UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Analysis of fillet function in wood-based sandwich construction Kaneko, Tatsuhei 1972

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata

Download

Media
831-UBC_1972_A6 K35.pdf [ 5.75MB ]
Metadata
JSON: 831-1.0101667.json
JSON-LD: 831-1.0101667-ld.json
RDF/XML (Pretty): 831-1.0101667-rdf.xml
RDF/JSON: 831-1.0101667-rdf.json
Turtle: 831-1.0101667-turtle.txt
N-Triples: 831-1.0101667-rdf-ntriples.txt
Original Record: 831-1.0101667-source.json
Full Text
831-1.0101667-fulltext.txt
Citation
831-1.0101667.ris

Full Text

ANALYSIS OF FILLET FUNCTION IN WOOD-BASED SANDWICH CONSTRUCTION . by TATSUHEI KANEKO B.Sc. ( F o r . ) , Hokkaido U n i v e r s i t y , 1960 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS. FOR THE DEGREE OF MASTER OF FORESTRY i n the Department of F o r e s t r y We accept t h i s t h e s i s as conforming t o the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA January, 1972 In p r e sen t i ng t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the requirements fo r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e fo r reference and s tudy. I f u r t h e r agree tha t pe rmiss ion for e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department o r by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed wi thout my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada ABSTRACT When a porous honeycomb core i s glued t o plane f a c i n g s to make a sandwich c o n s t r u c t i o n , glue f i l l e t s (concave menisci) are formed around the core c e l l edges. I t i s known t h a t glue f i l l e t s p l a y an important r o l e i n s t r e n g t h e n i n g the bond of the c o n s t r u c t i o n , but only few s t u d i e s on the r e a l f u n c t i o n of the f i l l e t have been reported. This t h e s i s i n v e s t i g a t e s the r e l a t i o n s h i p s between f i l l e t s i z e and bonding s t r e n g t h i n sandwich con-s t r u c t i o n f o l l o w e d by a s t r e s s a n a l y s i s of the f i l l e t s . Sandwich panels w i t h v a r i o u s f i l l e t s i z e s were produced by means of a glue a p p l i c a t o r of o r i g i n a l design u s i n g a modified p h e n o l - r e s o r c i n o l r e s i n g l u e , k r a f t paper honeycomb cores and Douglas f i r plywood f a c i n g s . T e n s i l e s t r e n g t h t e s t s normal to the sandwich specimens of 1 by 1 i n c h , and f l e x u r e t e s t s on the sandwich beams of 3.75 by 12 inches were performed. F i l l e t rupture s i z e s and a c t u a l f i l l e t dimensions were measured. A h i g h l y s i g n i f i c a n t c o r r e l a t i o n was found between f i l l e t s i z e and bonding s t r e n g t h . Larger f i l l e t s provided g r e a t e r bonding s t r e n g t h . When a sandwich was subjected t o t e n s i l e l o a d , a v e r t i c a l shear f a i l u r e took place at the center of the f i l l e t concave meniscus r e g a r d l e s s of f i l l e t s i z e . By assuming the u n i f o r m i t y of f i l l e t shape, the f o l l o w i n g equation: x B = my + d , was found to express the r e l a t i o n s h i p between the v e r t i c a l shear s t r e s s x B at the f r a c t u r e p o i n t B and the f i l l e t h eight y at B, where m and d were constants. Too l a r g e f i l l e t s had tendency to form voids or bubbles w i t h i n them r e s u l t i n g i n lowering s t r e n g t h v a l u e s . The appearance of f r a c t u r e i n the g l u e l i n e i n f l e x u r e t e s t specimens was s i m i l a r t o t h a t i n the t e n s i l e t e s t . Most of the sandwich specimens w i t h s m a l l e r f i l l e t s f a i l e d i n the g l u e l i n e , w h i l e those w i t h l a r g e r f i l l e t s mostly f a i l e d i n core shear. This o b s e r v a t i o n a l s o i n d i c a t e d the s u p e r i o r i t y of l a r g e r f i l l e t s i n bonding of honeycomb-to-plywood. The cause of g l u e l i n e f a i l u r e i n the f l e x u r e t e s t was deemed to r e s u l t from a complex system of shear, compres-s i o n and t e n s i l e s t r e s s e s . However, a mathematical expr e s s i o n d e s c r i b i n g t h a t system of s t r e s s e s was not found. i v TABLE OF CONTENTS Page ABSTRACT i i TABLE OF CONTENTS i v LIST OF TABLES v i i LIST OF FIGURES v i i i ACKNOWLEDGEMENTS . . . X INTRODUCTION 1 LITERATURE REVIEW 7 MATERIALS AND METHODS 15 Co n s t r u c t i o n of Glue A p p l i c a t o r 15 M a t e r i a l s 19 Pr e p a r a t i o n of Sandwich Panels 21 T e n s i l e Test Specimen and Test Procedure . . . . 23 Flex u r e Test Specimen and Test Procedure . . . . 26 RESULTS AND ANALYSIS OF DATA 30 T e n s i l e Test 3 0 1. F i l l e t Height and F i l l e t Width R e l a t i o n s h i p 31 2. F i l l e t Height and T e n s i l e Strength R e l a t i o n s h i p 33 3. F i l l e t Width and T e n s i l e Strength R e l a t i o n s h i p 35 4. D e f l e c t i o n at Fr a c t u r e and T e n s i l e Strength R e l a t i o n s h i p 37 5. Facing F a i l u r e and T e n s i l e Strength R e l a t i o n s h i p 40 6. F i l l e t Height and D e f l e c t i o n at Fr a c t u r e R e l a t i o n s h i p 40 V Page Fle x u r e Test 41 1. F i l l e t Height and F i l l e t Width R e l a t i o n s h i p 44 2 . F i l l e t Height and Shear Strength R e l a t i o n s h i p 47 3 . F i l l e t Width and Shear Strength R e l a t i o n s h i p 49 4 . D e f l e c t i o n at F r a c t u r e and Shear Strength R e l a t i o n s h i p 51 5 . F i l l e t Height and D e f l e c t i o n R e l a t i o n s h i p 51 DISCUSSION 54 F i l l e t Geometry 54 T e n s i l e Strength 59 Shear Strength 65 SUMMARY AND CONCLUSION 6 8 BIBLIOGRAPHY V I TABLES 74 APPENDICES 92 1 - Tables of A n a l y s i s of Variance and Duncan's New M u l t i p l e Range Test f o r F i l l e t Width Means i n T e n s i l e Test Specimens 9 3 2 - Tables of A n a l y s i s of Variance and Duncan's New M u l t i p l e Range Test f o r T e n s i l e Strength Means i n T e n s i l e Test Specimens . 94 3 - B a s i c Equations 95 4 - Tables of A n a l y s i s of Variance and Duncan's New M u l t i p l e Range Test f o r F i l l e t Width Means i n Flexure Test Specimens . . . . . . . 97 5 - Tables of A n a l y s i s of Variance and Duncan's New M u l t i p l e Range Test f o r Shear Strength Means i n Flexure Test Specimens . 