a n d b e n d i n g m o m e n t s is not constant b u t that it is a p p r o x i m a t e l y  the same f o r the t w o most  Table 2.2.  important  parameters  First-order analysis  Second-order analysis  Magnification  ^max  7.560 m m  9.276 m m  1.227  0.1659 k N m  0.2054 k N m  1.238  ^^2,max  0.4977 k N m  0.6162 k N m  1.238  Ni  -50.863 k N  -53.897 k N  1.060  0.863 k N  3.897 k N  4.516  11.444 k N / m  13.878 k N / m  1.213  1 > m a x  ^ 1 ,max ^2,max  1  v v  s,max  maximum  C o m p a r i s o n o f approximate and exact second-order results ( G i r h a m m a r a n d G o p u , 1991).  Displacement/ action  M  i n design:  Literature R e v i e w  62  displacement and b e n d i n g m o m e n t .  The m a g n i f i c a t i o n o f internal a x i a l forces is different f r o m  m a g n i f i c a t i o n s obtained f o r other internal actions since o n l y that p o r t i o n o f an internal axial force induced b y b e n d i n g is m a g n i f i e d b y the second order effect.  2.5.8.3 Critical Buckling Load  The m e t h o d o u t l i n e d above can also be used to determine the critical b u c k l i n g load and, subsequently, an effective b e n d i n g stiffness.  B y setting w = 0 i n the g o v e r n i n g d i f f e r e n t i a l  equation, the critical b u c k l i n g load is g i v e n by:  P  QUEIL  _  P  c  r  "  (EI),  1 +  _ 1  ( E j k 2_ a 1 + 0— —  2,cr  9  2 c r  p ,„  (Ei)  cr  -  (EI),  1 +  (  E I  1  ~  P  «  -  W ~ '  •  eff  ^  (  2  -  6  3  )  )o 2  . a 1+-  ^.cr  is a value associated w i t h the b u c k l i n g load. A p p r o x i m a t e c r i t i c a l loads can be obtained b y  u s i n g the characteristic value o f 6  6  2 c r  = — ,  2 c r  g i v e n f o r c o l u m n s w i t h f u l l composite action as:  where  u. = 2  Euler case 1, cantilever  (1 = 1  Euler case 2, s i m p l y supported  (X = 0.7  Euler case 3, f i x e d - p i n n e d  | l = 0.5  Euler case 4, f i x e d - f i x e d  (2.64)  A n approximate equation f o r the effective b e n d i n g stiffness o f a p a r t i a l l y c o m p o s i t e m e m b e r was then g i v e n as:  Literature R e v i e w  ( H )  63  - -  (mi  (Eji, •  r 1  +  (  '  (  ' i  E  ft  2  TT  2  2.5.9 Partial Composite Action (Kreutzinger) The design o f p a r t i a l l y composite members is c o d i f i e d i n an appendix o f Eurocode 5, the w o o d design code prevalent i n Europe, and is explained i n further detail b y K r e u t z i n g e r ( E N V 1 9 9 5 - 1 1, 1993; Kreutzinger,  1995).  T h i s m e t h o d is v e r y simple t o a p p l y and understand.  It is  applicable to b o t h T-beams and I-beams. T h e determination o f section properties is independent o f the l o a d i n g c o n f i g u r a t i o n .  Because a sinusoidal load c o n f i g u r a t i o n does n o t produce any  h y p e r b o l i c functions i n the solution o f section properties, it was chosen as the base case. I t has been s h o w n p r e v i o u s l y i n this chapter that the type o f l o a d i n g c o n f i g u r a t i o n has little effect o n the b e n d i n g stiffness o f a composite b e a m at the m i d - s p a n .  T h e m i d - s p a n effective b e n d i n g  stiffness o f a p a r t i a l l y composite m e m b e r was g i v e n b y :  (ElL=Z(E I +Y E A a?) i  i  i  i  (2-66)  i  i=l where 7, the connection e f f i c i e n c y factor, was g i v e n b y :  \  Yi = 1  +  T C  .  , f o r i = 1 and i = 3 , and Y = 1 • 2  E A i  k,L  (2.67)  i  2  The connection e f f i c i e n c y factor is equal t o one f o r a p e r f e c t l y r i g i d c o n n e c t i o n a n d zero f o r n o c o n n e c t i o n at all. T h e l o c a t i o n o f the neutral axis is f o u n d b y u s i n g the f o l l o w i n g (Figure 2.25): ^ a  2  =  .  (h. + h , ) ^ • '  .  (h, + h , ) 1  Z Y i E A i=l  .  (2.68)  Literature R e v i e w  64  h,  /  | 0.5h 1  Figure 2.25. Cross-section o f an I-shaped composite beam.  2.5.10 Partial Composite Action (Ceccotti) Ceccotti also p r o v i d e d alternate solutions to the exact deflections o f p a r t i a l l y composite members under several l o a d i n g configurations and showed the v a l i d i t y o f assuming a sinusoidal load d i s t r i b u t i o n as the basis f o r d e t e r m i n i n g a l l m e m b e r section properties independently f r o m the l o a d i n g c o n f i g u r a t i o n (Ceccotti, 2003).  T h e general s o l u t i o n f o r the deflection o f a s i m p l y  supported p a r t i a l l y composite T - b e a m m e m b e r was g i v e n b y :  A =A.  1  (2.61)  where the factor accounting f o r partial composite action due to a u n i f o r m l y distributed load, a central p o i n t load, and a sinusoidal load d i s t r i b u t i o n at m i d span was g i v e n b y , respectively:  Literature R e v i e w  65  8(3  2  5 L  2  48 ( l - ( 3 ) 2  1 +  5 5 L 2  2  2  L_5  cosh  (2.69)  + 1  v2pj  tanh 12 ( l - ( 3 ) 2  I +  V-HQ =  L 8 2  (2.70)  L_5  2  2(3  1 +  L5  v  I K  l + (3  ;  2  =  P = 2  L5  y  '  R  (EI)Q  (EI). '  E  r  ratio  (2.71)  and (EA)  (EA) =  The  •, where  ' 7t ^ v  5  y  i '' 2 2 A  between  connections  E  A  mid-span  and the deflection  (2.72)  deflection o f the  for  a timber-concrete  T-beam  same b e a m w i t h p e r f e c t l y  rigid  with  deformable  connections  was  determined f o r each o f the l o a d i n g configurations described above (Table 2.3). A s can be seen, and as was s h o w n p r e v i o u s l y , the error i n assuming a sinusoidal load d i s t r i b u t i o n d e t e r m i n i n g the properties o f a composite m e m b e r at the m i d - s p a n is l i m i t e d .  when  T h i s factor was  also used to determine an effective b e n d i n g stiffness f o r a composite m e m b e r : (El)  e f f  =tl  s i n  (El)„.  <  (2.73)  Literature R e v i e w  66  Table 2.3.  R a t i o o f m i d - s p a n d e f l e c t i o n f o r different l o a d i n g c o n f i g u r a t i o n s ( C e c c o t t i , 2003).  Loading Configuration  Short span T-beam  Long span T-beam  Concentrated load a mid-span  1.9313  1.3492  Uniform load  1.9039  1.3258  Sinusoidal load  1.9021  1.3190  I n a d d i t i o n to p r o v i d i n g exact solutions f o r d e t e r m i n i n g deflections o f p a r t i a l l y  composite  members, Ceccotti also p r o v i d e d a v a r i a t i o n o n the approximate solutions f o r equivalent b e n d i n g stiffness o u t l i n e d p r e v i o u s l y .  T h i s approximate solution f o r equivalent b e n d i n g stiffness was  given by: (El)  e f f  = ( E I ) + y [ ( E I ) , - ( E I ) J , where 0  1  Y=-  1  1+ v  L5  7t (EA)  (2.75)  2  K  1+  kL  y  (2.74)  r  2  2.5.11 Effective Flange Width (Mohler) T w o solutions f o r the effective w i d t h o f flange components have already been presented ( A m a n a & B o o t h , 1967; Polensek & K a z i c , 1991). Those solutions were derived i n c o n j u n c t i o n w i t h the s o l u t i o n o f either effective m e m b e r properties or deflection.  T h e s o l u t i o n b y M o h l e r , as  described b y Raadscelders and Blass (1995), is a mathematical d e r i v a t i o n o f effective flange w i d t h f o r a s i m p l y supported b e a m that is u n i f o r m l y loaded. T h i s s o l u t i o n takes into account the shear d e f o r m a t i o n i n the flange and was g i v e n b y :  b  A,, t a n h ( ( p , ) - X t a n h ( ( p ) =2L7r(A, - A, ) 2  2  e f  2  2  I n the previous f o r m u l a t i o n , the symbols are defined as f o l l o w s :  (2.76)  Literature R e v i e w  9,  A, ,7i  67  b  f  2L A 7t b y 2  <P  2L  2  A,  =^a + ^a  2  -(3  A =^a-Ja  - p  2  2  a= 2G  xy xy  by = the distance between w e b members minus the w i d t h o f a w e b m e m b e r (Figure 2.26).  V  V  t  c.e.f  ;///J >s//, >/\  —77777  u  J  1 „  f  h  /  1 /I  .M  ;_  r  m  • f.C  4 f-  Figure 2.26. Cross-section o f a t h i n - f l a n g e d d i a p h r a g m (Raadscelders & Blass, 1995).  2.5.12 Effective Flange Width (Eurocode 5) Eurocode 5 gives the f o l l o w i n g a p p r o x i m a t i o n f o r the effective flange w i d t h o f composite members i n a w o o d - f r a m e d i a p h r a g m ( E N V 1 9 9 5 - 1 - 1 , 1993): + b b  w  w  (or b  t e f  + b ) , where w  = the w i d t h o f the w e b member.  (2.77)  Literature R e v i e w  68  Values f o r effective flange w i d t h are g i v e n i n Table 2.4 that account f o r plate b u c k l i n g o n the compression face and shear lag o n the tension face o f a composite member.  Figure 2.27 shows  the relationship between the s i m p l i f i e d procedure presented i n Eurocode 5 and the theoretical solution b y M o h l e r .  Table 2.4. E f f e c t i v e flange w i d t h factors f r o m Eurocode 5 (Raadscelders & Blass, 1995). Flange M a t e r i a l  Shear l a g  Plate b u c k l i n g  Parallel t o the webs  0.1 L  25 h  s  Perpendicular to the webs  0.1 L  20 h  s  0.15 L  25 h  s  0.2 L  30 h  s  P l y w o o d , w i t h grain d i r e c t i o n i n the outer plies  Orientated strand b o a r d Particleboard or fibreboard w i t h r a n d o m fibre orientation  b /l f  Figure 2.27.  Effective flange w i d t h according to M o h l e r a n d E C 5 . (a) particleboard M o h l e r , ( b ) particleboard E C 5 , (c) p l y w o o d M o h l e r , ( d ) p l y w o o d E C 5 (Raadscelders & Blass, 1995).  2.5.13 Effective Flange Width (Kikuchi) A f o r m u l a f o r effective flange w i d t h was developed b y K i k u c h i (2000) and contains factors based o n the results o f a sensitivity analysis conducted o n g l u e d stressed-skin panels w i t h a single s k i n and double ribs.  T h e basic panel that was analyzed is s h o w n i n Figure 2.28. T h e  Literature Review  69  sensitivity analysis was conducted using the mathematical model developed by Amana and Booth described previously (Amana & Booth, 1967). The complete formula for effective flange width containing all of the modification factors was given by: b  eff  =K,K K K K b[l-e2  3  4  a ( L / b  5  - J , where p )  (2.78)  a = 0.3838 (3 = 0.4687. The exponent function in the brackets is related to rib spacing, and more specifically, to the rib spacing ratio of L/b. The a and (3 parameters are strictly for curve fitting.  L/4  1/4  Figure 2.28.  The basic panel that is the basis for the formulation by Kikuchi (Kikuchi, 2000).  Literature R e v i e w  70  The K i factor defines the effect o f v a r y i n g the r i b depth on the effective flange w i d t h .  This  factor, based o n a basic r i b depth o f 140 m m and a curve f i t t i n g parameter related to the r i b spacing ratio, was g i v e n by: 140  N  (d in m m )  Y = 2 ( L / b ) + 12.5  forL/b<4  Y=ll(L/b)-23.5  forL/b>4  (2.79)  V " J  I n contrast to the r i b depth, it was d e t e r m i n e d that v a r y i n g the r i b w i d t h , b , or the m o d u l u s o f w  elasticity o f the rib d i d not have a significant effect o n the effective flange w i d t h .  Those t w o  parameters were, therefore, neglected i n the f i n a l f o r m u l a t i o n .  Three parameters related to the properties o f the flange i t s e l f were f o u n d to be significant w i t h respect to the determination o f effective flange w i d t h except f o r panel configurations where the r i b spacing ratio is large. A factor a c c o u n t i n g for the v a r i a t i o n i n flange thickness, based u p o n a basic flange thickness o f 12 m m , was g i v e n b y : 0.766 (  10 V  K  2  =  K  2  =1  ^  LYt b  12  1 + .  (t i n m m )  for L / b < 1 0  (2.80)  for L / b > 1 0  The relationship between effective flange w i d t h and the m o d u l u s o f elasticity o f the flange, based u p o n a basic axial elastic m o d u l u s o f the flange o f 4,413 M P a , was g i v e n b y : 1(  —  9  K  3  I  L\  1 0 - bj  (4413  \  E y  \  -1 + 1 J  (E in MPa)  forL/b<10  (2.81)  for L / b > 1 0  = l  V a r i a t i o n i n the value o f shear m o d u l u s o f elasticity was also f o u n d to have a s i g n i f i c a n t effect o n the determination o f effective flange w i d t h .  The f o l l o w i n g a p p r o x i m a t e d this effect, where  the basic shear elastic m o d u l u s o f the flange was 392 M P a :  Literature R e v i e w  71  f 4  K  4  10  xy  i o - i  392  b  +1  (G in MPa)  forL/b<10  =1  (2.82)  for L / b > 1 0  F i n a l l y , the type o f l o a d i n g was f o u n d to have a significant effect on the effective flange w i d t h a l o n g the entire length o f a s i m p l y supported panel. The v a r i a t i o n o f effective w i d t h a l o n g the span was expressed as a linear relation to the rib spacing ratio as f o l l o w s : K =a(L/b)+b  (2.83)  5  where the parameters a and b are related to the location along the span and the type o f l o a d i n g applied to the panel. Those parameters are given i n Table 2.5.  Table 2.5. Values f o r coefficients a and b f o u n d i n equation (2.83) ( K i k u c h i , 2000).  F o u r t h p o i n t loads  Central p o i n t load  (F.P.L.)  U n i f o r m l y distributed load  (C.P.L.)  (U.D.L.)  y=0.5L  0.35L  0.1L  y=0.5L  0.35L  0.1L  y=0.5L  0.35L  0.1L  a  1  0.01067  0.01811  0.02226  0.00998  -0.01000  0.00972  0.01119  0.02035  b  1  0.8530  0.7247  0.6040  0.8754  1.1031  0.8554  0.8350  0.6533  2.6  SHEATHING BUCKLING  The current l i m i t o n the spacing o f studs i n shearwalls, as specified i n the Canadian W o o d D e s i g n Code, C S A 0 8 6 - 0 1 ( C S A , 2 0 0 1 ) , was based o n t w o papers that i d e n t i f i e d localized b u c k l i n g o f the sheathing as a mode o f failure o f t y p i c a l shearwalls b u i l t i n N o r t h A m e r i c a . Tissell l o o k e d at over one h u n d r e d tests that were c o m p i l e d b y the A m e r i c a n A s s o c i a t i o n since 1965 (Table 2.6) (Tissell, 1993).  Plywood  A l l shearwall specimens were fabricated  Literature R e v i e w  72  w i t h the longest panel length d i m e n s i o n parallel t o the studs. F r o m those tests, the potential f o r t h i n panels to b u c k l e was i d e n t i f i e d and a reduced capacity was r e c o m m e n d e d f o r w a l l s w i t h 610 m m ( 2 4 " ) stud spacing versus 406 m m ( 1 6 " ) stud spacing w i t h t h i n sheathing.  The reduced  capacity, h o w e v e r , was not necessary f o r sheathing panels that were at least 9.5 m m ( 1 5 / 3 2 " ) thick.  Therefore, the l i m i t o n stud spacing specified i n the Canadian W o o d D e s i g n Code is  d i r e c t l y applicable to the one sheathing thickness less than 9.5 m m g i v e n i n the design tables but has s h o w n to be conservative f o r thicker sheathing thicknesses.  Table 2.6. E f f e c t o f stud spacing o n shearwalls f r o m (Tissell, 1993).  Stud Spacing (mm)  Fastener Size  S  P " (mm) a c i  g  Panel Thickness (mm)  Target Design Shear (kN/m)  Load Factor  26.91  8.03  3.4  Ultimate Loads (kN/m) 3  No. of Tests  Min.  Max.  Avg.  Structural I Sheathin 406  8d  76  9.5  1  610  8d  76  9.5  7  16.58  22.08  19.88  6.71  3.0  406 610  lOd lOd  76 76  11.9 11.9  1 29  21.83  33.27  32.43 28.52  9.70 9.70  3.3 2.9  Rated Sheathing 406  8d  76  9.5  14  19.38  24.44  21.38  7.15  3.0  610  8d  76  9.5  17  16.87  24.52  20.31  5.98  3.4  406  lOd  76  11.9  1  27.74  8.76  3.2  610  lOd  76  11.9  30  19.61  28.66  23.98  8.76  2.7  406 610  lOd lOd  76 76  15.1 15.1  2 16  24.50 20.37  28.11 31.60  26.30 27.22  9.70 9.70  2.7 2.8  Notes: (a) M i n i m u m panel thickness f o r design shear, some w a l l s sheathed w i t h t h i c k e r panels (b) The load factor is determined b y d i v i d i n g the u l t i m a t e load b y the target design shear. The second paper referenced i n the Canadian W o o d D e s i g n Code also i d e n t i f i e d the potential f o r localized b u c k l i n g to occur i n the sheets o f a shearwall i f the sheets are v e r y t h i n (Kallsner,  Literature R e v i e w  73  1995). The w o r k done i n this paper was p u r e l y theoretical and was not related to test data. The critical shear stress i n a sheathing panel was g i v e n as: 7t E 2  x  =k  f O  2  (2.84)  For a sheet that is s i m p l y supported along all f o u r edges, an approximate expression f o r the coefficient k was g i v e n b y :  k = 5.35 + 4  b  (2.85)  Figure 2.29. Sheathing panel loaded w i t h a constant shear stress a l o n g the edges (Kallsner, 1995). For a sheet that is c l a m p e d along all four edges, the coefficient k was g i v e n as:  k = 8 . 9 8 + 5.6  (2.86)  Literature R e v i e w  74  I n equations (2.84) t h r o u g h ( 2 . 8 6 ) , the symbols and terms are d e f i n e d as f o l l o w s : E = m o d u l u s o f elasticity o f the sheathing panel = Poisson's ratio t = thickness o f the sheathing panel b = w i d t h o f the sheathing panel (Figure 2.29) a = length o f the sheathing panel (Figure 2.29).  2 . 7 NAILED CONNECTION LOAD-SLIP MODELS It was s h o w n i n section 2.5 that the effective m e m b e r properties o f a m e m b e r w i t h partial composite action are a f u n c t i o n o f the connection stiffness between the separate components.  A  parameter study conducted b y Polensek showed that the ultimate load, m a x i m u m stresses, and m a x i m u m deflections o f a composite member are greatly affected b y the stiffness o f the connection (Polensek, 1978). I f the p a r t i a l l y composite m e m b e r is connected w i t h nails then the load-displacement relationship o f the connection is important w i t h respect to the o v e r a l l response o f the member. with  nails  T o accurately predict the response o f p a r t i a l l y composite members connected  the load-displacement  response  o f the nailed connections  must,  therefore, be  q u a n t i f i e d and characterized b y one or m o r e functions.  T w o procedures w i l l be used t h r o u g h o u t the course o f this study.  T h e C E N procedure w i l l be  used to q u a n t i f y specific properties o f the load-displacement response o f n a i l e d connections i n order to compare connections w i t h varied parameters more easily ( C E N , 1995).  The C E N  procedure defines i n i t i a l stiffness b y the line that connects to points o n the load-slip curve at 0.1 F  m a x  and 0.4 F  m a x  , respectively (Figure 2.30).  The y i e l d load is the load o n the curve that  corresponds to the y i e l d displacement, w h i c h is defined as the displacement at the interception o f  Literature R e v i e w  75  the i n i t i a l stiffness line and a tangent line w i t h stiffness equal to 1/6 o f the i n i t i a l value.  The  ultimate displacement corresponds to the displacement at w h i c h the l o a d drops to 8 0 % o f the m a x i m u m load.  0.8P„  tan p = 0.167 t a n a  0.4P„  0.1 P„  Figure 2.30. D e f i n i t i o n o f the parameters o f the C E N procedure ( C E N , 1995).  W h i l e the C E N procedure a l l o w s f o r ease o f comparisons between load-displacement results, a f u n c t i o n is required for c o m p u t a t i o n a l ease o f m o d e l i n g composite members. A non-linear f i n i t e element p r o g r a m developed b y Foschi f o r w o o d - f r a m e d i a p h r a g m structures w i l l be used to predict the response o f full-scale test specimens later i n this study. That p r o g r a m employs a fiveparameter f u n c t i o n to m o d e l the load-slip behaviour o f t i m b e r j o i n t s , w h i c h was also developed b y Foschi (1974). That f u n c t i o n , s h o w n i n Figure 2 . 3 1 , was g i v e n b y the f o l l o w i n g equations:  p„  P = (P„- + K , u ) 1 - e  P = P +K,u 0  m a x  +K (u-u E  m a x  )  if u < u  n  (2.87)  ifu>u  n  (2.88)  Literature R e v i e w  76  Umax  Figure 2 . 3 1 . D e f i n i t i o n o f the parameters o f the f u n c t i o n b y Foschi ( F o s c h i , 1974).  It should be noted that a recent study has m o d i f i e d the f u n c t i o n b y Foschi to m o r e accurately account f o r the softening behaviour o f the j o i n t s ( G i r h a m m e r et. al., 2 0 0 4 ) .  The n e w f u n c t i o n ,  s h o w n i n Figure 2.32, was g i v e n b y : K,,u  \  P = ( P + K , u ) 1-e  (2.89)  0  The solution to this five-parameter f u n c t i o n was determined b y f o r c i n g the f u n c t i o n t h r o u g h the points ( u , P ) and ( u , P ) . P corresponds to a d e f i n e d p o i n t o f total collapse. The non-linear m  m  c  c  c  curve f i t was then reduced to f i n d i n g the best value o f three o f the parameters d e f i n e d b y Foschi: Ko, K i , and Po. The parameters a and P were f o u n d b y iteration u s i n g a s o l v i n g process.  Figure 2.32.  L o a d - s l i p curve m o d e l l e d b y a 5-parameter equation ( G i r h a m m e r et. al., 2004).  Literature R e v i e w  77  2.8 LATERAL-TORSIONAL BUCKLING Structural members loaded b y transversal loads i n the plane o f greatest stiffness m a y d e f o r m laterally and t w i s t (Figure 2.33).  T h i s type o f stability p r o b l e m is k n o w n as lateral-torsional  b u c k l i n g and results i n the loss o f increased resistance i n the transversal l o a d i n g d i r e c t i o n . P r o v i d i n g adequate support to the compression face o f a loaded m e m b e r can prevent lateraltorsional b u c k l i n g f r o m o c c u r r i n g .  W o o d - f r a m e t a l l w a l l s are especially susceptible to lateral-  torsional b u c k l i n g f o r several reasons.  F i r s t l y , the engineered w o o d products that are used as  studs i n tall w a l l construction have a large slenderness ratio (the ratio o f stud depth d to w i d t h b ) . A s w i l l be s h o w n later, the resistance o f rectangular members to lateral b u c k l i n g is a f u n c t i o n o f stud depth and w i d t h .  Second, u n l i k e f l o o r diaphragms, the transversal loads on w a l l s due to  w i n d pressure and suction can be a p p r o x i m a t e l y equal i n magnitude.  Therefore, b o t h faces o f  ("bJ  Figure 2.33.  Lateral-torsional b u c k l i n g o f a s i m p l y supported b e a m ( H o o l e y M a d s e n , 1964).  and  Literature R e v i e w  78  the w a l l w i l l be loaded to a p p r o x i m a t e l y the same compression stress.  F i n a l l y , u n l i k e regular  w o o d - f r a m e w a l l construction, b u i l d i n g s constructed w i t h tall w o o d - f r a m e w a l l s often utilize oversized sheathing panels.  T h i s removes the need to p r o v i d e b l o c k i n g at small increments  a l o n g the height o f the w a l l to p r o v i d e support to panel edges.  Lateral stability is addressed i n the Canadian W o o d D e s i g n Code i n t w o ways ( C S A , 2 0 0 1 ) . For regular w o o d - f r a m e construction, criteria are d e f i n e d f o r a lateral stability factor, K , based u p o n L  the slenderness ratio o f a member.  I f the m e m b e r meets the criteria set out and the slenderness  ratio, then the lateral stability factor m a y be taken as u n i t y . These requirements are based on the experience o f w h a t has w o r k e d over m a n y years. Otherwise, the lateral stability factor m a y be calculated i n accordance w i t h the requirements f o r glued-laminated timber.  These requirements  f o r lateral stability are based u p o n a f o r m u l a t i o n , v e r i f i e d w i t h testing, that was d e r i v e d b y H o o l e y and M a d s e n (1964). T h e y i d e n t i f i e d that the resistance o f a rectangular b e a m to lateral b u c k l i n g is not related to the slenderness ratio but is governed b y the ratio L d / b . 2  e  L  e  is the  effective length o f the m e m b e r and can be a f u n c t i o n o f the entire length o f the m e m b e r , i f it does not have any intermediate support, or the distance between intermediate supports.  A t a l l w o o d - f r a m e w a l l often consists o f slender studs w i t h a large spacing between b l o c k i n g , sheathed on the exterior face w i t h structural panel sheathing and sheathed o n the interior face v w i t h gypsum wallboard.  For the case o f w i n d pressure i n the transversal d i r e c t i o n , the exterior  face o f the stud m e m b e r w i l l be i n compression. The c o m m e n t a r y to the Canadian W o o d D e s i g n Code defines d i a p h r a g m - f o r m i n g panel sheathing as a suitable r i g i d d i a p h r a g m and so no r e d u c t i o n to the b e n d i n g m o m e n t resistance is required i n this d i r e c t i o n and the lateral stability factor can be taken as unity. Z a h n has s h o w n that b l o c k i n g contributes v e r y little to p r e v e n t i n g  Literature R e v i e w  79  lateral torsional b u c k l i n g , h o w e v e r , w h e n used i n c o n j u n c t i o n w i t h a s t i f f d i a p h r a g m ( Z a h n , 1984).  Conversely, g y p s u m w a l l b o a r d does not meet the criteria f o r f o r m i n g a r i g i d d i a p h r a g m o n the interior face o f the w a l l and often the w a l l does not meet the slenderness criteria f o r regular wood-frame walls.  Therefore, the lateral stability factor must be d e t e r m i n e d based o n the  m e t h o d presented f o r glued-laminated timber. b l o c k i n g spacing m u l t i p l i e d b y 1.92.  I n this case, the effective length is equal to the  I n m a n y cases, the lateral stability factor can be less than  0.50, w h i c h means that the b e n d i n g m o m e n t resistance i n one d i r e c t i o n is less than h a l f o f the b e n d i n g m o m e n t resistance o f the other d i r e c t i o n even t h o u g h the a p p l i e d load is a p p r o x i m a t e l y equal.  The interpretation o f the code requirements is v a r i e d i n practice.  A w o o d - f r a m e w a l l design  guide p u b l i s h e d b y a producer o f engineered w o o d products provides lateral stability factors f o r g i v e n b l o c k i n g spacing and sheathing l i m i t s .  Firstly, g y p s u m w a l l b o a r d is described as an  acceptable material to p r o v i d e lateral support.  Second, instead o f increasing the distance  between b l o c k i n g supports b y 9 2 % to determine an effective length, this distance is reduced b y 1 5 % b y assuming a b u c k l i n g length coefficient o f 0.85. For an example w a l l characterized b y 38 m m b y 235 m m  studs w i t h b l o c k i n g spaced at 2,440 m m  o n centre, the result o f this  interpretation is that the code requires a p p r o x i m a t e l y a 7 0 % r e d u c t i o n i n b e n d i n g m o m e n t resistance w h i l e the design guide prescribes o n l y a 3 0 % reduction.  T h i s clearly identifies the  need f o r c l a r i f i c a t i o n on w h a t is an acceptable design procedure to account f o r lateral-torsional b u c k l i n g and p o s s i b l y the need f o r further testing.  Literature R e v i e w  80  2.9 ROTATIONAL RESTRAINT AND STUD CONNECTIONS The structural models that are t y p i c a l l y used i n design incorporate s i m p l i f i c a t i o n s o f actual structures.  assumptions that are  I n almost all cases, the assumptions are conservative and  result i n a structural m o d e l that predicts the m a x i m u m displacements and m e m b e r stresses to be larger than w h a t occurs i n actual structures.  A  simplification commonly employed  when  designing w o o d - f r a m e structures is to m o d e l the supports at each end o f a f l o o r or d i a p h r a g m as b e i n g p i n n e d . rotation.  wall  Therefore, the support does not p r o v i d e any restraint against  Polensek and S c h i m e l i d e n t i f i e d the need to q u a n t i f y the effect that intercomponent  connections i n l i g h t - f r a m e w o o d b u i l d i n g s , such as those between w a l l s , f l o o r s , and foundations, have o n the displacement o f w a l l diaphragms (Polensek and S c h i m e l , 1986).  