9 8 v i Page 6 - Tables of A n a l y s i s of Variance and Duncan's New M u l t i p l e Range Test f o r D e f l e c t i o n Means i n Flexure Test Specimens 99 7 - Sequences of F i l l e t Width Means 1 0 0 8 - Values of k/m f o r the Four F i l l e t Height Groups 100 9 - Core Shear St r e s s under Two-Point Loading 101 v i i LIST OF TABLES Table Page 1. P a r t i a l R e s u l t s of P r e l i m i n a r y Test f o r Determination of Loading System 75 2. Results of T e n s i l e Test f o r F i l l e t Height Group [0.5] 7 6 3. Results of T e n s i l e Test f o r F i l l e t Height Group [1.0] 77 4. R e s u l t s of T e n s i l e Test f o r F i l l e t Height Group [1.5] 78 5. Re s u l t s of T e n s i l e Test f o r F i l l e t Height Group [2.0] 79 6. Glue Depth and F i l l e t Height i n T e n s i l e Test Specimens 80 7. F r a c t u r e / F i l l e t - W i d t h R a t i o i n Se l e c t e d T e n s i l e Test Specimens 81 8. A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of T e n s i l e Test Results -(A) 82 9. A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of T e n s i l e Test R e s u l t s - ( B ) 84 10. Results of Flexure Test f o r F i l l e t Height Group [0.5] 85 11. Results of Flexure Test f o r F i l l e t Height Group [1.0] 86 12. Results of Flexure Test f o r F i l l e t Height Group [1.5] 87 13. Results of Flexure Test f o r F i l l e t Height Group [2.0] 88 14. F r a c t u r e / F i l l e t - W i d t h R a t i o i n Sel e c t e d Flexure Test Specimens 89 15. A u x i l i a r y Table f o r S t a t i s t i c a l A n a l y s i s of Flexure Test R e s u l t s . 90 v i i i LIST OF FIGURES Fig u r e Page 1. F i l l e t s . . 6 2. S t r e s s Concentration Factors i n Tension 12 3. Glue A p p l i c a t o r - Base P l a t e 17 4. Glue A p p l i c a t o r - Four Doctor Blades 18 5. K r a f t Paper Honeycomb 20 6. Dimensional Nomenclature of Expanded Honeycomb 22 7. T e n s i l e Test Specimen i n Loading F i x t u r e 2 4 8. Honeycomb C e l l S e c t i o n 26 9. Apparatus f o r Conducting Flexure Test of Sandwich C o n s t r u c t i o n 2 8 10. F i l l e t Height and F i l l e t Width R e l a t i o n s h i p i n T e n s i l e Test Specimens 34 11. F i l l e t Height and T e n s i l e Strength R e l a t i o n s h i p 36 12. F i l l e t Width and T e n s i l e Strength R e l a t i o n s h i p 38 13. T e n s i l e Strength and D e f l e c t i o n R e l a t i o n s h i p 39 14. S e l e c t e d L o a d - D e f l e c t i o n Curves i n F l e xure Tests 42 15. F i l l e t Height and F i l l e t Width R e l a t i o n s h i p i n Flexure Test Specimens 45 16. F i l l e t Height and Shear Strength R e l a t i o n s h i p 48 17. F i l l e t Width and Shear Strength R e l a t i o n s h i p 50 i x F i g u r e Page 18. F i l l e t Height and D e f l e c t i o n R e l a t i o n -s h i p i n Flexure Test Specimens 53 19. Dimensional Nomenclature on F i l l e t S e c t i o n and Shear S t r e s s D i s t r i b u t i o n . . . . 58 X ACKNOWLEDGEMENTS The Author wishes to thank the f o l l o w i n g people: Mr. L. Va l g , A s s i s t a n t P r o f e s s o r , F a c u l t y of F o r e s t r y , the U n i v e r s i t y of B r i t i s h Columbia, f o r h i s suggestions throughout the experiment and great help i n the pr e p a r a t i o n of the manuscript. Dr. N.C. Franz, P r o f e s s o r of the F a c u l t y of F o r e s t r y at the U n i v e r s i t y of B r i t i s h Columbia, f o r h i s needed advice and c r i t i c i s m which improved the q u a l i t y of t h i s t h e s i s . Dr. R.W. Wellwood, P r o f e s s o r of the F a c u l t y of F o r e s t r y at the U n i v e r s i t y of B r i t i s h Columbia,for a s s i s -tance i n a l l my s t u d i e s over the past two years. Mr. L. Adamovich, A s s o c i a t e P r o f e s s o r of the F a c u l t y of F o r e s t r y at the U n i v e r s i t y of B r i t i s h Columbia, f o r reading and c o r r e c t i n g the manuscript from the viewpoint of an engineer. The author i s a l s o indebted to h i s w i f e f o r her understanding, patience and encouragement d u r i n g the co m p i l a t i o n of t h i s t h e s i s . INTRODUCTION A laminated c o n s t r u c t i o n which c o n s i s t s of two f a c i n g s or covers and a core i s g e n e r a l l y r e f e r r e d to as a sandwich c o n s t r u c t i o n . The sandwich-panel c o n s t r u c t i o n t h a t i s a la m i n a t i o n of two t h i n f a c i n g s w i t h a t h i c k core and designed to give a high strength-weight r a t i o i s c a l l e d a s t r u c t u r a l sandwich c o n s t r u c t i o n . According to the Standard of the American S o c i e t y f o r T e s t i n g and M a t e r i a l s (5), a s t r u c t u r a l sandwich c o n s t r u c t i o n i s de f i n e d as: "A laminar c o n s t r u c t i o n comprising a combination of a l t e r n a t i n g d i s s i m i l a r simple or composite m a t e r i a l s assembled and i n t i m a t e l y f i x e d i n r e l a t i o n to each other so as to use the p r o p e r t i e s of each to a t t a i n s p e c i f i c s t r u c t u r a l advantages f o r the whole assembly." The s t r u c t u r a l design of sandwich c o n s t r u c t i o n may be compared t o an I-beam i n which flanges c a r r y compressive and t e n s i l e l o a d s , w h i l e the web c a r r i e s shear loads when the beam i s subjected to a bending moment (25, 39). In s t r u c t u r a l sandwich c o n s t r u c t i o n s the f a c i n g s correspond t o the flanges of the I-beam, w h i l e the core f u n c t i o n s as the web. Not a l l sandwich panels are used f o r s t r u c t u r a l purposes. Some are simply designed to act as thermal or a c o u s t i c a l b a r r i e r s , w h i l e others may be intended f o r 2 weather s h i e l d s or f i r e w a l l s (21). The major p r o p e r t i e s of a sandwich panel are determined by the combination of the f a c i n g and core m a t e r i a l s . In other words, the choice of the f a c i n g and core m a t e r i a l s f o r a sandwich-panel construc-t i o n depends upon the purpose of the panel use. Wood-based sandwich c o n s t r u c t i o n s have found a wide use i n house and b u i l d i n g c o n s t r u c t i o n s t a k i n g advantage of good i n s u l a t i o n c h a r a c t e r i s t i c s , r e l a t i v e l y low cost and easy p r o c e s s i n g (22). Plywood, veneer, hardboard and paperboard are s u i t a b l e f o r the f a c i n g s . Balsawood, paper honeycomb, f i b r e b o a r d and wood e x c e l s i o r board have been used as the core m a t e r i a l s . Various combinations of wood-based and non-wood-based m a t e r i a l s , or combinations of two d i f f e r e n t wood-based m a t e r i a l s can produce e i t h e r s t r u c t u r a l or n o n - s t r u c t u r a l sandwich c o n s t r u c t i o n s . In any sandwich-panel c o n s t r u c t i o n , the f a c i n g must be attached t o the core by means of bonding or other s u i t a b l e methods. I f the j o i n t between the core and the f a c i n g should separate, the panel i s u s e l e s s . A strong j o i n t i s p a r t i c u l a r l y important f o r a s t r u c t u r a l sandwich c o n s t r u c t i o n i n which the j o i n t must s u s t a i n approximately the same shear s t r e s s as the core. While s o l d e r i n g , b r a z