The research carried out b y Polensek and S c h i m e l included the creation o f a non-linear f i n i t e element m o d e l to predict the actual response o f the w a l l components that were tested. a d d i t i o n to testing representative sections o f w o o d - f r a m e w a l l s w i t h connections f o u n d i n structures i n N o r t h A m e r i c a , they tested w a l l sections w i t h simple  In  commonly construction  m o d i f i c a t i o n s that increased the amount o f end restraint. A total o f nine panels were tested three times w i t h different m o d i f i c a t i o n s .  The predicted deflections u s i n g the f i n i t e element m o d e l  closely agreed w i t h the corresponding experimental results.  The t y p i c a l c o n n e c t i o n system  between w a l l , f l o o r , and f o u n d a t i o n that was investigated is s h o w n i n Figure 2.34.  For design purposes, a simple m e t h o d to incorporate the reduction i n m i d - s p a n d e f l e c t i o n o f a w a l l w i t h support restraint was p r o v i d e d . Partial support restraint was accounted f o r b y a d d i n g springs that restrained support r o t a t i o n at the ends o f a b e a m - c o l u m n . The c o e f f i c i e n t o f restraint  Literature R e v i e w  81  SHEATHING STUD INTERIOR COVERING SOLE PLATE  NAIL  UNDERLAYMENT SUBFLOOR JOIST  HEADER  SILL PLATE FOUNDATION WALL  Figure 2.34  T y p i c a l intercomponent connection system between a w a l l , f o u n d a t i o n (Polensek and S c h i m e l , 1986).  was d e f i n e d as the spring stiffness, a , o f the b e a m - c o l u m n m o d e l .  floor,  and  The spring stiffness was  determined f r o m the ratio o f the m i d - s p a n deflections o f the restrained and unrestrained b e a m , y and y respectively. For u n i f o r m load, a was g i v e n as: 0  a =  10EIR  (2.90)  [L(4-5R)]  where R = l - y / y . 0  Several important findings resulted f r o m the testing and parametric study that was conducted u s i n g the f i n i t e element m o d e l . Firstly, the m i d - s p a n deflection r e d u c t i o n f o r w a l l s constructed i n the c o n v e n t i o n a l w a y w i t h 38 m m b y 89 m m ( 2 " x 4 " ) studs was less than 2 % .  Hammering  t w o a d d i t i o n a l nails at each stud between the sheathing and the sill plate and six a d d i t i o n a l nails at each stud between the sheathing and the header p r o v e d to be the most successful m o d i f i c a t i o n to the o r i g i n a l c o n n e c t i o n and reduced the m i d - s p a n d e f l e c t i o n b y  13%.  F i n a l l y , it was  determined that the coefficient o f support restraint gets smaller w i t h increasing lateral load  Literature R e v i e w  82  because o f the non-linear behaviour o f the w o o d components themselves and the connections o f those components.  The a x i a l load on a w a l f c a n either be i n compression or i n tension. W i n d can cause s u c t i o n o n the leading edges o f roofs.  W h i l e m o s t o f the research to date o n w o o d structures under w i n d  u p l i f t has focused on fastening the r o o f sheathing to the r o o f j o i s t s , a study was conducted at Clemsen U n i v e r s i t y i n South C a r o l i n a that addressed the u p l i f t capacity o f regular w o o d - f r a m e stud w a l l s ( R o s o w s k i , 2000).  Some o f the objectives o f the research were to determine the  failure modes o f w a l l s w i t h various sheathing orientations and hurricane strap installations and to determine the u l t i m a t e  load c a r r y i n g capacities  o f the w a l l s  tested f o r comparison  with  theoretical predictions.  Four critical points on the load path o f these w a l l s were determined: the sheathing to the top plate c o n n e c t i o n ; the connection f r o m the sheathing to the w a l l stud; the n a i l i n g pattern at the inter-story d e t a i l ; and the sheathing to b o t t o m plate connection.  The results indicated that  h o r i z o n t a l l y oriented sheathing m i g h t be able to carry the u p l i f t loads i n a w a l l system, assuming that an adequate n u m b e r o f nails are present i n the sheathing. the  eccentricity  o f the  straps was  identified  as a failure  I n a d d i t i o n , top plate r o l l due to mode  with  significant  design  i m p l i c a t i o n s . The capacity o f the w a l l s w i t h this type o f failure m o d e was up to 5 0 % l o w e r than w a l l s w i t h other types o f connection details.  T w o solutions suggested to r e m e d y this type o f  failure were to place the straps o n the outside o f the w a l l or to use a strap that d i r e c t l y connects the rafters to the studs on the inside o f the w a l l .  Literature R e v i e w  2.10  83  WOOD DIAPHRAGM MODELS  N u m e r o u s s i m p l i f i e d methods f o r d e t e r m i n i n g the effective properties o f composite members were presented i n section 2.5. These members represented one stud or one j o i s t o f a larger w a l l or f l o o r d i a p h r a g m .  A m e t h o d was also presented where the composite members were j o i n e d  together to f o r m a d i a p h r a g m using a beam-spring analog.  Wood-frame  structures are a  complicated a m a l g a m o f non-linear members, however, j o i n e d together b y hundreds o f n o n linear connections.  T o m o r e accurately predict the response o f an entire w o o d system a m o r e  advanced m e t h o d o f analysis is thus required. W i t h the onset o f personal computers in the late I 9 7 0 ' s , researchers began to develop computer programs that used f i n i t e elements to m o d e l w o o d diaphragms.  O v e r the years, researchers have attempted to predict the response o f w o o d  diaphragms w i t h sophisticated models, some o f w h i c h w i l l n o w be presented.  2.10.1 FINWALL (Polensek) F I N W A L L , one o f the first computer programs to m o d e l w o o d diaphragms, was developed b y Polensek at the U n i v e r s i t y o f O r e g o n (Polensek, 1976b). The p r o g r a m subjects w a l l s to constant axial and increasing transversal loads. It is capable o f b o t h linear and non-linear analysis.  The  finite element m e t h o d o f analysis is c o m b i n e d w i t h a linear step-by-step procedure to calculate w a l l performance. The stud and sheathing c o n n e c t i o n properties are assumed to be constant over the f u l l height o f a g i v e n stud and s y m m e t r i c a l about the m i d - h e i g h t o f the w a l l .  The f i n i t e  element mesh is, thus, rather coarse (Figure 2.35).  A m e t h o d f o r c a l c u l a t i n g partial composite action similar to that d e r i v e d b y A m a n a and B o o t h , described i n section 2.5.3 ( A m a n a and B o o t h , 1967), was used to calculate the stiffness o f I-  Literature R e v i e w  84  NODAL  X  WALL COVERINGS  Figure 2.35. Finite element mesh f o r the F I N W A L L p r o g r a m (Polensek, 1976b).  b e a m c o l u m n elements, c o m p r i s e d o f a stud and t w o layers o f sheathing (Figure 2.36). A f t e r the c o l u m n stiffness o f the I-beam was calculated, the contributions o f the t w o layers o f sheathing were a n a l y t i c a l l y l u m p e d into a single plate f o r evaluation o f their l o a d - d i s t r i b u t i o n ability.  It  was assumed that the l o a d - d i s t r i b u t i o n properties o f the plate c o u l d be m o d e l e d b y s i m p l y a d d i n g the stiffness o f the t w o layers o f sheathing.  D i s c o n t i n u i t i e s i n the sheathing layers were  accounted f o r b y r e d u c i n g the sheathing stiffness at the d i s c o n t i n u i t y .  A f t e r the stiffness values were c o m p i l e d i n a stiffness m a t r i x , the stresses and deflections i n the w a l l were calculated. Secondary m o m e n t s induced b y axial loads were calculated b y an iterative procedure.  Failure o f an i n d i v i d u a l stud was c o m p u t e d w h e n the m i d - h e i g h t d e f l e c t i o n o f the  stud exceeded the value input as its failure deflection. The f a i l e d stud was then assigned a near-  Literature R e v i e w  85  zero stiffness i n the stiffness m a t r i x f o r the next iteration o f the p r o g r a m . T h e p r o g r a m d e f i n e d w a l l failure as the failure o f t w o adjacent studs.  T h e m o d e l assumed that w a l l failure was  governed b y the b e n d i n g strength o f the studs and that stud failures were complete.  Based o n  tests that were conducted to v e r i f y the m o d e l , described later i n this chapter, m o d e l accuracy was i n the range o f less than 1 0 % error at first stud failure and up to a p p r o x i m a t e l y 2 0 % at w a l l failure.  x  Figure 2.36. A s s e m b l y o f I-beam c o l u m n and plate elements (Polensek, 1976b).  2.10.2  FEAFLO and NONFLO (Thompson, Vanderbilt, and Goodman)  The differential equations developed b y G o o d m a n and Popov ( 1 9 6 8 ) , presented i n section 2.5.2, were the basis f o r the Finite Element A n a l y s i s o f F L O o r s ( F E A F L O ) p r o g r a m developed b y T h o m p s o n , G o o d m a n , and V a n d e r b i l t at C o l o r a d o State U n i v e r s i t y ( T h o m p s o n et. a l . , 1975). The sheathing is m o d e l e d as a series o f parallel strips perpendicular to the j o i s t s (Figure 2.37). The  differential  equations  f o r the p a r t i a l l y  composite  T-beams  are c o u p l e d  by  strain  Literature R e v i e w  86  c o m p a t i b i l i t y at the c o m m o n b o u n d a r y o f the sheathing strips. F E A F L O was able to account f o r interlayer slip between the j o i s t s and the sheathing, intralayer gaps between sheathing sheets, and composite and t w o - w a y action. The c o n t r i b u t i o n f r o m torsional stiffness was i g n o r e d since the ratio o f sheathing m o d u l u s o f r i g i d i t y to the m o d u l u s o f elasticity is small i n this case and because the torsional stiffness o f a T - b e a m is small compared to its b e n d i n g stiffness. The flange w i d t h was equal to the j o i s t spacing.  Sheathing  Span  Sheathing Strips  Joists  A  A / y  /  /  /  /  /  /  /  / / /  / /  /  / /  /  .  T / — * /  Sheathing beams  >  (B) T-bea ms  s h e a t h i n g beam cross section  T-beam coss section  Figure 2.37.  Idealization o f a w o o d - j o i s t R o b i n s o n , 1997).  f l o o r system i n F E A F L O  (Pellicane  and  Literature R e v i e w  87  Since its development, several m o d i f i c a t i o n s to the basic p r o g r a m have been made. The a b i l i t y to account f o r m u l t i p l e load cases and evaluate interlayer shears, v e r t i c a l shears, a x i a l forces, and m o m e n t i n the system was incorporated.  W h e a t , V a n d e r b i l t , and G o o d m a n made the most  significant increase i n accuracy b y a d d i n g the effects o f sheathing connection n o n - l i n e a r i t y to the finite element analysis ( W h e a t et. al., 1983).  The n e w p r o g r a m called, N O N - l i n e a r  FLOor  analysis ( N O N F L O ) , o n l y considered the n o n - l i n e a r i t y due to connector d e f o r m a t i o n s since this was deemed to be the m a j o r source o f f l o o r n o n - l i n e a r i t y f o r loads close to the failure load.  F E A F L O and its various incarnations have been used i n numerous studies to predict the response o f tested specimens.  D e f l e c t i o n comparisons o f floors showed that the predictions made b y the  non-linear p r o g r a m were more accurate than the earlier developed linear analysis p r o g r a m f o r behaviour at i m p e n d i n g f l o o r failure under short-term l o a d i n g .  I n a d d i t i o n , far m o r e realistic  magnitudes o f connector forces above the service load level were p r o v i d e d b y the non-linear analysis ( W h e a t et. al., 1983).  2.10.3 FAP and PANEL (Foschi) Foschi has developed several computer programs to m o d e l w o o d - f r a m e d i a p h r a g m structures. T h e y include: F l o o r A n a l y s i s P r o g r a m ( F A P ) (Foschi, 1989); W a l l A n a l y s i s P r o g r a m ( W A P ) (Foschi, 1992); D i a p h r a g m A n a l y s i s P r o g r a m ( D A P ) (Foschi, 1993); and P A N E L 1999).  (Foschi,  The programs were all based o n his o r i g i n a l p r o g r a m that was characterized b y a  c o m b i n e d Fourier series and f i n i t e element analysis o f a w o o d f l o o r ( F o s c h i , 1982).  The structural idealization o f the f l o o r s h o w n i n Figure 2.38 was based on a f i n i t e  strip  f o r m u l a t i o n made up o f an assemblage o f T-beams.  were  The d e f o r m a t i o n s o f the f l o o r  represented b y a Fourier series i n the d i r e c t i o n parallel to the j o i s t s and b y a one-dimensional  Literature R e v i e w  88  f i n i t e element discretization in the direction perpendicular to the joists.  The m o d e l i n this  p r o g r a m included lateral and torsional d e f o r m a t i o n o f the j o i s t s as degrees o f freedom.  This  permited the consideration o f the effect that j o i s t b r i d g i n g has o n m a x i m u m f l o o r deflection and m a x i m u m b e n d i n g stresses.  The F E A F L O m o d e l restricted those degrees o f freedom and,  therefore, resulted i n a m o d e l that was stiffer than the actual structure, w h i c h was s h o w n b y experimental data ( T h o m p s o n et. al., 1975). The original m o d e l b y Foschi p r o v i d e d reliable estimates f o r deflections and the influence o f different gaps configurations w h e n compared w i t h tests conducted on full-scale floors.  Plate Cover  (a)  (b)  Figure 2.38. (a) w o o d f l o o r assembly and (b) T - b e a m element strip (Foschi, 1989).  P A N E L was used i n this study to predict the response o f full-scale w a l l specimens.  It was  designed to m o d e l stressed skin panels consisting o f a frame connected to top and b o t t o m covers. The connections were assumed to be n o n - r i g i d w i t h non-linear load-slip properties.  The loads,  w h i c h c o u l d be a p p l i e d i n the transversal d i r e c t i o n or i n the plane o f the w a l l , c o u l d be incremented simultaneously or i n d i v i d u a l l y u n t i l the ultimate capacity was reached.  Ultimate  capacity was defined b y the f o l l o w i n g : excessive connection d e f o r m a t i o n ; b u c k l i n g o f either o f  Literature R e v i e w  89  the sheathing layers; b u c k l i n g o f the frame; tearing o f the edge o f the covers i m p l y i n g local connection failure; or b e n d i n g failure o f the frame members. The models e m p l o y e d i n this study are described i n detail i n A p p e n d i x C.  2.10.4 BSAF (Lui and BuIIeit) The programs described p r e v i o u s l y do not consider the post failure b e h a v i o u r o f the system components o f a w o o d - f r a m e d i a p h r a g m .  E v e n programs that include the non-linear b e h a v i o u r  o f the connections are not adequate in this regard since they do not include the non-linear behaviour o f the partial composite members.  The overload b e h a v i o u r o f w o o d systems is  d i r e c t l y related to this non-linear b e h a v i o u r o f the partial composite members.  The system-  failure criteria o f a system can o n l y be predicted t h r o u g h the use o f a p r o g r a m that incorporates the non-linear b e h a v i o u r o f a l l o f the components o f the system.  Lui  and B u l l e i t  incorporated the b e a m - s p r i n g analog m e t h o d developed b y  McCutcheon,  presented i n section 2.5.6.2, into a computer p r o g r a m called B e a m - S p r i n g A n a l o g f o r Floors ( B S A F ) ( L u i and B u l l e i t , 1995). The p r o g r a m included: t w o - w a y action o f the sheathing; partial composite  action between  the  sheathing, connectors,  and  lumber  members;  the  random  mechanical properties o f the l u m b e r m e m b e r s ; and the r a n d o m p o s t - y i e l d properties o f the partial composite  members.  A  trilinear  spring m o d e l (Figure 2.39) and a  member-replacement  technique were i n t r o d u c e d to account f o r the non-linear behaviour o f the partial composite members.  The p r o g r a m d i d not represent the w o o d - f r a m e system u s i n g the f i n i t e element m e t h o d and was thus an a p p r o x i m a t i o n w i t h several assumptions to s i m p l i f y the procedure. The t r i - l i n e a r m o d e l and m e m b e r replacement technique i n B S A F to predict the non-linear b e h a v i o u r o f a sheathed  Literature R e v i e w  90  lumber system compared w e l l w i t h test data o n floors. U s i n g this p r o g r a m , the p r i m a r y factors affecting system o v e r l o a d b e h a v i o u r were determined along w i t h appropriate  system-failure  criteria.  Figure 2.39. S p r i n g l o a d - d e f o r m a t i o n curve ( L u i and B u l l e i t , 1995).  2.10.5 Equivalent Finite Element Model (Kasal and Leichti) W i t h the advent o f m o d e r n structural m o d e l i n g software, it is possible f o r c o n s u l t i n g engineers to r o u t i n e l y use packaged f i n i t e element programs to design structures.  U n l i k e the programs that  have been described p r e v i o u s l y that assess the response o f an isolated w a l l or f l o o r i n a b u i l d i n g , it is n o w possible to predict the g l o b a l response o f a structure under load b y m o d e l i n g the entire structure. A n actual w o o d - f r a m e structure'is v e r y c o m p l e x , however, and the n u m b e r o f degrees o f f r e e d o m is enormous. T o address this p r o b l e m , Kasal and L e i c h t i developed a s i m p l i f i e d , or equivalent, f i n i t e element m o d e l o f a w o o d - f r a m e w a l l that c o u l d be used as a c o m p o n e n t i n a three-dimensional m o d e l o f an entire w o o d - f r a m e structure (Kasal a n d L e i c h t i , 1992).  Literature R e v i e w  Figure 2.40.  91  Finite element mesh o f a (a) sheathed w a l l and (b) w a l l frame ( K a s a l and L e i c h t i , 1992).  U s i n g an o f f - t h e - s h e l f f i n i t e element p r o g r a m , a detailed m o d e l o f an actual w o o d - f r a m e w a l l was created (Figure 2.40). shell  elements.  Three  The studs and sheathing were m o d e l e d as linear t w o - d i m e n s i o n a l one-dimensional  springs  were  used  to  represent  the  non-linear  characteristics o f each j o i n t : one f o r w i t h d r a w a l and one each f o r shear i n each coordinate. a d d i t i o n , gap elements were used where the sheathing was not continuous.  In  Tests o n w a l l s  w i t h o u t openings b y Polensek were used to v e r i f y the detailed m o d e l (Polensek, 1975). N e x t , an equivalent m o d e l was developed i n order to m i n i m i z e the degrees o f f r e e d o m w h i l e r e t a i n i n g the response o f the detailed m o d e l under a x i a l , transversal, and lateral loading.  The degrees o f  f r e e d o m associated w i t h the equivalent m o d e l were global degrees o f f r e e d o m corresponding to  Literature R e v i e w  92  geometrical locations in a real structure ( F i g u r e 2.41).  The equivalent m o d e l had o n l y 55  elements compared to over 2 5 0 0 i n the detailed m o d e l .  BEAM ELEMENT  ice a B J O J T TRUSS ELEMENT TOI  NONLINEAR SPRING  P  I  N  192 in. (488 cm)  Figure 2 . 4 1 . Finite element mesh o f equivalent w a l l m o d e l (Kasal and L e i c h t i , 1992).  2.11  PREVIOUS FULL-SCALE W A L L TESTING  It is clear f r o m section 2.5 that there has been extensive research conducted on the effects o f composite m e m b e r properties as they relate to w o o d - f r a m e diaphragms.  M o s t o f this research  has been c o m p a r e d w i t h tests o n single composite members, w h i c h represent the i n d i v i d u a l load resisting elements i n a d i a p h r a g m , or w i t h tests o n full-scale f l o o r diaphragms. V e r y f e w studies have conducted tests o n full-scale w a l l specimens loaded under axial loads, representing the loads transmitted t h r o u g h a w a l l f r o m the floors and r o o f o f a structure, and transversal loads, representing loads due to w i n d pressure and suction o n the face o f a w a l l . Three test programs that have l o o k e d at this c o m b i n a t i o n o f loads o n regular w o o d - f r a m e w a l l s w i l l n o w presented.  be  Literature R e v i e w  93  2.11.1 Polensek The finite element p r o g r a m F I N W A L L , described i n section 2 . 1 0 . 1 , was v e r i f i e d against f u l l scale w a l l tests conducted b y the author o f the p r o g r a m at the Forest Research L a b o r a t o r y at O r e g o n State U n i v e r s i t y (Polensek, 1976b).  The w a l l s were loaded b o t h a x i a l l y and i n the  transversal d i r e c t i o n (Figure 2.42). The transversal load was applied b y u s i n g an inflated plastic bag to simulate a u n i f o r m l y  distributed load on the w a l l .  The a x i a l load was  applied  eccentrically to the top o f the w a l l b y a cantilevered w e i g h t o n a steel roller.  WOOD  PARAPET  GYPSUM 2X4  BOARD  STUD  P L A S T I C BAG  Figure 2.42. W a l l test arrangement f o r tests b y Polensek (Polensek and A t h e r t o n , 1976).  A l t h o u g h o n l y f o u r w a l l s i n total were constructed and tested i n this study, tests o n each c o m p o n e n t o f the w a l l s were also conducted i n order to increase the accuracy o f the analytical models.  The m o d u l u s o f elasticity o f each stud was d e t e r m i n e d b y non-destructive testing.  Samples o f all sheathing materials were tested to determine axial and b e n d i n g m o d u l i  of  elasticity. D o u b l e shear connection specimens were tested to determine the stiffness o f one-nail joints.  A n d f i n a l l y , fifteen I-beams representing the composite load-resisting members i n the  Literature R e v i e w  94  w a l l s were tested. Because o f the detailed k n o w l e d g e o f the properties o f each component o f the walls tested, the analytical models accurately predicted their response.  2.11.2 Gromala  T e n full-scale w a l l s w i t h varied w a l l sheathing and stud spacing were tested b y G r o m a l a (1983) as part o f the l i g h t - f r a m e construction research p r o g r a m initiated at the Forest  Products  L a b o r a t o r y i n M a d i s o n , W i s c o n s i n (Hans et. al., 1977). T h e goal o f the study was to accurately predict the response o f these w a l l s .  F I N W A L L was once again used f o r this purpose.  T h e test  set-up was v e r y s i m i l a r t o one described i n the previous section (Figure 2.43 a n d Figure 2.44). Once  again,  the a x i a l  load  was applied  eccentrically.  In  Figure 2.43. Photo o f the overall test set-up ( G r o m a l a , 1983).  addition,  the  properties  Literature R e v i e w  95  o f all o f the studs, sheathing materials, and connection configurations were d e t e r m i n e d as input values f o r the c o m p u t e r p r o g r a m .  For some o f the w a l l s , internal d e f l e c t i o n transducers were  placed inside the w a l l to measure the slippage between the sheathing and the studs.  z3i  ° < MM  m  LEVER ARM _ *-  ~-  ^  AIR BAG (IN CAVITY) — S T R O N G BACK PANEL *—TEST  WALL  DEAD WEIGHT  Figure 2.44. Schematic o f the test set-up ( G r o m a l a , 1983).  The predictions o f d e f l e c t i o n b y F I N W A L L  were on average 6 % higher than test values.  Predictions f o r w a l l strength were not as accurate and p r o v e d to be v e r y sensitive to the material properties used as input.  O f significance to this study was the r e c o m m e n d a t i o n w i t h respect to  the effect o f the test set-up. It was determined that the negative stud deflections induced b y the applied eccentric a x i a l load were sometimes not overcome u n t i l the application o f a large transversal load.  It was concluded that large axial loads m i g h t not be present i n an actual  structure w h e n design-level transversal loads are present and so the ' r e i n f o r c i n g ' effect o f the eccentric load was deemed to be unrealistic. Therefore, the author r e c o m m e n d e d that future w a l l testing should not include an eccentric load that reinforces the w a l l .  Literature Review  96  2.11.3 Stefanescu et. al. The finite element program P A N E L , discussed in section 2.10.3, was verified with tests conducted on four walls at Clemsen University in South Carolina (Stefanescu et al., 2000). The walls had varied stud depth and nail spacing and were sheathed on both sides. The transversal loads were applied by inflating air bags. Hydraulic jacks just below the bottom beam applied the axial loads (Figure 2.45 and Figure 2.46). The properties of the studs, sheathing, and nailed connections were all determined prior to testing the full-scale walls. The walls were rotated 180 degrees about the middle stud between each of the four loading cycles to simulate both wind pressure and suction.  Figure 2.45. Schematic of the wall test set-up (Stefanescu et. al., 2000).  Literature Review  97  The end conditions affected the results o f the analytical predictions for this study as well. The top steel beam was fixed on the columns o f the testing frame while the bottom steel beam was free to rotate and move vertically. This caused partial fixity at the top o f the wall. P A N E L does not have the capability to apply partial fixity to the end reactions o f a wall model by applying rotational springs and so two models were used to predict the response o f each wall test: one assuming the top o f the wall was fully fixed and one assuming it was free to rotate.  It was  concluded that the boundary conditions had less o f an effect on the walls with deeper studs.  Figure 2.46. Photo o f the wall test set-up described by Stefanescu et. al. (2000).  Literature R e v i e w  98  Because the experimental results f e l l i n between the predictions using the t w o end reaction assumptions, it was c o n c l u d e d that the m o d e l was in g o o d agreement w i t h the test results.  In  a d d i t i o n , the comparisons between the predicted and experimental deflections m a y have been affected b y the use o f the average m o d u l u s o f elasticity o f all the studs tested f o r each stud i n the models.  T h i s i n d i r e c t l y increased the transverse (in-plane) stiffness o f the w a l l m o d e l s b y  assuming that the stiffness o f the studs along the length o f the w a l l was u n i f o r m .  C o n n e c t i o n L o a d - S l i p Tests  99  3. CONNECTION LOAD-SLIP TESTS One o f the most important parameters to q u a n t i f y w h e n a t t e m p t i n g to calculate the amount o f partial composite action between the studs and the sheathing o f a w o o d frame w a l l is the connection stiffness. I f this connection is g l u e d then it can be assumed that the interface is f u l l y r i g i d and the stiffness is i n f i n i t e .  I f the sheathing is connected to the studs w i t h mechanical  fasteners, h o w e v e r , then the c o n n e c t i o n has a f i n i t e stiffness that can v a r y depending o n the load level applied to it and the n u m b e r o f previous load cycles it has undergone.  The most c o m m o n  mechanical fastener used to connect sheathing to studs i n N o r t h A m e r i c a is the n a i l . studies have  l o o k e d at the  load-deformation,  or load-slip, properties  of  Numerous  sheathing-to-stud  connections w i t h a v a r i e t y o f n a i l types and sizes as w e l l as sheathing and stud types.  The tall  w a l l s i n this study, and w a l l s that have recently been designed i n practice, have been constructed u s i n g c o m b i n a t i o n s o f nails, studs, and sheathing that have not p r e v i o u s l y been studied, w h i c h necessitate the testing o f these particular c o m b i n a t i o n s .  