i n g and welding are a p p l i c a b l e to produce a l l - m e t a l sandwiches of e x c e p t i o n a l s t r e n g t h and heat r e s i s t a n c e , adhesive bonding i s adaptable to almost any combinations of m a t e r i a l s . In f a c t , the development of s t r u c t u r a l sandwich c o n s t r u c t i o n may be 3 c r e d i t e d t o t h e r a p i d a d v a n c e m e n t i n t h e a d h e s i v e t e c h n o l o g y a f t e r W o r l d War I I . E x t e n s i v e s t u d i e s on t h e s t r u c t u r a l p r o p e r t i e s o f s a n d w i c h c o n s t r u c t i o n h a v e b e e n u n d e r t a k e n a l m o s t e x c l u s i v e l y b y t h e U.S. F o r e s t P r o d u c t s L a b o r a t o r y f o r t h e p a s t t w o d e c a d e s (1). The p r i m a r y o b j e c t i v e o f t h e s e s t u d i e s was d i r e c t e d t o w a r d s t h e a p p l i c a t i o n o f s a n d w i c h c o n s t r u c t i o n t o a i r c r a f t a n d m i s s i l e s (16/ 17, 26, 28, 3 0 ) . The L a b o r a t o r y h a s p u b l i s h e d a l a r g e number o f t e c h n i c a l p a p e r s o n s t r u c t u r a l s a n d w i c h c o n s t r u c t i o n , b u t o n l y a few o f t h e p u b l i c a t i o n s h a v e d e a l t w i t h t h e r e l a t i o n s h i p s b e t w e e n t h e g l u e l i n e g e o m e t r y a n d t h e b o n d i n g s t r e n g t h . R e c e n t l y , t h e g l u e l i n e g e o m e t r y i n a s a n d w i c h c o n -s t r u c t i o n h a s d r a w n some r e s e a r c h e r s ' a t t e n t i o n (11). The r e c o g n i t i o n o f t h e i m p o r t a n c e o f g l u e l i n e g e o m e t r y m i g h t h a v e a r i s e n f r o m t h e p r a c t i c e s o f e f f i c i e n t u s e o f a g i v e n a d h e s i v e r a t h e r t h a n i n v e n t i n g new a d h e s i v e s . U n d e r s u c h c i r c u m s t a n c e s , i t was f o u n d t h a t t h e m o s t e f f i c i e n t g l u e -l i n e i n a s a n d w i c h c o n s t r u c t i o n s h o u l d f o r m a " f i l l e t . " A f i l l e t , o r g l u e f i l l e t , may b e d e f i n e d a s : t h e g l u e b o d y t h a t i s f i l l i n g t h e c o r n e r b e t w e e n t h e c o r e c e l l w a l l a n d t h e f a c i n g ( F i g u r e 1). The s i z e a nd s h a p e o f a f i l l e t v a r i e s w i t h t h e t y p e o f c o r e c e l l a n d t h e a d h e s i v e u s e d . The c o r e c e l l , i n t h i s c o n t e x t , i m p l i e s s m a l l p o r e s o f c o n t i n u o u s c o r e s , s u c h a s b a l s a , f o a m e d r u b b e r s , a n d f o a m e d r e s i n s , as w e l l a s c e l l s o f o p e n - c e l l e d o r g r i d d e d t y p e 4 c o r e s s u c h as honeycomb ( 8 ) . The m a i n o b j e c t i v e o f t h i s t h e s i s w i l l be t o a n a l y s e t h e f i l l e t f u n c t i o n i n wood-based s a n d w i c h c o n s t r u c t i o n i n t e r m s o f t h e r e l a t i o n s h i p b e t w e e n g l u e l i n e g e o m e t r y , o r f i l l e t s i z e , and b o n d i n g s t r e n g t h . F o r t h i s p u r p o s e , k r a f t p a p e r honeycomb was c h o s e n f o r t h e c o r e m a t e r i a l s i n c e i t s u n i f o r m i t y o f c e l l s h ape and s i z e s i m p l i f i e s t h e measurement o f f i l l e t s i z e . P l y w o o d was c h o s e n f o r t h e f a c i n g s b e c a u s e i t h as p r a c t i c a l c o n s t r u c t i o n a p p l i c a t i o n s . S i n c e f i l l e t s h a p e d e p e n d s upon g l u e f l o w c h a r a c t e r -i s t i c s and t h e s u r r o u n d i n g c o n d i t i o n s , t h e a p p l i c a t i o n o f s e v e r a l a d h e s i v e s w o u l d i n d u c e d i f f i c u l t i e s i n c o m p a r i n g one g l u e f i l l e t t o a n o t h e r . The c o m p a r i s o n o f f i l l e t i n g e f f e c t s w i t h g l u e v a r i a t i o n s i s r e c o g n i z e d as a v a r i a b l e o f g r e a t i n t e r e s t , b u t was b e y o n d t h e i m m e d i a t e s c o p e o f t h i s s t u d y . The sample p a n e l s were made w i t h o n l y one k i n d o f a d h e s i v e , n a m e l y a m o d i f i e d p h e n o l - r e s o r c i n o l r e s i n a d h e s i v e w h i c h was e a s y t o h a n d l e and s e t s a t room t e m p e r a t u r e s o f 7 0 ° F. I n o r d e r t o t e s t f i l l e t i n g e f f e c t s on b o n d i n g s t r e n g t h , two commonly e m p l o y e d t e s t i n g methods were c a l l e d f o r . T h o s e were " S t a n d a r d M ethod o f T e n s i o n T e s t o f F l a t S a n d w i c h C o n s t r u c t i o n s i n F l a t w i s e P l a n e (ASTM D e s i g n a t i o n : C 2 9 7 - 6 1 ) " and " F l e x u r e T e s t o f F l a t S a n d w i c h C o n s t r u c t i o n s (ASTM D e s i g n a t i o n : C 3 9 3 - 6 2 ) . " The f o r m e r c o v e r s t h e p r o c e d u r e f o r d e t e r m i n i n g t h e s t r e n g t h i n t e n s i o n f l a t w i s e o f t h e b ond b e t w e e n c o r e and f a c i n g s o f an a s s e m b l e d s a n d w i c h 5 panel. The e x p r e s s i o n , " t e n s i o n f l a t w i s e , " means t e n s i o n normal to the plane of the sandwich (8). The l a t t e r covers a procedure f o r determining p r o p e r t i e s of f l a t sandwich c o n s t r u c t i o n s subjected to f l a t w i s e f l e x u r e i n such a manner that the a p p l i e d moments produce curvature of the plane of a sheet of the sandwich c o n s t r u c t i o n . This t e s t may be p r i m a r i l y conducted to determine f l e x u r a l and shear modulus, and shear s t r e n g t h of the c o r e , or compressive or t e n s i l e s t r e n g t h of the f a c i n g s . However, the t e s t to evaluate core shear s t r e n g t h may a l s o evaluate bonds between core and f a c i n g s inasmuch as core shear s t r e s s values may be lower than a c t u a l core shear s t r e n g t h , thus i n d i c a t i n g t h a t f a i l u r e i n i t i a t e d i n the bond ( 4 ) . F i l l e t h e i g h t , X = F i l l e t w i d t h , t = Honeycomb w a l l t h i c k n e s s F i g u r e 1. F i l l e t s 7 LITERATURE REVIEW Hundreds of p u b l i c a t i o n s on sandwich c o n s t r u c t i o n have been issued,mostly by the U.S. Department of A g r i c u l t u r e , d u r i n g the past quarter century (16, 17, 24, 26, 27, 28, 30, 38, 42). These p u b l i c a t i o n s cover almost a l l aspects on sandwich c o n s t r u c t i o n i n c l u d i n g the problems of adhesives, cores and t e s t i n g methods as fundamental s t u d i e s on mechanical p r o p e r t i e s . In these s e r i e s of p u b l i c a t i o n s , however, nothing has been mentioned about f i l l e t e f f e c t s i n bonding a porous m a t e r i a l l i k e a honeycomb core to another m a t e r i a l . I t i s not c l e a r when importance of f i l l e t was f i r s t r e cognized, but i t seems th a t the