O n l y m o n o t o n i c testing was done  because this study is concerned w i t h the response o f tall w o o d - f r a m e w a l l s under quasi-static a x i a l and transversal loads as imposed b y dead, live, and w i n d loads.  W i n d loads are here  considered quasi-static, as it is c o m m o n l y done i n practice, although it c o u l d be argued that they should be treated as d y n a m i c loads. The t e r m m o n o t o n i c indicates that the loads are a p p l i e d i n one d i r e c t i o n o n l y and at rates s l o w enough so that the material strain rate effects do not influence the results.  The f i n d i n g s f r o m m o n o t o n i c tests to determine the l o a d - d e f o r m a t i o n response o f connections associated w i t h tall w o o d - f r a m e w a l l s are presented i n this chapter.  The l o a d - d e f o r m a t i o n tests  represent the first part o f the experimental p r o g r a m presented i n this thesis.  The rest o f the  C o n n e c t i o n L o a d - S l i p Tests  100  experimental p r o g r a m , w h i c h includes w i t h d r a w a l connection tests, composite T - b e a m tests, shearwall tests to examine sheathing b u c k l i n g , and full-scale tall w a l l tests are presented i n the subsequent chapters.  3.1  OBJECTIVES AND SCOPE  The stiffness and l o a d - d e f o r m a t i o n response o f w o o d - f r a m e  w a l l s under w i n d l o a d i n g  influenced b y the amount o f composite action between the sheathing and the studs.  is  Since i n  w o o d construction the sheathing is m o s t c o m m o n l y connected to the studs b y nails, the first part o f the experimental p r o g r a m was focused o n d e t e r m i n i n g the stiffness o f these connections a l o n g w i t h their associated failure modes.  Once this i n f o r m a t i o n is k n o w n , analytical models f o r  p r e d i c t i n g the connection response can be developed and calibrated and further models can be used to predict  the response o f composite  members  and full-scale w a l l s .  Displacement  c o n t r o l l e d m o n o t o n i c tests were conducted on several connections w i t h different stud material, sheathing material, and n a i l sizes.  The m o n o t o n i c l o a d - d e f o r m a t i o n connection tests were  conducted i n the W o o d E n g i n e e r i n g L a b o r a t o r y o f F o r i n t e k Canada C o r p . i n V a n c o u v e r .  3.2 METHODS AND MATERIALS 3.2.1  Connection Specimens  A large n u m b e r o f connection specimens, over 2 7 0 , were tested i n order to b u i l d a database o f connection  properties  that  is representative  o f the most  common  combinations  of  nails,  sheathing, and stud types that are, or c o u l d be, used i n w o o d tall w a l l construction. O n l y a f e w o f these c o n n e c t i o n results have been used to predict the response o f the c o m p o n e n t and f u l l scale tests described i n subsequent chapters. The database, h o w e v e r , can n o w be d r a w n u p o n to p r o v i d e stiffness values f o r tall w a l l response predictions not tested i n this study, and i n d o i n g so determine the most efficient use o f materials. Because o f the large n u m b e r o f nails e m p l o y e d i n  C o n n e c t i o n L o a d - S l i p Tests  101  connecting the sheathing to the studs i n w a l l construction, the average n a i l properties are t y p i c a l l y o f interest to the designer, rather than the values at the t a i l ends o f the d i s t r i b u t i o n curve. Therefore, o n l y f i v e replicates o f each specimen type were i n i t i a l l y tested to determine a reasonable average response.  For each test g r o u p , the v a r i a t i o n o f results w i t h i n the g r o u p was  q u a n t i f i e d and additional replicates were tested i f it was deemed that the v a r i a t i o n was too h i g h . T h i s w i l l be discussed further i n this chapter.  T a l l w a l l s require a significant n u m b e r o f nails to be used to connect the sheathing to the studs d u r i n g construction. For this reason, nails guns are almost always used f o r the task o f c o n n e c t i n g the t w o components. spiral n a i l .  T he most c o m m o n type o f n a i l c u r r e n t l y b e i n g used i n n a i l guns is the  It is f o r this reason that spiral nails were used to connect the sheathing to the stud  material i n this test p r o g r a m . A t y p i c a l connection test specimen is s h o w n i n Figure 3 . 1 . A s can be seen, the nailed connection is loaded i n single shear.  Three spiral n a i l lengths were used,  n a m e l y 65 m m (2 '/i"), 76 m m ( 3 " ) , and 102 m m ( 4 " ) as s h o w n i n Figure 3.2. Th e c o n n e c t i o n test m a t r i x is s h o w n i n Table 3 . 1 . Th e three n a i l lengths corresponded to the sheathing thickness they were connecting to, so that an appropriate embedment length, a p p r o x i m a t e l y 50 m m ( 2 " ) , i n t o the stud was left for each test.  F o u r stud materials were chosen f o r the load-slip c o n n e c t i o n testing: spruce-pine-fir N o . 2 or better (SPF), laminated veneer l u m b e r ( L V L ) , l a m i n a t e d strand l u m b e r ( L S L ) , and SPF g l u e d l a m i n a t e d l u m b e r ( g l u l a m ) . T he stud members were 38 b y 76 m m ( I - V 2 " x 3") i n cross section. T h e sheathing material corresponding to each stud consisted o f f i v e thicknesses o f Canadian s o f t w o o d p l y w o o d (CSP) and f i v e thicknesses o f oriented strandboard ( O S B ) .  Th e sheathing  material was tested b o t h parallel and perpendicular to the strong axis since sheathing i n c o m m o n c o n s t r u c t i o n practice can be installed w i t h the strong axis b e i n g either v e r t i c a l or h o r i z o n t a l . The  C o n n e c t i o n L o a d - S l i p Tests  102  Spiral nail (SPR)  O S B or CSP sheathing  SPF, L V L , L S L , or g l u l a m stud Figure 3 . 1 . T y p i c a l detail o f a nailed stud-to-sheathing connection.  results f r o m previous load-slip tests on connections w i t h nails have s h o w n that the differences between connections tested w i t h the stud strong d i r e c t i o n parallel to the direction o f loading and perpendicular to the d i r e c t i o n o f l o a d i n g are w i t h i n the m a r g i n o f error (Jenkins et. al, 1979). Furthermore, because this study is p r i m a r i l y concerned w i t h the response o f tall w o o d - f r a m e walls under axial and transversal, or out-of-plane, l o a d i n g and not r a c k i n g , the slippage between  I Figure 3.2. Spiral nail lengths used i n connection testing.  C o n n e c t i o n L o a d - S l i p Tests  103  Table 3 . 1 . C o n n e c t i o n load-slip test m a t r i x  Specimen Nail Group Length Number (mm)  Sheathing Material  Sheathing Orientation  N  Stud Specimen Nail Member Group Length Material Number (mm)  Sheathing Material  Sheathing Orientation  Stud Member Material  001  65  9.5 CSP  PAR  SPF  026  65  18.5 CSP  PAR  LSL  002  65  15.5 CSP  PAR  SPF  027  76  28.5 CSP  PAR  LSL  003  65  18.5 CSP  PAR  SPF  051  102  28.5 CSP  PAR  LSL  049  102  28.5 CSP  PAR  SPF  028  65  9.5 OSB  PAR  LSL  004  65  9.5 OSB  PAR  SPF  \ 053  65  15.5 OSB  PAR  LSL  005  65  15.5 OSB  PAR  SPF  029  65  18.5 OSB  PAR  LSL  006  65  18.5 OSB  PAR  SPF  030  76  28.5 OSB  PAR  LSL  050  102  28.5 OSB  PAR  SPF  052  102  28.5 OSB  PAR  LSL  007  65  9.5 CSP  PERP  SPF  031  65  9.5 CSP  PERP  LSL  008  65  15.5 CSP  PERP  SPF  032  65  18.5 CSP  PERP  LSL  009  65  18.5 CSP  PERP  SPF  033  76  28.5 CSP  PERP  LSL  010  65  9.5 OSB  PERP  SPF  034  65  9.5 OSB  PERP  LSL  011  65  15.5 OSB  PERP  SPF  035  65  18.5 OSB  PERP  LSL  012  65  18.5 OSB  PERP  SPF  036  76  28.5 OSB  PERP  LSL  013  65  12.5 CSP  PAR  LVL  037  65  9.5 CSP  PAR  Glulam  014  65  18.5 CSP  PAR  LVL  038  65  18.5 CSP  PAR  Glulam  015  76  28.5 CSP  PAR  LVL  039  76  28.5 CSP  PAR  Glulam  016  65  12.5 OSB  PAR  LVL  040  65  9.5 OSB  PAR  Glulam  017  65  18.5 OSB  PAR  LVL  041  65  18.5 OSB  PAR  Glulam  018  76  28.5 OSB  PAR  LVL  042  76  28.5 OSB  PAR  Glulam  019  65  12.5 CSP  PERP  LVL  043  65  9.5 CSP  PERP  Glulam  020  65  18.5 CSP  PERP  LVL  044  65  18.5 CSP  PERP  Glulam  021  76  28.5 CSP  PERP  LVL  045  76  28.5 CSP  PERP  Glulam  022  65  12.5 OSB  PERP  LVL  046  65  9.5 OSB  PERP  Glulam  023  65  18.5 OSB  PERP  LVL  047  65  18.5 OSB  PERP  Glulam  024  76  28.5 OSB  PERP  LVL  048  76  28.5 OSB  PERP  Glulam  025  65  9.5 CSP  PAR  LSL  the sheathing and the stud occurs along the stud length and n o t a r o u n d the entire panel. It is f o r these reasons that tests were not conducted w i t h the stud material strong d i r e c t i o n perpendicular to the d i r e c t i o n o f loading.  C o n n e c t i o n L o a d - S l i p Tests  104  The nailed connections were fabricated b y hand u s i n g a h a m m e r , since the nails c o u l d be m o r e accurately placed w h e n using a h a m m e r rather than a nail gun. T h e L S L studs required that the nails be h a m m e r e d into p r e - d r i l l e d holes equal to 7 0 % o f the n a i l diameter i n order t o a v o i d b e n d i n g o f the nail.  T h e Canadian W o o d D e s i g n Code, C S A 0 8 6 ( C S A , 2 0 0 1 ) , recommends  that a p r e - d r i l l e d hole be u p to 7 5 % o f the nail diameter t o a v o i d failure i n the c o n n e c t i o n w h e n p l a c i n g the n a i l .  A l l material used f o r testing was d r y a n d had been stored i n a laboratory  e n v i r o n m e n t at an average temperature o f 20° ± 3 ° C and relative h u m i d i t y o f 6 0 % ± 1 0 % f o r at least one week. T h e L S L prisms were cut f r o m larger specimens left over f r o m previous testing that h a d been stored i n the laboratory f o r at least six months.  I n accordance w i t h the testing  standard used, A S T M D 1761 ( A S T M , 1995), the specimens were tested w i t h i n one h o u r after assembly and n o t c o n d i t i o n e d i n the laboratory e n v i r o n m e n t f o r an extended p e r i o d o f t i m e t o a l l o w f o r the relaxation o f the w o o d fibres around the nails.  3.2.2 Testing Apparatus and Instrumentation A p h o t o o f the set-up is s h o w n i n Figure 3.3 and a schematic o f the test set-up f o r the load-slip connection tests is s h o w n i n Figure 3.4. Each component o f the connected specimen, the stud and the sheathing, were, a p p r o x i m a t e l y 2 5 0 m m ( 1 0 " ) i n length, w h i l e the o v e r a l l specimen length was a p p r o x i m a t e l y 4 0 0 m m ( 1 6 " ) . Each end o f the specimen was connected t o the testing apparatus b y f r i c t i o n u s i n g steel c l a m p i n g plates and bolts. T h e bolts were tightened b y hand so that the b o l t was turned one f u l l r e v o l u t i o n after the plates were snug.  T h e collars at the base  were not placed d i r e c t l y adjacent t o the c l a m p i n g plate connector so that the specimen c o u l d rotate i n t w o p r i n c i p a l directions. p r i n c i p a l direction.  T h e top o f the specimen was o n l y free to rotate i n one  Connection L o a d - S l i p Tests  105  Three data measurements were collected d u r i n g the tests: applied load; m o v e m e n t o f the actuator head (stroke); and the relative displacement o f the stud w i t h respect to the sheathing.  The  loading was u n i d i r e c t i o n a l and d o w n w a r d s , or in compression, at a rate o f 12.7 m m ( 1 " ) per m i n u t e . T w o load cells were used over the course o f the testing p r o g r a m w i t h 89 k N (20,000 lb.) and 22 k N (5,000 lb.) capacities. T h e y were attached to a 222 k N (50,000 lb.) universal testing machine that delivered the load. C o n n e c t i o n slip was measured using a displacement transducer ( D C D T ) that had a total displacement measuring range o f 76 m m ( 3 " ) .  The transducer was  connected to the stud b y w a y o f a m o u n t i n g bracket that was i n t u r n connected to the c l a m p i n g plate. A n angle bracket screwed to the sheathing p r o v i d e d a resting place for the extending end o f the transducer.  Data was acquired using F o r i n t e k ' s data acquisition software on a personal  computer and was analysed using a c o m m e r c i a l spreadsheet software package.  Figure 3.3.  Photo o f the test set-up f o r d e t e r m i n i n g the load-slip properties o f stud-tosheathing connections.  APR 1, 2004 ~FCC~C:/MY DOCUMENTS/FIGURES/LOAD-SLIP TEST.DWG DLEON  13 Z3 CD O r-t-  o' 13  o  Q CL|  I  col 03  o  m —i  > CO  o m m =3 GO O  GO  —I  <z o > m  c  "D  >  O I  TI  o  r  -  >  XI  GO  r;  o  m  00 o >  Cn —  *  rv  ?  03 m  o o  o m  Jo o  o  03  C o n n e c t i o n L o a d - S l i p Tests  3.2.3  107  Material Properties  R a n d o m samples o f each o f the tested materials were taken after testing was completed to determine  their relative  densities.  From  previously  conducted tests o n similar  material  specimens it was k n o w n that the material had a moisture content o f a p p r o x i m a t e l y 5%.  The  average relative densities o f the specimen materials are s h o w n i n Figure 3.5.  0.8  A V G + STD  0.7  AVG A V G - STD  0.6 £ 0.5 -J  a  u  0.4  £  0.3  i  0.2 4 0.1 0.0 ^  ,<?  V  ^  r£>  V  &  oP  rp  •• sy-  rfi  <y  :oP  J?  J&  rJ?  rf'^  Figure 3.5. Relative w o o d densities o f specimen materials.  Three o f the stud materials that were used (Figure 3.6) are proprietary products that w i l l be described i n greater detail.  Tembec Inc. o f V i l l e - M a r i e , Quebec, manufactured the laminated  veneer l u m b e r that was used (Figure 3.6 (a)). The trade name o f the product is S l e c T e m ® L V L and this particular product was manufactured b y l a m i n a t i n g 3.2 m m t h i c k veneers o f aspen w i t h the grain o f the veneers orientated a l o n g the length o f the member.  The layers o f veneer are  b o n d e d w i t h an exterior-type adhesive ( p h e n o l - f o r m a l d e h y d e ) and hot pressed under a specified t i m e , pressure, and temperature cycle.  