problem was brought up o r i g i n a l l y i n the sandwich panel i n d u s t r y . In 1957, Manning (10), answering a question about a p p l i c a t i o n methods of contact type adhesives, mentioned from h i s experience t h a t he would p r e f e r a spray a p p l i c a t i o n to the r o l l e r coat f o r the purpose of b u i l d i n g up a f i l l e t on the top edge of the honeycomb core. Although i t was not d e s c r i b e d why a spray a p p l i c a t i o n b u i l t up a b e t t e r f i l l e t than a r o l l e r coat and what the f i l l e t was l i k e , he e x p l a i n e d t h a t formation of t h i s f i l l e t had a very important f u n c t i o n or r e q u i s i t e i n adhesive performance, because i t i n c r e a s e d the area of c o n t a c t , p a r t i c u l a r l y when a contact type glue was used. 8 Gathering data on sandwich c o n s t r u c t i o n , Humke (20) presented a s e l e c t i o n guide f o r sandwich panel m a t e r i a l s , i n which he pointed out t h a t epoxies and v i n y l b u t y r a l p h e n o l i c adhesives had s e l f - f i l l e t i n g c h a r a c t e r i s t i c s , w h i l e elastomer m o d i f i e d p h e n o l i c , neoprene-rubber base, n i t r i l e - r u b b e r base and p o l y v i n y l acetate adhesives had no s e l f - f i l l e t i n g p r o p e r t i e s . He des c r i b e d t h a t s e l f - f i l l e t i n g or beading was extremely important i n honeycomb sandwich, f o r the bead t h a t clung to the edge of each c e l l flowed i n t o a f i r m double f i l l e t when the f a c i n g was pressed i n p l a c e , r e s u l t i n g i n added bond area and a stronger s t r u c t u r e . A f u r t h e r d i s c u s s i o n about the importance of f i l l e t -i n g was presented by Houwink and Salmon (19). "In the most common case, we have a t h i n f o i l edge, 0.0 3 mm., at r i g h t angles t o cover p l a t e . This core f o i l edge represents only 1/200 of the t o t a l f a c i n g m a t e r i a l area, yet must r e s i s t the same shear s t r e s s e s as the core. The most e f f i c i e n t adhesives f o r t h i s a p p l i c a t i o n form a f i l l e t , a concave meniscus, between the face sheet and the honeycomb c e l l w a l l . Such adhesives become l i q u i d i n the c u r i n g o p e r a t i o n , form the f i l l e t by c a p i l l a r y a c t i o n , and proceed to cure to a s o l i d s t a t e . Those adhesives which do not begome t r u l y flowable dur i n g c u r i n g , are placed i n a s o l v e n t s o l u t i o n , and r o l l e r coated, dipped, or sprayed onto the core to a i d formation of f i l l e t s . " 9 Recently, D i e t z (12) suggested t h a t i t was p r e f e r -able to coat the inner side of plywood faces w i t h glue i n a d d i t i o n to a p p l y i n g glue to the core f o r best r e s u l t s i n bonding honeycomb core to plywood s k i n . He a l s o proposed t h a t i t was wise to coat the plywood very l i g h t l y and t o apply most of the adhesive to the core both f o r economic reasons and i n order t o save weight. This i s , according to D i e t z , the e f f i c i e n t way of making a good f i l l e t w i t h the minimum amount of adhesive. Grimes (15) s t u d i e d the e f f e c t of f i l l e t i n g on the core p r o p e r t i e s . F i r s t , he made a comparison between two d i f f e r e n t adhesives on the shear strengths of s m a l l and medium f i l l e t s . The small f i l l e t (0.09 l b s . per square foot) of modified epoxy adhesive gave the core l e s s " e f f e c t i v e s t r e n g t h " and " e f f e c t i v e s t i f f n e s s " than the medium epoxy-phenolic f i l l e t (0.135 lb s . per square f o o t ) . This type of comparison, as he recognized, may be u n f a i r i n t h a t i f the former adhesive were i n c r e a s e d i n weight to t h a t of the l a t t e r , i t might p o s s i b l y provide as good or b e t t e r f i l l e t i n g and core p r o p e r t i e s . Comparisons were a l s o made f o r beam shear, drum p e e l , and f l a t w i s e t e n s i l e s trengths between two d i f f e r e n t adhesive weights using the same adhesive. In every comparison the increase of glue weight r e s u l t e d i n the higher s t r e n g t h . Conducting some other experiments, he confirmed t h a t the weight of adhesive w i t h i n each type was not so important as the f i l l e t s i z e . 10 Grimes concluded t h a t the f i l l e t s i z e was the most important p h y s i c a l f a c t o r i n o b t a i n i n g the maximum st r e n g t h p r o p e r t i e s of honeycomb cores and sandwich c o n s t r u c t i o n s . As f o r the f i l l e t s i z e and a c t u a l s t r e s s e s at the f i l l e t , Grimes assumed t h a t : (a) s t r e s s e s occur i n a plane p e r p e n d i c u l a r to the c e l l w a l l at approximately i t s edge, (b) t h a t the width of the f i l l e t s t r e s s plane i s a f u n c t i o n of c e l l s i z e and f i l l e t s i z e , (c) t h a t the length of the f i l l e t plane i s equal t o b, the c e l l w a l l f l a t w i d t h , (d) t h a t the f i l l e t s t r e s s plane t o t a l width i s (LF) l a r g e f i l l e t r/2 (MP) medium f i l l e t r/3 ( S F ) s m a l l f i l l e t r/4, and (e) t h a t the f i l l e t s t r e s s plane area f o r each f l a t then becomes (LF); A f = b r/2 = r 2 t a n 30° = 0.577r 2 (square inch) (MF); A f = b r/3 = 0.384r 2 (SF); A = b r/4 = 0.288r 2, where r i s the r a d i u s of the i n s c r i b e d c i r c l e of a c e l l . According t o h i s e x p l a n a t i o n the f l a t w i s e t e n s i l e load from the c e l l w a l l to the adhesive i s passed v i a shear, and t h i s load then must be t r a n s m i t t e d t o the face through the f i l l e t plane by t e n s i o n . 11 Timoshenko and Goodier (37) have shown the s t r e s s d i s t r i b u t i o n p a t t e r n at the f i l l e t of a metal p l a t e by the p h o t o e l a s t i c method. Although the f i l l e t they showed was not t h a t of the g l u e l i n e i n sandwich c o n s t r u c t i o n , the f o l l o w i n g d i s c u s s i o n provides u s e f u l suggestions f o r the study of f i l l e t s i z e and f u n c t i o n . These workers confirmed t h a t the maximum s t r e s s occurred at the end of a p l a t e of two d i f f e r e n t widths submitted t o c e n t r a l l y a p p l i e d t e n s i o n . The r a t i o of t h i s maximum s t r e s s t o the average s t r e s s i n the narrower p o r t i o n of the p l a t e i s c a l l e d the " s t r e s s c o n c e n t r a t i o n f a c t o r . " I t depends on the radi u s R of the f i l l e t t o the width d of the p l a t e . S e v e r a l values of the s t r e s s c o n c e n t r a t i o n f a c t o r obtained e x p e r i m e n t a l l y (40) are given i n Figure 2. I t i s seen i n the f i g u