Scarf j o i n t s are used to j o i n shorter pieces a l o n g the  length o f the m e m b e r and these j o i n t s are staggered between adjacent layers.  108  C o n n e c t i o n L o a d - S l i p Tests  (a)  (b)  (c)  Figure 3.6. Proprietary products used i n testing: (a) L V L , (b) L S L , (c) G l u l a m .  Trus Joist, a Weyerhaeuser business out o f Boise, Idaho manufactured the laminated strand lumber used i n testing, w h i c h has the trade name T i m b e r S t r a n d ® L S L (Figure 3.6 (b)).  This  product is manufactured b y b l e n d i n g w o o d species or species combinations oriented i n a p r e d o m i n a n t l y parallel d i r e c t i o n w i t h an isocyanate-based adhesive into f o r m e d mats o f various thicknesses. A steam i n j e c t i o n press is then used to press the mats to the required thickness.  Western A r c h r i b , based i n E d m o n t o n , A l b e r t a , manufactured the glued laminated lumber used i n testing (Figure 3.6 (c)). The trade name f o r this product is W e s t l a m ® Structural L u m b e r ( W S L ) and it is constructed o f western spruce and lodgepole pine boards.  The grain o f each 19 m m  t h i c k board is r u n n i n g m a i n l y parallel to the length o f the member. together w i t h an exterior-type phenol-resorcinol adhesive.  The boards are bonded  E n d j o i n t s w i t h i n each layer m a y be  either a finger j o i n t or a scarf j o i n t .  The b e n d i n g characteristics o f the spiral nails used were also sought i n order to predict u l t i m a t e load c a r r y i n g capacities o f the specimens tested and the corresponding failure modes. The nails were tested i n the test apparatus that is s h o w n i n Figure 3.7 a l o n g w i t h the test set-up. apparatus is based on a fastener b e n d i n g prototype developed i n the T i m b e r  The  Engineering  Laboratory o f the U n i v e r s i t y o f Karlsruhe ( E h l b e c k et. al., 1990). The fastener is placed into a  C o n n e c t i o n L o a d - S l i p Tests  109  f i x i n g device and bent d i r e c t l y b y hand and the applied loads as w e l l as the bending angle are recorded.  A description o f the nails and the average results f r o m testing are s h o w n i n Table 3.2.  Ten  replicates o f each o f the three spiral nail lengths were tested. The l o a d - d e f o r m a t i o n relationships i n bending o f each o f the replicates are s h o w n in Figure 3.8 a l o n g w i t h the failure modes o f the 102 m m l o n g nails tested.  M o s t o f the nails had to be bent back to their starting position and  thus do not s h o w a significant bend.  There are several definitions o f y i e l d m o m e n t depending  upon w h i c h standard is b e i n g referenced. A s w i l l be described later i n this chapter, the m e t h o d presented i n Eurocode 5 was used to characterize the load-slip response o f the connections tested ( E N V 1 9 9 5 - 1 - 1 , 1993). For this m e t h o d , y i e l d m o m e n t o f a nail is d e f i n e d as the smaller value o f the m a x i m u m b e n d i n g m o m e n t and the m o m e n t at a d e f o r m a t i o n o f 45 degrees. This is h o w the y i e l d m o m e n t values i n Table 3.2 were determined.  The Eurocode 5 m e t h o d o l o g y is less  conservative than the m e t h o d e m p l o y e d i n the U n i t e d States, w h i c h uses a 5 % diameter offset f r o m the i n i t i a l stiffness to determine y i e l d strength, but it contains a large adjustment factor to account f o r the v a r i a b i l i t y .  (a)  (b)  Figure 3.7. Fastener b e n d i n g (a) test apparatus and (b) test set-up.  Connection Load-Slip Tests  110  Table 3.2. Average nail bending properties obtained from testing. Specimen Group Number  Nail Nail Number of Length Diameter Specimens (mm) (mm)  601 602 603  10 10 10  65 76 102  2.46 2.99 3.27  Yield Coefficient Moment of Variation of Nail (%) (Nmm)  2437 4257 5666  6.18 5.32 1.79  45  60  Calculated Yield Stress (MPa)  982 955 972  Design Yield Overstrength Moment (Test/Design) (Eurocode 5)  1869 3105 3918  1.30 1.37 1.45  "§ 1600 09 800 0  15  30 Rotation (degrees)  (a)  (b)  Figure 3.8. (a) Load-deformation curves and (b) failure modes of spiral nails in bending. The yield stress in Table 3.2 was calculated using the plastic section modulus and is given by the following equation: 6-M„  (3.1)  where d is the diameter of the nail. The characteristic yield moment in Table 3.2, as defined in Eurocode 5, is as follows: M  =180d . 26  (3.2)  111  C o n n e c t i o n L o a d - S l i p Tests  3.3  RESULTS AND  DISCUSSION  A s m e n t i o n e d p r e v i o u s l y , the purpose o f c o n d u c t i n g numerous load-slip connection tests was to b u i l d a database o f values i n order to interpret component and full-scale tests that were conducted later i n this study.  Therefore this section w i l l not closely examine each and every  connection group tested. Plots o f all load-slip tests conducted are p r o v i d e d in A p p e n d i x A .  This  section w i l l , however, p r o v i d e results and illustrate general trends that were observed.  3.3.1  A  Connection Properties  t y p i c a l l o a d - d e f o r m a t i o n curve obtained f r o m m o n o t o n i c compression tests on the nail  connections is presented i n Figure 3.9.  Included i n the figure are the average value o f the  replicates tested, the average value plus and m i n u s the standard deviation o f the replicates, and the coefficient o f v a r i a t i o n o f the replicates o f one test group.  I f the coefficient o f v a r i a t i o n  obtained was higher than a reasonable value f o r this type o f testing ( i n this case assumed at a p p r o x i m a t e l y 30 %) then additional replicates were tested so that the coefficient o f v a r i a t i o n  Displacement ( m m ) Figure 3.9. T y p i c a l c o n n e c t i o n load-slip results.  C o n n e c t i o n L o a d - S l i p Tests  112  c o u l d be reduced. T h i s was o n l y necessary f o r one test group ( 0 2 3 ) . I n general, the coefficient o f v a r i a t i o n was b e l o w 2 0 % .  It was also f o u n d to increase w i t h decreasing n a i l embedment  length. This w i l l be discussed further i n the next chapter on n a i l w i t h d r a w a l testing.  A v e r a g e properties such as i n i t i a l stiffness, u l t i m a t e load, y i e l d load, ultimate displacement, and overstrength determined f r o m each test group are presented i n Table 3.3.  The m o s t i m p o r t a n t  004 005 006 050 007 008 009 010 011 012 013 014 015 016 017 018 019 020 021 022 023 024 025  y  4.04  1.111  18.40  24.20  224  5.99  15.5  0.714  3.48  1.270  27.00  30.50  225  8.76  2.75  18.5  0.619  1.64  1.238  19.40  28.00  389  17.07  2.45  28.5  1.307  2.64  2.477  22.20  33.00  526  12.50  2.62  9.5  0.745  2.10  1.403  15.00  24.40  361  11.62  2.96  15.5  0.672  2.30  1.270  19.00  30.50  300  13.26  2.30  18.5  0.601  1.72  1.169  20.60  31.00  369  18.02  2.02  28.5  1.166  1.30  2.530  19.40  31.50  954  24.23  2.56  9.5  0.643  3.14  1.165  14.60  18.40  232  5.86  2.85  15.5  0.545  2.70  1.063  18.60  33.00  229  12.22  2.30  18.5  0.578  2.72  1.108  21.80  35.00  235  12.87  2.19  9.5  0.686  2.62  1.165  12.10  23.60  287  9.01  2.45  15.5  0.623  1.48  1.248  16.40  26.00  475  17.57  2.26  18.5  0.526  1.06  1.044  15.80  26.00  567  24.53  1.80  12.5  0.732  4.42  1.232  19.60  , 25.00  195  5.66  2.60  18.5  0.841  5.40  1.557  30.50  35.50  171  6.57  3.05  28.5  1.023  2.48  2.123  16.60  37.50  448  15.12  2.64  12.5  0.673  2.40  1.259  18.80  36.50  303  15.21  2.38  18.5  0.672  3.18  1.395  25.50  37.00  229  11.64  2.37  28.5  0.836  1.30  1.890  24.00  37.50  616  28.85  2.24  12.5  0.808  4.74  1.441  20.80  35.00  194  7.38  3.04  i .5 x  * e  1* ca  m  _  F ax  0  (mm)  0.781  ca  Displacement at  9.5  > r O fe, 2.71  y  Initial Stiffness (N/mm)  049  Ultimate Displacement A u (mm)  003  Yield Displacement A (mm)  002  SPF 5 SPF SPF 5 SPF 5 5 SPF SPF 5 6 SPF 5 SPF SPF 5 5 SPF 5 SPF SPF 5 SPF 6 SPF 5 LVL 5 5 LVL 5 LVL 6 LVL 5 LVL 5 LVL 5 LVL 5 . LVL 5 LVL 6 LVL LVL 6 5 LVL 5 LSL  Yield Load F (kN)  5  -a  Sheathing Thickness (mm)  Number of Specimens  001  Stud Member Material  Specimen Group Number  Table 3.3. A v e r a g e connection properties obtained f r o m tests. -£ ^  ab •=?  Is  1 £ JU  x «  E  18.5  0.837  5.50  1.550  27.00  37.50  174  6.82  3.04  28.5  1.167  3.00  2.492  24.80  38.00  439  12.67  3.10  12.5  0.718  2.44  1.383  27.50  38.00  293  15.57  2.61  18.5  0.651  2.06  1.415  22.80  34.50  332  16.75  2.41  28.5  0.937  1.54  2.155  29.50  41.50  564  26.95  2.56  9.5  0.651  3.00  1.177  15.20  17.40  .233  5.80  2.62  C o n n e c t i o n L o a d - S l i p Tests  113  Ultimate Displacement A (mm)  Initial Stiffness (N/mm)  2.94  1.427  17.60  22.00  264  7.48  2.61  5  28.5  1.557  3.06  3.324  21.80  30.00  556  9.80  3.75  051  5  LSL  28.5  1.670  3.14  3.597  24.40  34.50  557  10.99  3.41  028  5  LSL  9.5  0.863  2.08  1.768  15.00  17.80  437  8.56  3.35  053  6  LSL  15.5  0.890  2.22  1.773  13.80  22.80  419  10.27  2.93  029  5  LSL  18.5  0.766  1.30  1.739  14.70  21.60  579  16.62  2.66  030  5  LSL  28.5  1.379  1.64  3.064  17.40  25.50  869  15.55  3.26  5  LSL  28.5  1.294  1.26  2.782  14.10  21.40  1076  16.98  2.49  031  5  LSL  9.5  0.698  1.88  1.399  10.40  13.20  436  7.02  3.11  032  5  LSL  18.5  0.977  4.74  1.685  15.80  23.80  254  5.02  3.09  033  5  LSL  28.5  1.508  2.84  3.314  21.40  29.50  578  10.39  3.74  034  5  LSL  9.5  0.855  2.22  1.558  11.40  15.60  411  7.03  2.95  035  5  LSL  18.5  0.855  1.62  1.945  18.00  22.40  522  13.83  2.97  036  5  LSL  28.5  1.404  1.44  3.114  16.00  24.40  1036  16.94  3.31  037  5  GLU  9.5  0.626  1.76  1.127  22.60  25.50  358  14.49  2.73  038  5  GLU  18.5  0.704  2.78  1.445  22.00  27.50  268  9.89  2.83  039  5  GLU  28.5  0.956  1.66  2.098  20.60  39.00  591  23.49  2.62  040  5  GLU  9.5  0.615  1.82  1.221  16.20  28.50  367  15.66  2.55  5  GLU  18.5  0.604  1.14  1.329  19.20  34.50  491  30.26  2.26  5  GLU  28.5  0.860  1.70  1.836  19.40  39.00  531  22.94  2.18  043  5  GLU  9.5  0.713  2.02  1.392  14.30  21.00  377  10.40  3.37  044  5  GLU  18.5  0.624  1.80  1.365  19.20  34.50  359  19.17  2.68  045  5  GLU  28.5  0.901  1.48  1.985  18.20  38.00  625  25.68  2.47  046  5  GLU  9.5  0.773  3.56  1.403  18.20  23.60  228  6.63  2.92  047  5  GLU  18.5  0.588  0.86  1.357  23.00  34.50  690  40.12  2.31  048  5  GLU  28.5  0.903  1.58  1.926  17.80  34.00  618  21.52  2.29  027  052  041 042  Fmax  m  F ax  u  Yield Displacement A (mm)  0.759  (mm)  Yield Load F (kN)  18.5  LSL  y  Displacement at  Sheathing Thickness (mm)  LSL  (kN)  Stud Member Material  5  Maximum Load  Number of Specimens  026  y  Specimen Group Number  Table 3.3 C o n t i n u e d . A v e r a g e connection properties obtained f r o m tests.  2 ^  id  •£ M  ""e  -1?  I £ S i o t,  parameter obtained f r o m the test data is the i n i t i a l stiffness because the displacements between the sheathing and the studs along the height o f the studs i n tall w a l l s are r e l a t i v e l y s m a l l .  The  procedure described i n the European C E N p r o t o c o l ( C E N , 1995) was used to calculate the properties g i v e n i n Table 3.3. The load-slip relationship developed b y Foschi (Foschi, 1974) has been used to m o r e accurately m o d e l the c o n n e c t i o n behaviour using f i n i t e element analysis in  C o n n e c t i o n L o a d - S l i p Tests  114  subsequent chapters, but it does not a l l o w f o r easy c o m p a r i s o n between test results.  Thus the  C E N p r o t o c o l has been used f o r such a c o m p a r i s o n o f the test results. Figure 2.30 i n Section 2.7 presented a t y p i c a l l o a d - d e f o r m a t i o n curve w i t h the parameters d e f i n e d b y the C E N procedure.  The C E N procedure defines i n i t i a l stiffness as the slope o f the line that connects points o n the load-slip curve at 0.1 F  m a x  and 0.4 F  m a x  respectively. T h e y i e l d load is the load o n the curve that  corresponds to the y i e l d displacement, w h i c h is d e f i n e d as the displacement at the interception o f the i n i t i a l stiffness line and a tangent line w i t h stiffness equal to 1/6 o f the i n i t i a l one.  The  ultimate displacement corresponds to the displacement at w h i c h the load drops to 8 0 % o f the m a x i m u m load. T h e overstrength factor is a ratio o f the m a x i m u m load to the design load. The procedure set out i n Eurocode 5, based u p o n a theory developed b y Johansen f o r j o i n t s made w i t h d o w e l - t y p e fasteners i n single shear, was used to calculate the design load.  The m e m b e r  density values and n a i l b e n d i n g strengths described p r e v i o u s l y were used i n these calculations. The Canadian W o o d D e s i g n Code was not used because it does not contain a procedure f o r d e t e r m i n i n g the resistance o f nailed connections using proprietary products.  A s can be seen i n  Table 3.3, the overstrength factor is quite variable, r a n g i n g f r o m 1.80 to 3.75.  T h i s large  v a r i a t i o n i n results m a y be due to the fact that Eurocode 5 o n l y gives one set o f equations f o r the characteristic embedment strength o f the stud material based u p o n testing conducted o n sawn lumber. Engineered l u m b e r behaves d i f f e r e n t l y than sawn l u m b e r i n m a n y applications and m a y require alternative a p p r o x i m a t i o n s f o r this material property.  A d d i t i o n a l l y , Johansen's y i e l d  m o d e l does not include p u l l o u t or p u l l - t h r o u g h failures, w h i c h were the most c o m m o n modes o f failure observed and w i l l be discussed i n detail later i n this chapter.  Several different comparisons are made between load-slip tests i n Figure 3.10. W h i l e not every load-slip curve is s h o w n , the ones that are s h o w n p r o v i d e insight into general trends that have been observed.  T h e numbers i n brackets refer to the specimen group number.  The terms SPR  C o n n e c t i o n L o a d - S l i p Tests  115  2.0 ,  2.0  18.5 mm O S B P A R SPR-65 mm L S L (029)  .6  L V L (017)  L V L (014) ^ - G l u l a m (038)  Z  1  -  2  •a  Jo.8  -j  0.4  0.0 0  5  10  15  20  25  30  35  0  40  5  10  (a) 18.5 m m CSP sheathing 2  20  25  30  35  40  (b) 18.5 m m O S B sheathing  SPF C S P P A R / "  2.4 -  15  Displacement (mm)  Displacement (mm)  28.5 mm (049) SPR-I02mm  SPFOSB PAR  28.5 mm (050) "SPR-102 mm  2.4  2.0 9.5 mm (004)  15.5 mm (005)  il.6  10  15  20  25  30  35  40  Displacement (mm)  (c) CSP sheathing w i t h SPF studs  10  15  20  25  30  35  40  Displacement (mm)  (d) O S B sheathing w i t h SPF studs  40  (e) CSP sheathing w i t h L S L studs Figure 3.10. L o a d - s l i p curves f r o m testing.  ( f ) O S B sheathing w i t h L S L studs  C o n n e c t i o n L o a d - S l i p Tests  116  and P A R refer to spiral nail length and parallel sheathing orientation, respectively.  The  sheathing thickness is s h o w n either at the top o f the graphs or before the specimen group number.  I n Figure 3.10 (a) the difference between the f o u r stud materials tested f o r this  particular sheathing thickness is v e r y m i n i m a l . This can b y explained be e x a m i n i n g the relative density values o f the stud materials and that o f the 18.5 m m CSP sheathing g i v e n i n Figure 3.5. The relative density o f the sheathing is, i n this case, less than the stud materials so the strength o f the connection is governed b y the embedment strength o f the sheathing alone. T h i s is contrasted w i t h Figure 3.10 (b) where the relative density o f the 18.5 m m O S B sheathing is larger than all o f the stud materials except the L S L .  The strength is once again related to the component w i t h  the weakest relative density, i n this case the studs, w h i c h results i n the load-slip response o f each o f these test groups b e i n g m o r e v a r i e d than Figure 3.10 (a) because the relative density o f the studs are varied.  It is clear f r o m Figures 3.10 (c) and (d) that the strength o f these particular connections is d i r e c t l y related to the w i t h d r a w a l strength o f the nail i n the stud member.  The relative densities  o f the CSP sheathing and the O S B sheathings are quite different but the average stiffnesses and m a x i m u m loads achieved i n the connections are a p p r o x i m a t e l y the same.  The mode o f failure  that occurred i n these connections is characterized b y the nail p u l l i n g out f r o m the stud.  The  load-slip response is entirely due to the nail length irrespective o f the sheathing type and thickness.  T h i s pattern d i d not emerge i n the load-displacement responses o f the connections  s h o w n i n Figures 3.10 (a) and (b) because the sheathing d i d not consistently have a higher relative density compared w i t h the stud material.  It is m o r e d i f f i c u l t to p i n p o i n t the failure m o d e o f the curves i n Figures 3.10 (e) and ( f ) because, as w i l l be s h o w n i n the next chapter, the w i t h d r a w a l strength o f L S L is v e r y h i g h . It is clear that the relative density o f the O S B sheathing is s u f f i c i e n t l y large enough that the responses o f the  C o n n e c t i o n L o a d - S l i p Tests  117  connections i n Figure 3.10 ( f ) w i t h 65 m m spiral nails are due to the nail and the stud m e m b e r o n l y because the average stiffnesses a n d m a x i m u m loads achieved b y the connections w i t h three different O S B thicknesses are a p p r o x i m a t e l y the same.  T h i s is i n contrast to the connections  w i t h 65 m m spiral nails i n Figure 3.10 (e) where the response is governed b y the sheathing, as the relative density o f the C S P is quite l o w compared t o the L S L stud material. stiffness and strength o f the c o n n e c t i o n w i t h  T h e average  18.5 m m CSP sheathing is higher than the  connection w i t h 9.5 m m C S P sheathing due to the mode o f failure b e i n g concentrated i n the w e a k sheathing component.  T w o distinct modes o f failure are evident f r o m the curves o f the load-slip response o f 102 m m spiral nails w i t h the L S L stud material w i t h C S P and O S B sheathing.  W h i l e the w i t h d r a w a l  strength o f b o t h o f these connections should be a p p r o x i m a t e l y equivalent and quite large, the connection w i t h the CSP sheathing p r o d u c e d a larger m a x i m u m load. T h i s is due t o the fact that O S B sheathing, because o f the structure o f the material, is more l i k e l y to have the nail p u l l t h r o u g h the sheathing as the m o d e o f failure. I n a d d i t i o n , the connection w i t h O S B sheathing, an L S L stud, and a 102 m m l o n g spiral n a i l was weaker than the same c o n n e c t i o n w i t h a 76 m m l o n g spiral nail (Figure 3.10 ( f ) ) . T h e longer n a i l h a d a higher w i t h d r a w a l resistance than the shorter one and the sheathing p u l l e d t h r o u g h at a l o w e r lateral load.  T h i s p u l l - t h r o u g h failure  w i l l also be described i n m o r e detail later i n this chapter.  3.3.2 Effect of Sheathing Orientation A s m e n t i o n e d i n this chapter, it has been s h o w n i n previous testing that there is v e r y little difference i n the l o a d - d e f o r m a t i o n characteristics o f nailed sheathing-to-stud connections h a v i n g the stud length parallel o r perpendicular t o the d i r e c t i o n o f l o a d i n g . T h e test results presented i n Figures 3.11 (a) to (d) show the difference b e t w e e n the responses o f n a i l e d connections w i t h  C o n n e c t i o n L o a d - S l i p Tests  118  different sheathing orientation, as sheathing can be placed in both the vertical and h o r i z o n t a l direction w h e n constructing w a l l s .  A s can be seen f r o m the figure, there is v e r y little difference i n the connection properties o f sheathing orientated i n the strong d i r e c t i o n versus the weak, or perpendicular, d i r e c t i o n o f loading.  A n y difference that is observable is certainly w i t h i n the coefficient o f variation f o r  Displacement (mm)  (a) CSP sheathing w i t h SPF studs  Displacement (mm)  (c) CSP sheathing w i t h L S L studs  Displacement (mm)  ( b ) O S B sheathing w i t h SPF studs  Displacement (mm)  ( d ) O S B sheathing w i t h L S L studs  Figure 3 . 1 1 . L o a d - s l i p curves w i t h sheathing parallel and perpendicular.  C o n n e c t i o n L o a d - S l i p Tests  these tests.  119  T h i s m a y be due to the modes o f failure that were described previously.  I f the  connection f a i l e d due to w i t h d r a w a l o f the nail f r o m the stud, or p u l l - t h r o u g h o f the nail t h r o u g h the sheathing, then a change in the sheathing orientation w o u l d not produce different results.  3.3.3  Failure Modes  T w o distinct failure modes d o m i n a t e d the c o n n e c t i o n tests i n this study: p u l l o u t and p u l l through.  These t w o failure modes are s h o w n i n Figures 3.12 and 3.13 respectively.  involves the sheathing and the nail p u l l i n g out f r o m the stud.  Pullout  This mode o f failure is thus  d i r e c t l y related to the w i t h d r a w a l characteristics o f the n a i l , w h i c h is the focus o f the next chapter.  P u l l - t h r o u g h occurs w h e n the head o f the nail pulls through the sheathing, leaving  b e h i n d the stud and the n a i l .  A s m e n t i o n e d p r e v i o u s l y , the analytical m e t h o d e m p l o y e d to predict the strength o f the connections does not include these t w o failure modes. Johansen's y i e l d m o d e l predicts t w o other modes o f failure f o r all o f the connections that were modeled. T h e y were: the f o r m a t i o n o f one plastic hinge i n the nail in the stud, and the f o r m a t i o n o f t w o plastic hinges i n the nail i n both the  Figure 3.12. P u l l o u t failure mode.  C o n n e c t i o n L o a d - S l i p Tests  120  Figure 3.13. P u l l - t h r o u g h the sheathing failure mode.  stud and the sheathing material.  M o s t o f the connections tested l i k e l y achieved one o f the  predicted failure modes p r i o r to a p u l l o u t or p u l l - t h r o u g h failure. I n real structures the sheathing is somewhat restrained f r o m l i f t i n g o f f f r o m the stud b y the large n u m b e r o f nails that attach it to the stud member.  This means that p u l l o u t and p u l l - t h r o u g h failures due to w i n d loading w o u l d  be far less l i k e l y i n actual structures than were f o u n d i n this test p r o g r a m . A connection test w i t h restrained sheathing w o u l d not l i k e l y result i n increased stiffness and m a x i m u m strength but w o u l d have a m u c h more pronounced load plateau than was f o u n d in the unrestrained tests that were conducted.  3.4  SUMMARY  The results o f load-slip nail connection tests clearly demonstrate that h a v i n g a connection w i t h a high-strength component does not necessarily mean that the connection w i l l become stronger. The mode o f failure w i l l usually f i n d the weakest component o f the system and so further increase o f the strength o f a stronger c o m p o n e n t i n the connection does little to increase the overall strength o f the connection. That said, h o w e v e r , the strength o f a connection was s h o w n  C o n n e c t i o n L o a d - S l i p Tests  121  to increase s i g n i f i c a n t l y w h e n the failure m o d e was located i n a denser stud or sheathing component or w h e n c h a n g i n g a c o m p o n e n t m o v e d the mode o f failure to the other, stronger component i n the connection. T h i s increase is demonstrated most d r a m a t i c a l l y w h e n c o m p a r i n g specimens 012 and 035 where the o n l y difference between these t w o connections is the stud material. Specimen 035 w i t h an L S L stud was f o u n d to have an average m a x i m u m load that was 8 6 % greater than specimen 012 w i t h an SPF stud.  O v e r a l l , connections w i t h L S L studs p r o v e d to be stronger o n average than connections w i t h the other stud materials as the L S L studs are m u c h denser.  Connections w i t h the other three stud  materials gave s i m i l a r results, as the densities o f these studs are s i m i l a r even t h o u g h the m a n u f a c t u r i n g process used to make t h e m is not. The i n i t i a l stiffness o f the connections, w h i c h w i l l prove to be an i m p o r t a n t parameter w i t h respect to partial composite action i n subsequent chapters, v a r i e d s i g n i f i c a n t l y between c o n n e c t i o n specimens.  Connections consisting o f L S L  studs w i t h O S B sheathing gave the highest values f o r i n i t i a l stiffness.  N a i l W i t h d r a w a l Tests  122  4. NAIL WITHDRAWAL TESTS L i k e the c o n n e c t i o n load-slip tests, the results f r o m n a i l w i t h d r a w a l tests are needed i n order to develop a m o r e comprehensive  m o d e l o f the b e h a v i o u r  o f tall wood-frame  walls.  Nail  w i t h d r a w a l resistances are required w h e n a n a l y z i n g a w a l l under suction l o a d i n g but, as m e n t i o n e d i n the previous chapter, they also relate closely w i t h the resistances o f laterally loaded connections, as w i t h d r a w a l o f the n a i l is a m o d e o f failure.  T h i s chapter w i l l present the findings f r o m m o n o t o n i c tests to determine the w i t h d r a w a l response o f the connection specimens presented in the previous chapter.  The w i t h d r a w a l test i t s e l f is  rather simple i n nature and the n u m b e r o f test specimens is greatly reduced f r o m the previous chapter as there are o n l y t w o parameters to consider: the stud and the n a i l .  4.1  OBJECTIVES AND SCOPE  W i n d l o a d i n g m a y act i n b o t h directions perpendicular to the face o f the w a l l s o f a b u i l d i n g . the load is acting a w a y f r o m the b u i l d i n g then suction w i l l occur o n the face o f the w a l l .  If  Under  this scenario the load must be transferred f r o m the sheathing to the studs t h r o u g h the nails i n tension, or w i t h d r a w a l f r o m the studs. This part o f the experimental p r o g r a m takes a l o o k at the response  o f nails  and studs t y p i c a l l y  found  in tall wood-frame  wall  construction  under  w i t h d r a w a l l o a d i n g . T h i s i n f o r m a t i o n is also valuable w h e n a n a l y z i n g the response o f laterally loaded nailed connections, as one possible failure mode o f this type o f c o n n e c t i o n is w i t h d r a w a l o f the n a i l and sheathing f r o m the stud.  Displacement controlled monotonic  tests were  conducted o n a small n u m b e r o f specimens w i t h different stud material and n a i l sizes.  The  m o n o t o n i c w i t h d r a w a l tests were conducted i n the W o o d E n g i n e e r i n g L a b o r a t o r y o f F o r i n t e k Canada C o r p . i n V a n c o u v e r .  N a i l W i t h d r a w a l Tests  123  4.2 METHODS AND MATERIALS 4.2.1 Withdrawal Specimens The same combinations o f studs and nails that were presented f o r the connections i n the previous chapter  were  tested under  withdrawal  loading.  This  is  representative  of  the  possible  combinations o f nails and stud types that are, or c o u l d be, used in tall w o o d - f r a m e  wall  construction. The average nail properties are once again o f greater importance than the tail end o f the d i s t r i b u t i o n curves because o f the large n u m b e r o f nails e m p l o y e d i n c o n n e c t i n g the sheathing to the studs i n w a l l construction.  