r e t h a t the maximum s t r e s s i s r a p i d l y i n c r e a s i n g as the r a t i o R/d i s decreasing. When R/d = 0.1 the maximum s t r e s s i s more than twice the average t e n s i l e s t r e s s . I n v e s t i g a t i n g ten methods of i n s p e c t i n g bonds between the cores and facin g s of sandwich panels of the a i r c r a f t type, Heebink and Mohaupt (16) reported t h a t none of the t e s t s i n v e s t i g a t e d presented p r a c t i c a l and dependable means of i n s p e c t i n g sandwich panels f o r q u a l i t y of j o i n t s . I t a l s o appeared t h a t any combination of these t e s t methods would o f f e r l i t t l e promise of improvements. These are: (1) v i s u a l i n s p e c t i o n , (2) s p e c i a l l i g h t i n g , (3) tap p i n g , (4) supersonic i n s p e c t i o n , (5) exposure to vacuum, 12 u o 4-> 1 I I I I I 1_ 0 .1 .2 .3 .4 .5 R a t i o R/d Figure 2 S t r e s s Concentration F a c t o r s i n Tension From S. Timoshenko and J.N. Goodier, "Theory of E l a s t i c i t y , " 2nd Ed. (6) vacuum-cup t e s t , (7) i n t e r n a l pressure t e s t , (8) h e a t i n g complete pa n e l , (9) l o c a l h e a t i n g , and (10) b u t t o n - t e n s i o n t e s t . Heebink and Mohaupt concluded t h a t c a r e f u l l y c o n t r o l l e d process s p e c i f i c a t i o n s , s u b s t a n t i a t e d by s u f f i c i e n t number of d e s t r u c t i v e t e s t s and supplemented by r i g i d i n s p e c t i o n must be r e l i e d upon to i n s u r e u n i f o r m l y h i g h - q u a l i t y j o i n t s i n sandwich panels. E i c k n e r (13) c a r r i e d out f l a t w i s e t e n s i l e t e s t s t o evaluate the d u r a b i l i t y of the glue j o i n t s i n aluminum and end-grain b a l s a sandwich c o n s t r u c t i o n . The p r i n c i p l e s of the t e s t method and t e s t i n g apparatus were l a t e r employed 13 i n the ASTM Designation C297-52 ( r e v i s e d i n 1961). For f a b r i c a t i o n of the t e n s i o n and shear specimens of plywood-faced sandwich panels, the U.S. Forest Products Laboratory (38) recommended the use of room temperature s e t t i n g r e s o r c i n o l r e s i n adhesives which should always be a p p l i e d t o both surfaces of the glue j o i n t . Intermediate temperature s e t t i n g phenol r e s i n adhesives were a l s o recommended i f s h o r t e r p r e s s i n g periods were d e s i r a b l e . Further d e t a i l s about specimen s i z e and l o a d i n g methods proposed i n the r e p o r t were the same as those which were l a t e r taken up i n the ASTM standard methods (7, 8). According to Kuenzi (27) the best l o a d i n g method i n f l e x u r e t e s t i s t o apply the concentrated load at the q u a r t e r -span p o i n t s on a beam simply supported at the supports. The reason given i s t h a t the maximum moment and the maximum shear s t r e s s induced i n the beam loaded at the quarter-span p o i n t s are equal t o those induced i n the beam on which the load i s un i f o r m l y d i s t r i b u t e d . This i s e a s i l y proved by elementary mechanics. The s i n g l e concentrated l o a d i n g at the mid-span of the beam i s the s i m p l e s t way of ap p l y i n g the l o a d . But, t h i s l o a d i n g produces s t r e s s c o n c e n t r a t i o n at the l o a d i n g p o i n t as much as twice the corresponding s t r e s s c o n c e n t r a t i o n s at the supports. Hence, i t may happen t h a t the s i n g l e concentrated l o a d i n g method cannot d e t e c t a f a u l t which i s l o c a t e d near the supports (27). In order to evaluate the shear s t r e n g t h of the core-t o - f a c i n g bond, however, the abovementioned two-point l o a d i n g i s not appropriate (19). I t i s known t h a t the c e n t r a l p o r t i o n between two l o a d i n g p o i n t s i s not subjected t o shear s t r e s s . That i s , i f quarter-span p o i n t l o a d i n g i s employed, the g l u e l i n e shear s t r e n g t h of one h a l f of the span cannot be t e s t e d . Houwink and Salmon (19) s t a t e d t h a t the usual method of t e s t i n g the sandwich bond st r e n g t h i n shear i s t o load a sh o r t sandwich beam specimen under t h r e e - p o i n t l o a d i n g ( i . e . mid-span loading) and t o c a l c u l a t e the shear s t r e n g t h from the f a i l i n g load u s i n g the simple beam theory. This method i s a p p l i c a b l e when the compressive or t e n s i l e s t r e n g t h of the f a c i n g i s not l e s s than the g l u e l i n e shear s t r e n g t h . I f the f a c i n g cannot wi t h s t a n d the a p p l i e d load and i f i t f a i l s i n f l e x u r e before f a i l u r e takes place i n the g l u e l i n e , the s t r e n g t h of the c o r e - t o - f a c i n g bond cannot be evaluated. The c o n v e n t i o n a l o v e r l a p shear t e s t used t o evaluate s t r u c t u r a l adhesives i s not app r o p r i a t e to measure the str e n g t h of adhesive to f i l l e t i n sandwich c o n s t r u c t i o n (19). In order t o evaluate adhesives f o r bonding core to f a c i n g s , sandwich panels should be prepared. F o l l o w i n g t h i s , the shear s t r e n g t h of g l u e l i n e s as w e l l as the a b i l i t y of the t o t a l s t r u c t u r e to c a r r y a load i s determined i n beam f l e x u r e t e s t s (34). A d d i t i o n a l adhesive s t r e n g t h values are obtained from f l a t w i s e t e n s i l e t e s t s . 15 MATERIALS AND METHODS Since the o b j e c t i v e of t h i s t h e s i s i s t o i n v e s t i g a t e the r e l a t i o n s h i p between f i l l e t s i z e and bonding s t r e n g t h , f i l l e t s of d i f f e r e n t s i z e must be prepared. V a r i a t i o n of f i l l e t s i z e can e a s i l y be generated by d i p p i n g the edge of the honeycomb i n . uniformly spread glue l a y e r s of v a r i o u s depths. A f t e r being dipped i n the g l u e , the honeycomb i s placed on the f a c i n g and l e f t under the c o r r e c t pressure u n t i l the glue hardens. In the meantime, the glue flows and forms a f i l l e t . From the p r e l i m i n a r y experiments i t was lea r n e d t h a t l a t e r a l glue flow on plywood was not s a t i s f a c -t o r y f o r making a good f i l l e t . T herefore, i n the main t e s t a l l of the i n n e r s i d e s of the plywood f a c i n g s were l i g h t l y coated w i t h thinned glue of the same type t o l e t the glue on the core flow onto the plywood. The same procedure was f o l l o w e d f o r the other s i d e of the core and, thus, a sandwich was produced. C o n s t r u c t i o n of Glue A p p l i c a t o r In order t o produce uniform glue l a y e r s of v a r i o u s depths, s e v e r a l methods of making uniform l a y e r s of p a i n t and s i m i l a r m a t e