The n u m b e r o f replicates for each specimen group  was increased to seven f r o m the f i v e tested f o r the laterally loaded connections  because  w i t h d r a w a l has a m u c h w i d e r scatter o f results. The v a r i a t i o n o f results w i t h i n each group was quantified and additional replicates were tested i f it was deemed that the v a r i a t i o n was too h i g h based on the results o f previous tests o f this type.  The same three nail types and f o u r stud materials described i n the previous chapter were tested under w i t h d r a w a l loading.  A t y p i c a l specimen is s h o w n i n Figure 4.1 and the w i t h d r a w a l test  Spiral nail  SPF, L V L , L S L , or g l u l a m stud  Figure 4 . 1 . T y p i c a l details o f a nailed connection prepared f o r w i t h d r a w a l testing.  N a i l W i t h d r a w a l Tests  124  m a t r i x is s h o w n i n Table 4 . 1 . T h e embedment lengths s h o w n i n the table correspond to the depth the nails were d r i v e n into the studs. These lengths were chosen after o b t a i n i n g the depth o f embedment f o r each n a i l i n the load-slip connection tests and c a l c u l a t i n g an average f o r the combinations o f nails and studs s h o w n i n the m a t r i x . Table 4 . 1 . N a i l w i t h d r a w a l c o n n e c t i o n test m a t r i x Specimen Nail Group Length Number (mm)  ,  Sheathing Material  Embedment Length (mm)  101  65  SPF  49.5  108  102  SPF  76.5  102  65  LVL  49.5  103  76  LVL  62.2  104  65  LSL  49.5  105  76  LSL  50.5  109  102  LSL  62.2  106  65  Glulam  49.5  107  76  Glulam  50.5  The connections were fabricated b y hand u s i n g a hammer.  Once again the L S L studs required  that the nails be h a m m e r e d into p r e - d r i l l e d holes equal t o 7 0 % o f the nail diameter i n order to a v o i d b e n d i n g o f ' t h e n a i l . I n a l l cases, studs that were used i n the load-slip c o n n e c t i o n tests were re-used f o r the w i t h d r a w a l tests. I n accordance w i t h the standard used, A S T M D 1761 ( A S T M , 1995), the specimens were tested w i t h i n one h o u r after assembly and not c o n d i t i o n e d i n the laboratory environment.  4.2.2 Testing Apparatus and Instrumentation A p h o t o o f the test set-up is s h o w n i n Figure 4.2 and a schematic o f the test set-up f o r the n a i l w i t h d r a w a l tests is s h o w n i n Figure 4.3. Each end o f the stud was connected to the testing apparatus u s i n g steel c l a m p i n g angles a n d bolts.  T h e bolts were tightened b y hand so that the  N a i l W i t h d r a w a l Tests  125  angles were snug. T h e stud was not free to rotate or displace in any direction and the nail was l i n e d up to be w i t h d r a w n in a purely vertical direction.  Figure 4.2.  Photo o f the test set-up for d e t e r m i n i n g the w i t h d r a w a l characteristics o f nails.  Three data measurements were collected d u r i n g the tests: applied load; m o v e m e n t o f the actuator head (stroke); and the relative displacement between the head o f the nail and the stud. l o a d i n g was u n i d i r e c t i o n a l and upwards, or i n tension, at a rate o f 12.7 m m ( 1 " ) per m i n u t e .  The A  4.5 k N (1000 lb.) load cell was attached to the 89 k N (20,000 lb.) universal testing machine that delivered the load. The nail w i t h d r a w a l was measured u s i n g a displacement transducer ( D C D T ) that had a displacement measuring range o f 76 m m ( 3 " ) .  The transducer was connected to the  bracket h o l d i n g the nail head, w h i c h was r i g i d l y connected to the load cell, and rested on the top o f the stud. Data was acquired using F o r i n t e k ' s data acquisition software on a personal computer and was analyzed u s i n g a c o m m e r c i a l spreadsheet software package.  APR 7, 2004 ~FCC~C:/MY DOCUMENTS/FIGURES/WITHDRAWAL TEST.DWG DLEON  Q_  Q 3E  CD w  o m —i >  cn  O CD S  -<  > z 2  O ° ^ o Xl —I m x o o m  ^> °?  -n O -X) o o TJ  li -s  CD  o  >  >  o  00 CD  0  XI  m  cn  CO  o m =! co o m  Si >  — O  o m  CO —I X) CZ  o  I— r-  > r~  s^ X) I > z  o  oo o >  cn  2  1 o  CD  cn  m  —I >  I  I  s F =) t d—'  n  r>  — ! : : • " ! : L  F  =)  1J  ,  '  J  I  O O  o  tog o. • I  o  ro  N a i l W i t h d r a w a l Tests  4.2.3  127  Material Properties  The same stud specimens and the same nail types f r o m the load-slip connection tests were used for the nail w i t h d r a w a l tests.  Therefore the results f r o m the material tests from the load-slip  connection tests are v a l i d for the w i t h d r a w a l testing as w e l l .  T h i s data can be f o u n d i n Figure  3.5. The properties o f the spiral nails used i n the w i t h d r a w a l tests can be f o u n d i n Table 3.2 and Figure 3.8 (a).  4.3  4.3.1  RESULTS A N D DISCUSSION  Connection Properties  A t y p i c a l load-displacement curve obtained f r o m a m o n o t o n i c w i t h d r a w a l test is presented i n Figure 4.4. Included in the figure are the average curve o f the replicates tested, the average plus and m i n u s one standard d e v i a t i o n curves o f the replicates, and the coefficient o f variation curve. I f the coefficient o f v a r i a t i o n was higher than a reasonable value for this type o f testing, i n this case a p p r o x i m a t e l y 4 0 % , then additional replicates were tested to determine i f the coefficient o f  Test Group 109  40% - A V G +STD -AVG - A V G -STD  e 30% •£ a °E  P Replicates  ea  > 20% ©  a  _o "u  £ 10% 0% 10  15  20  25  30  Displacement (mm)  Figure 4.4. T y p i c a l w i t h d r a w a l connection results.  35  40  « U  N a i l W i t h d r a w a l Tests  128  v a r i a t i o n c o u l d be reduced. v a r i a t i o n (101).  O n l y one test group was re-tested to reduce the coefficient o f  I n general, the coefficient o f v a r i a t i o n was around 2 5 % and was f o u n d to  increase w i t h decreasing nail penetration length.  Because a larger penetration length results i n  the surface area o f the nail c o m i n g i n contact w i t h a greater p r o p o r t i o n o f the cross section o f the stud the results o f the w i t h d r a w a l test are more l i k e l y to reflect that o f the average properties o f the stud material and thus give similar results between replicates.  R e d u c i n g the penetration  length increases the chances o f a defect i n the stud negatively i m p a c t i n g the test results and thus increasing the v a r i a b i l i t y between tests.  Properties  such as i n i t i a l  stiffness, ultimate  load, y i e l d  load, u l t i m a t e  displacement,  and  overstrength were d e t e r m i n e d f r o m each test group and are presented i n Table 4.2. Once again, the procedure described i n the European C E N p r o t o c o l ( C E N , 1995) was used to calculate the properties g i v e n i n Table 4.2. described i n Section 3 . 3 . 1 .  This procedure has been s h o w n g r a p h i c a l l y i n Section 2.7 and  T h e overstrength factor is a ratio o f the m a x i m u m load to the  factored design load, w h i c h is based u p o n the procedure set out i n Eurocode 5 ( E N V 1 9 9 5 - 1 - 1 ,  Table 4.2. A v e r a g e connection properties obtained f r o m tests.  0.437  0.36  0.694  108  7  1.273  0.60  1.864  5.10  102  7  0.527  0.42  0.762  3.18  103  7  1.307  0.62  1.806  3.34  11.00  2681  17.74  3.04  104  9  0.879  0.52  1.417  4.30  8.10  2184  15.58  1.58  105  10  1.722  0.96  2.170  4.54  10.70  2054  11.15  2.11  109  9  1.705  0.62  2.296  3.78  14.00  3885  22.58  1.30  106  7  0.409  0.50  0.694  5.40  12.80  1280  25.60  1.66  107  7  0.979  0.60  1.417  4.10  7.50  1806  12.50  2.97  „  3  „  .1  1  X P- •  C3  5 E B B  £ 1 9eft  11.60  1642  32.22  1.80  14.20  2802  23.67  2.01  13.20  1806  31.43  1.80  u  Yield Displacement A (mm)  y  Yield Load F (kN)  O  Initial Stiffness (N/mm)  7  C3  Ultimate Displacement A (mm)  Number of Specimens  101  5 3.22  y  Specimen Group Number  -a  P-  ^  .  B<  ad  •£ M  -5?  1£ •~-  X  <u « > r o &, E  N a i l W i t h d r a w a l Tests  129  1993). The factored resistance o f an a x i a l l y loaded nail was g i v e n i n Eurocode 5 as: f dl  f o r all nails  l d  min  k mod,i  f  f  2  d  d  i,k  (4.1)  f o r threaded nails  2  (4.2)  ,i = l,2  f l,k  (l8xl0- )p  f. 2,k  (300xl0" )p^  6  (4.3)  2  (4.4)  6  I n the previous f o r m u l a t i o n , the symbols are d e f i n e d as f o l l o w s : fj  k  and fj  d  = specified and factored characteristic strength  d = n a i l diameter 1 = p o i n t side penetration length p  k  = mass density  k  m o d  y  M  ; = l o a d - d u r a t i o n factor (0.9 f o r short-term loading) = material properties factor (1.3 f o r wood-based materials)  The overstrength factor is quite variable r a n g i n g f r o m 1.30 to 3.04.  T h i s large v a r i a t i o n i n  results m a y again be due to the fact that Eurocode 5 o n l y gives one set o f equations for the characteristic penetration strength o f the stud material based u p o n testing conducted o n sawn lumber.  The overstrength factors f o r the t w o groups tested w i t h sawn lumber, groups 101 and  108, have s i m i l a r values o f 1.80 and 2.01 respectively.  A l l the average load-displacement curves f r o m the nine groups tested are presented i n Figure 4.5. The numbers i n brackets refer to the specimen group number.  The terms SPR and P E N refer to  spiral nail length and nail penetration length, respectively. The curves i n Figure 4.5 (a) s h o w the results o f tests w i t h the same n a i l type and penetration length b u t w i t h d i f f e r e n t stud materials.  N a i l W i t h d r a w a l Tests  130  The three stud materials w i t h similar relative densities have similar responses w h i l e the L S L stud, w h i c h has a m u c h higher relative density, has a m u c h higher w i t h d r a w a l strength. This is s h o w n again i n Figure 4.5 ( b ) and (c) f o r the 76 m m and 102 m m spiral nails, although the penetration lengths are not the same f o r a l l o f the groups.  Finally, Figure 4.5 ( d ) shows that  increasing penetration length f o r spiral nails w i t h L S L studs increases the m a x i m u m  load  attained i n w i t h d r a w a l to a greater extent than increasing nail diameter. Because the L S L is v e r y stiff, even a small increase i n penetration length w i l l have an effect o n the w i t h d r a w a l strength.  2.4 SPR-76 mm 2.0  L V L (103) "~62.2 P E N  1.6 , \  0.8  L S L (105)  \K~  1.2  50.5 PEN  Glulam (107)  J 50.5  PEN  0.4 0.0 10  15  20  25  35  30  40  10  Displacement (mm)  15  20  25  30  35  40  35  40  Displacement (mm)  (a) 65 m m spiral n a i l .  (b) 76 m m spiral n a i l .  2.4 SPR-102 mm 2.0  L S L (109) S~—62.2 PEN  1.6 1.2  SPF (io8) 76.5 PEN  0.8 0.4 0.0 5  10  15  20  25  30  35  40  10  Displacement (mm)  (c)  102 m m spiral nail.  15  20  25  Displacement (mm)  (d) L S L studs.  Figure 4.5. L o a d - d e f l e c t i o n curves f r o m w i t h d r a w a l testing.  30  N a i l W i t h d r a w a l Tests  4.3.2  131  Failure Modes  There is o n l y one desired failure m o d e f o r this type o f testing: w i t h d r a w a l o f the n a i l f r o m the stud.  T h i s type o f failure is s h o w n i n Figure 4.6.  Some o f the test specimens failed, h o w e v e r ,  w h e n the head o f the nail fractured o f f or y i e l d e d i n the cradle that was supporting t h e m . A n e w cradle for the heads o f the nails was fabricated after the first f e w occurrences o f this failure mode. N o n e o f the tests that f a i l e d w i t h the brittle fracture o f the head o f the nail were i n c l u d e d i n the results and all the replicates that were i n c l u d e d had reached their m a x i m u m load p r i o r to failure.  Figure 4.6. T y p i c a l nail w i t h d r a w a l failure mode.  4.4 SUMMARY The results f r o m nail w i t h d r a w a l testing show that the response is related to the density o f the stud material, the length o f penetration, and the diameter o f the nail w i t h the significance o f each o f those parameters b e i n g i n the descending order that they were listed.  The  withdrawal  resistance o f these specimens is d i r e c t l y related to the load-slip response o f the connections tested i n the previous chapter since w i t h d r a w a l o f the sheathing and the nail was a c o m m o n failure mode.  C o m p o s i t e T - B e a m Tests  132  5. COMPOSITE T-BEAM TESTS Several theoretical methods presented i n chapter 2.  f o r d e t e r m i n i n g the properties  o f a composite m e m b e r  were  T h i s chapter includes the test results o f m o n o t o n i c and c y c l i c tests to  determine the stiffness o f composite T-beams, w h i c h consist o f a stud and its t r i b u t a r y w i d t h o f sheathing, and compare t h e m w i t h theoretical solutions.  Such composite T - b e a m members are  closely associated w i t h t a l l w o o d - f r a m e w a l l construction.  5.1  OBJECTIVES A N D SCOPE  A m a i n objective o f this research is to determine the structural performance o f tall w o o d - f r a m e w a l l s , so that they can be constructed i n a w a y that makes t h e m e c o n o m i c a l l y c o m p e t i t i v e w i t h other materials c u r r e n t l y b e i n g used b y the construction industry.  One w a y to m a k e tall w o o d -  frame w a l l s m o r e e c o n o m i c a l l y feasible is to consider some changes i n the standard design approach f o r regular w o o d - f r a m e w a l l s . The current design approach a l l o w s the designer to o n l y account f o r the studs i n the w a l l as the sole load-resisting elements, and does not treat the entire w a l l system as an equivalent composite m e m b e r consisting o f all the elements that make up the wall.  C o m p o s i t e action is i