r i a l s were explored (2, 3, 6, 32, 33). A TLC c o a t i n g u n i t f o r chromatography was a l s o t r i e d . A l l of these were designed to meet the requirement of making a u n i f o r m l a y e r o n l y once on a p a r t i c u l a r p l a t e o r a s h e e t . F o r t h e purpose o f making a u n i f o r m g l u e l a y e r on one p l a t e r e p e a t e d l y so t h a t a s p e c i f i c g l u e h e i g h t c o u l d be t r a n s -f e r r e d t o t h e honeycomb c o r e a t each a p p l i c a t i o n , t h e above-mentioned a p p a r a t u s was found t o be i n c o n v e n i e n t . Conse-q u e n t l y , a s i m p l e , y e t e f f i c i e n t g l u e a p p l i c a t o r o f o r i g i n a l d e s i g n was c o n t r i v e d f o r t h i s e x p e r i m e n t . T h i s g l u e a p p l i c a t o r c o n s i s t s o f a s e t o f d o c t o r b l a d e s and a base p l a t e ( F i g u r e s 3, 4). The base p l a t e i s a f l a t p l a t e w h i c h i s made o f a l a m i n a t e d p l a s t i c s h e e t g l u e d on a o n e - i n c h - t h i c k plywood s h e e t w i t h t w o - s t e p p e d s i d e r a i l s f i x e d on b o t h l o n g i t u d i n a l edges o f t h e p l a t e . The s i d e r a i l s a r e made o f l a m i n a t e d p l a s t i c s t r i p s . The t h i c k n e s s o f one s t e p o f t h e r a i l i s t h a t o f t h e l a m i n a t e d p l a s t i c s t r i p and a c t u a l t h i c k n e s s i s 1.4 mm. The d o c t o r b l a d e s a r e r u l e r - l i k e s t e e l b a r s and have s t r a i g h t edges. There a r e f o u r d o c t o r b l a d e s p r e p a r e d so as t o produce f o u r d i f f e r e n t d e p t h s o f t h e g l u e f i l m . Two o f t h e d o c t o r b l a d e s have a l e n g t h t h a t can b r i d g e t h e l o w e r s t e p s o f t h e s i d e r a i l s a c r o s s t h e p l a t e . The o t h e r two b l a d e s a r e e x t e n d e d i n l e n g t h t o b r i d g e t h e upper s t e p s . One o f t h e b l a d e s o f each l e n g t h i s n o t c h e d a t t h e edge on b o t h ends so t h a t t h e c l e a r a n c e between t h e b l a d e edge and t h e p l a t e bed pro d u c e s a h a l f t h i c k n e s s o f one s t e p o f t h e r a i l ( F i g u r e 4, A) o r on e - a n d - o n e - h a l f t h i c k n e s s o f t h e s t e p ( F i g u r e 4, C ) . Top View 4 50 ±1.4-200 Unit: mm. Side View Scale: Three-Eighths Figure 3. Glue Applicator — Base Plate Doctor blade Glue Base plate (A) Glue depth : [0.5] (B) f l.O] (c) [1.53 (D) [2.0] Figure 4. Glue Applicator — Four Doctor Blades 19 In order to make a uniform glue l a y e r on the p l a t e , the doctor blade i s moved by hand from one end of the p l a t e t o the other s l i d i n g on the side r a i l s . The clearance between the blade edge and the p l a t e bed c o n t r o l s the glue depth, f o r the blade edge scrapes o f f the excess glue poured on the p l a t e and l e v e l s the glue l a y e r . The glue depth produced by a h a l f step clearance was r e f e r r e d to as [0.5]. S i m i l a r l y , the glue depths produced by one st e p , one-and-one-half s t e p , and two step clearances were r e f e r r e d to as [1.0], [1.5] and [2.0], r e s p e c t i v e l y . These numbers enclosed i n b rackets are the names of glue depth treatments, and represent n e i t h e r a c t u a l glue depth nor r a t i o s . These symbols were a l s o used f o r exp r e s s i n g the f i l l e t h eight groups. For example, the f i l l e t h e i g h t group [1.0] means those f i l l e t s which were made by the glue depth treatment [1.0]. M a t e r i a l s F a cing . . . . Douglas f i r plywood; 1/4 inch t h i c k , sanded, good one s i d e . Core . . . . K r a f t paper honeycomb; H e x c e l l , HNC 3/8 - 80 (18) E, 1 inch t h i c k , 3/8 i n c h c e l l s i z e (Figure 5). Adhesive . . . M o d i f i e d p h e n o l - r e s o r c i n o l r e s i n glue; P a c i f i c Resins, Resorsabond 2600. C a t a l y s t . . . P a c i f i c Resins, Parac CR 40. Figure 5 . Kraft Paper Honeycomb 21 P r e p a r a t i o n o f S a n d w i c h P a n e l s P l y w o o d was sawn i n t o r e c t a n g u l a r p i e c e s o f 4 b y 14 i n c h e s w i t h the f a c e g r a i n d i r e c t i o n p a r a l l e l t o t h e l o n g e r d i m e n s i o n . Honeycomb was c u t i n t o s i m i l a r s i z e as t h e p l y -wood w i t h t h e t r a n s v e r s e r i b b o n d i r e c t i o n ( F i g u r e 6) p a r a l l e l t o t h e l e n g t h . The sawn p l y w o o d and t h e honeycomb p i e c e s h a d b e e n k e p t u n d e r t h e c o n d i t i o n o f 70 ± 1°F and 50 ± 1% h u m i d i t y f o r more t h a n two weeks b e f o r e t h e y were g l u e d . P r i o r t o b o n d i n g t h e c o r e t o t h e f a c i n g , t h e s a n d e d f a c e o f p l y w o o d was w e t t e d by b r u s h i n g i t w i t h t h i n n e d g l u e ( t h e m i x t u r e o f p h e n o l - r e s o r c i n o l r e s i n , c a t a l y s t a n d w a t e r i n t h e r a t i o o f 10:1:5 b y w e i g h t ) . The mean c o v e r a g e was 6.3 grams p e r s q u a r e f o o t i n t h e t h i n n e d f o r m . T h i s f i g u r e was o b t a i n e d e m p i r i c a l l y by a p r e l i m i n a r y t e s t . F o r t h e g l u i n g o f c o r e - t o - f a c i n g , t h e m i x t u r e o f 10 p a r t s o f p h e n o l - r e s o r c i n o l r e s i n a n d 1 p a r t o f c a t a l y s t b y w e i g h t was u s e d . Twenty-two honeycomb c o r e s f o r e a c h o f t h e f o u r g l u e d e p t h t r e a t m e n t s were a p p l i e d w i t h g l u e b y d i p p i n g t h e c o r e i n t o t h e g l u e l a y e r u n t i l t h e c o r e edge t o u c h e d t h e p l a t e b e d . A f t e r r e m a i n i n g i n t h e g l u e f o r a b o u t t h r e e s e c o n d s t h e c o r e was c a r e f u l l y p u l l e d up and t h e n p l a c e d on a p r e - w e t t e d p l y w o o d . F o l l o w i n g e a c h a p p l i c a t i o n t h e n e c e s s a r y amount o f g l u e was a d d e d t o t h e a p p l i c a t o r s o t h a t o r i g i n a l g l u e d e p t h was r e s t o r e d . The s e m i - a s s e m b l i e s o f t h e c o r e and one f a c i n g were s t a c k e d i n s u c h a manner t h a t t h e c o r e was p l a c e d 22 SINGLE CELL WALL L - RD = L o n g i t u d i n a l r i b b o n d i r e c t i o n W - RD = Transverse r i b b o n d i r e c t i o n T . = Honeycomb t h i c k n e s s Figure 6. Dimensional Nomenclature of Expanded Honeycomb 23 a b o v e t h e f a c i n g and p r e s s e d u n d e r a p p r o x i m a t e l y 50 p s i . f o r more t h a n 12 h o u r s a t room t e m p e r a t u r e . A f t e r r e m o v i n g t h e p r e s s u r e , t h e s e s e m i - a s s e m b l i e s were t r e a t e d w i t h t h e same d e p t h o f g l u e on t h e o t h e r edge o f t h e c o r e . The g l u e -t r e a t e d s e m i - a s s e m b l y was t h e n p l a c e d on a p r e - w e t t e d p l y w o o d m a k i n g a s a n d w i c h , and p r e s s e d i n t h e same way as b e f o r e . T h u s , a u n i f o r m f i l l e t s h a p e on b o t h e d g e s o f t h e c o r e was a c h i e v e d by a v o i d i n g t h e i n t e r f e r i n g e f f e c t s o f g r a v i t y . T e n s i l e T e s t S p e c i m e n and T e s t P r o c e d u r e T e n t e s t s p e c i m e n s f o r one f i l l e t h e i g h t g r o u p were made f r o m two r a n d o m l y c h o s e n s a n d w i c h p a n e l s b y c u t t i n g f i v e 1 by 1 i n c h s p e c i m e n s f r o m one p a n e l . A l o a d i n g b l o c k made o f 1 b y 1 b y 1 i n c h D o u g l a s f i r wood was b o n d e d t o e a c h f a c e o f t h e s p e c i m e n s u s i n g t h e same a d h e s i v e as i n t h e c o r e - t o - f a c i n g b o n d i n g . The t e s t s p e c i m e n s were s u b j e c t e d t o 70 ± 1°F and 50 ± 1% o f h u m i d i t y f o r more t h a n t e n d a y s b e f o r e t h e i n i t i a t i o n o f t e s t i n g p r o c e d u r e s . The l o a d i n g f i x t u r e was made t o meet t h e r e c o m m e n d a t i o n g i v e n i n t h e ASTM D e s i g n a t i o n C297-61 ( F i g u r e 7). A T i n i u s O l s e n u n i v e r s a l t e s t i n g m a c h i n e was u s e d t o a p p l y a l o a d t o t h e s p e c i m e n s a t a c o n s t a n t r a t e o f b a s e movement o f 0.0 2 i n c h p e r m i n u t e . The maximum s t r e n g t h i n t e n s i o n f l a t -w i s e , t h e p e r c e n t a g e o f f a c i n g f a i l u r e and t h e f i l l e t s i z e were r e c o r d e d . F i l l e t s i z e was m e a s u r e d by v e r n i e r c a l i p e r s 24 Figure 7. Tensile Test Specimen in Loading Fixture f o r the f i l l e t h eight and width at four random p o i n t s on the f a i l e d s i d e of each specimen a f t e r s e p a r a t i n g the f a c i n g from the core. The measurement of f i l l e t width was made f o r the t o t a l width around a s i n g l e c e l l w a l l i n c l u d i n g the c e l l w a l l t h i c k n e s s . Facing f a i l u r e was expressed by the per-centage of the area exposed where the f a c i n g plywood was s t r i p p e d o f f (maximum of one-ply deep) to the whole f a c i n g area. In order to o b t a i n the s t r e n g t h of adhesive f i l l e t per u n i t f i l l e t l ength the ASTM Designation C297-61 (8) i s c a l l e d f o r . F l a t w i s e T e n s i l e Strength Strength of Adhesive F i l l e t = F i l l e t Length/Unit Core Area where f i l l e t l e n g t h per u n i t core area can be found by con-s i d e r a t i o n of the core c e l l geometry. For cores w i t h hexa-gonal or square c e l l s i t has been found t h a t f i l l e t l e ngth per u n i t core area equals four d i v i d e d by the c e l l s i z e . Proof f o r a hexagonal c e l l : Let the length of a s i d e of hexagon be b (Figure 8), then Core C e l l S i z e = v ^ ~ 3 b, and Core C e l l Area = j /~~3 b . Therefore, rT . , _ , F i l l e t Length F i l l e t Length per U n i t Core Area = —r-^ —? ^ r Core C e l l Area 6b 4 4 3 / ^ , 2 , Core C e l l S i z e j / 3 b / 3 b 26 F i g u r e 8 Honeycomb C e l l S e c t i o n Hence, t h i s f i l l e t l e ngth i s the length of the core c e l l edge i n contact w i t h the f a c i n g . F l e x u r e Test Specimen and Test Procedure The remaining twenty sandwich panels from each f i l l e t h e i g h t group, e i g h t y panels f o r four f i l l e t h e i g h t groups i n t o t a l , were trimmed i n t o 3.75 by 12 inch specimens f o r f l e x u r e t e s t . Since the o b j e c t i v e of the f l e x u r e t e s t i n t h i s study was to evaluate the shear s t r e n g t h of the glu,.eline between core and f a c i n g , i t was deemed d e s i r a b l e t h a t the f a i l u r e should take place i n g l u e l i n e shear r a t h e r than i n core b u c k l i n g or shear, or f a c i n g t e n s i o n or compression. A p r e l i m i n a r y t e s t was c a r r i e d out to determine the optimum l o a d i n g system f o r the f l e x u r e specimens. Usual l o a d i n g systems f o r f l e x u r e t e s t of sandwich panels are mid-span l o a d -i n g and two-point l o a d i n g . In the l a t t e r , the l o a d i n g p o i n t s are g e n e r a l l y s e t at a quarter-span or one-third-span. Mid-span l o a d i n g has an advantage i n t e s t i n g h o r i z o n t a l shear s i n c e the f u l l span i s subjected t o shear s t r e s s , but a f a i l u r e may occur i n the f a c i n g , because the modulus of rupture of the f a c i n g i n bending i s maximum at the mid-span (Appendix 3 ) . In the case of two-point l o a d i n g , the modulus of rupture of f a c i n g i n bending decreases as the i n t e r n a l length between the two l o a d i n g p o i n t s i n c r e a s e s , but the area t h a t i s s ubjected t o h o r i z o n t a l shear s t r e s s decreases s i n c e the p o r t i o n between the two l o a d i n g p o i n t s i s not under shear s t r e s s . In the p r e l i m i n a r y t e s t s , an e f f o r t was made to f i n d the minimum i n t e r n a l length between the two l o a d i n g p o i n t s where no f a i l u r e was expected to take place i n the f a c i n g s . As a r e s u l t , a quarter-span was found t o be the most s u i t a b l e i n t e r n a l length and was employed i n t h i s experiment. The specimen was supported by two round s t e e l bars of 1 inch i n diameter at a d i s t a n c e of 1 inch from both ends of the beam. Load was a p p l i e d by a T i n i u s Olsen u n i v e r s a l t e s t i n g machine through two round s t e e l bars of the same s i z e as the supporting bars (Figure 9). The r a t e of movement of the base p l a t e of the t e s t i n g machine was 0.02 i n c h per minute. The d e f l e c t i o n s were measured by a A p p a r a t u s f o r C o n d u c t i n g F l e x u r e T e s t o f S a n d w i c h C o n s t r u c t i o n d i a l i n d i c a t o r by means of the machine base p l a t e movement. The maximum l o a d , d e f l e c t i o n at f r a c t u r e and f a i l u r e c h a r a c t e r i s t i c s were recorded f o r each specimen (Table 1). 30 RESULTS AND ANALYSIS OF DATA T e n s i l e Test Tables 2, 3, 4, and 5 show the r e s u l t s of t e n s i l e t e s t s f o r the four f i l l e t h eight groups [0.5], [1.0], [1.5], and [2.0], r e s p e c t i v e l y . The maximum load a p p l i e d t o the specimen d i r e c t l y gives the t e n s i l e s t r e n g t h i n p s i . , s i n c e the cross s e c t i o n a l area of the specimen i s 1 square i n c h . The s t r e n g t h of adhesive f i l l e t can be obtained by d i v i d i n g the t e n s i l e s t r e n g t h by the f i l l e t l e ngth per u n i t core area. For the measurement of the f i l l e t h e i g h t and w i d t h , four s i n g l e c e l l w a l l s (Figure 6 ) and corresponding f o u r f i l l e t l i n e s which were l e f t on the separated plywood were randomly chosen. A l l measurements, were made at the center of s i n g l e c e l l w a l l edges where the e f f e c t s of core c e l l geometry due t o the surface t e n s i o n system were considered to be minimum. This i s because the f a c t o r s a f f e c t i n g f i l l e t shape and s i z e at the center of s i n g l e c e l l w a l l edges were deemed to be l e s s v a r i a b l e than those at a double c e l l w a l l or around the corner of an hexagonal c e l l . The mean value of the four observations i n each specimen was computed and recorded i n Tables 2, 3, 4, and 5. Standard d e v i a t i o n s and other b a s i c f i g u r e s needed f o r 31 a n a l y s i s o f v a r i a n c e and c o r r e l a t i o n a n a l y s i s a r e r e c o r d e d i n T a b l e s 8 and 9. As t h e r e s u l t s show, t h e g l u e d e p t h e s t a b l i s h e d on t h e a p p l i c a t o r and t h e r e s u l t i n g f i l l e t h e i g h t d i d n o t a g r e e . B u t d i f f e r e n c e s b etween t h e g l u e d e p t h and t h e f i l l e t h e i g h t mean v a l u e s were n e a r l y c o n s t a n t t h r o u g h o u t a l l f i l l e t h e i g h t g r o u p s . T h e s e f a c t s i n d i c a t e t h a t t h e r e were n e a r l y c o n s t a n t g l u e e l e v a t i o n s on t h e c e l l w a l l s due t o t h e s u r f a c e t e n s i o n i n t h e l i q u i d - s o l i d s y s t e m ( T a b l e 6) . F i v e s p e c i m e n s f r o m e a c h f i l l e t h e i g h t g r o u p were r a n d o m l y s e l e c t e d f o r t h e measurement o f f r a c t u r e / f i l l e t w i d t h r a t i o ( T a b l e 7). The measurement was made on f o u r s i n g l e c e l l t r a c e s on t h e f a c i n g o f e a c h s p e c i m e n u s i n g v e r n i e r c a l i p e r s r e a d i n g t o 0.05 mm. 1. F i l l e t H e i g h t and F i l l e t W i d t h R e l a t i o n s h i p Analysis of Variance. U s i n g t h e d a t a g i v e n i n T a b l e 8, t h e e f f e c t s o f f i l l e t h e i g h t t r e a t m e n t s on f i l l e t w i d t h means were i n v e s t i g a t e d b y a n a l y s i s o f v a r i a n c e ( A p p e n d i x 1-a). The h i g h l e v e l o f s i g n i f i c a n c e o f t h e F v a l u e i n d i c a t e s t h a t t h e f i l l e t w i d t h means were n o t a l l t h e same. I n o r d e r t o a n a l y z e t h e r e l a t i o n s h i p s b e t w e e n f i l l e t w i d t h means, Duncan's New M u l t i p l e Range (N.M.R.) T e s t was c a r r i e d o u t ( A p p e n d i x 1-b). A c c o r d i n g t o Duncan's N.M.R. T e s t , t h e r e was no s i g n i f i c a n t d i f f e r e n c e b e t w e e n f i l l e t w i d t h means o f [1.5] 32 group and [2.0] group at the 5% l e v e l . The ranking of f i l l e t width means was; [0 . 5 ] < [ 1. 0 ] < [1. 5 ] , [2.0], Correlation Analysis (Based on data i n Table 9 ) . F i l l e t h e i g h t : X F i l l e t width : X„ SS = 22.4962, SS = 67.3752, SP = 28.99 x l x2 X 1 X 2 SP X X b i - - s i r - 2 = i - 2 8 9 ' b o = h ~ h i H = -°-07  x i Simple r e g r e s s i o n equation : X£ = -0.0 7 + 1.289X^ (SP ) 2 2 X 1 X 2 C o e f f i c i e n t of determination : r = ^ :— = 0.5548 X l X2 2 F = r ( n ~ 2 ) = 47.29** (n = 40) 1 - r ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and f i l l e t width was h i g h l y s i g n i f i c a n t (Figure 10). 2. F i l l e t Height and T e n s i l e Strength R e l a t i o n s h i p Analysis of Variance. Using the data given i n Table 8, the e f f e c t s of f i l l e t h e i g h t treatments on t e n s i l e s t r e n g t h means were i n v e s t i g a t e d by a n a l y s i s of variance (Appendix 2-a). The s i g n i f i c a n c e of F value i n d i c a t e s t h a t the t e n s i l e s t r e n g t h means were not a l l the same. In order to analyze the r e l a t i o n s h i p s between t e n s i l e s t r e n g t h means, Duncan's N.M.R. Test was c a r r i e d out (Appendix 2-b). According to Duncan's N.M.R. Test, there were no s i g n i f i c a n t d i f f e r e n c e i n the t e n s i l e s t r e n g t h means between [0.5] and [1.0], and between [2.0] and [1.5] at the 5% l e v e l . The ranking of t e n s i l e s t r e n g t h means was; [0.5], [1.0] < [2.0], [1.5] C o r r e l a t i o n Analysis (Based on data i n Table 9 ) . F i l l e t h e i g h t : X1 T e n s i l e s t r e n g t h : Y SS = 22.4962, SS = 7481.6, SP = 223.54 x x y x x y SP bi = s s ^ = H T 4 T T = 9" 9 3 7' bo = 5 - b A = 3 8' 0 4 Simple r e g r e s s i o n equation : Y = 38.04 + 9.94 X F i g u r e 10. F i l l e t H e i g h t a n d F i l l e t W i d t h R e l a t i o n s h i p i n T e n s i l e T e s t S p e c i m e n s 35 (SP ) 2 2 X 4 Y C o e f f i c i e n t of determination : r = g-g g^— = 0 .2969 x l " Y C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.545 F = r 2 ( n " 2 ) = 16.05** (n = 40) 1 - r ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and t e n s i l e s t r e n g t h was h i g h l y s i g n i f i c a n t (Figure 11). 3. F i l l e t Width and T e n s i l e Strength R e l a t i o n s h i p C o r r e l a t i o n Analysis (Based on data i n Table 9 ). F i l l e t width : X 2 T e n s i l e s t r e n g t h : Y SS = 67.375, SS = 7481.6, SP = 410.26 x 2 y * 2 y b x = s s * = 6.089 , b Q = Y - h± ^ = 43.30 x 2 y x Simple r e g r e s s i o n equation : Y = 43.30 + 6.09 X 2 2 (SP ) 2 X 2 Y C o e f f i c i e n t of determination : r = :—gg— = 0. 3339 x' y C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.578 T 50 • A -t-a [0.5] [1.0] [1.53 [2.0] Y « 38.04 + 9.94X, -L 1 2 3 F i l l e t Height (mm.) Figure 11. F i l l e t Height and Tensile Strength Relatlonshi 37 r 2 fn - 2) ** F = — [ — £L = 19.06. (n = 40) 1 - r ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between f i l l e t width and t e n s i l e s t r e n g t h was h i g h l y s i g n i f i c a n t (Figure 12). 4. D e f l e c t i o n at Fr a c t u r e and T e n s i l e Strength R e l a t i o n s h i p Correlation Analysis (Based on data i n Table 9). D e f l e c t i o n : X^ T e n s i l e s t r e n g t h : Y SS = 3.514, SS = 7481.6, SP = 110.69 x 3 y x 3 y SP x.y b i = S g . = 3 1 - 5 0 ' b o = Y " b i X 3 = 3 8 - 5 " X3 Simple r e g r e s s i o n equation : Y = 38.5 + 31.5 X^ (SP ) 2 2 x 3 y C o e f f i c i e n t of determination : r = ^ ss~~ = ^.466 x 3 * y C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.683 r 2 ( n - 2) ** F = —^ 7^- = 33.16 . (n = 40) 1 - r ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s the l i n e a r r e l a t i o n s h i p between d e f l e c t i o n at f r a c t u r e and • C0.5] [1.0] [1.5] [2.0] • ++ 5 0 W •P hfl d <i> CO 0) r • 43.30 + 6.09x2 CO a) 2 3 F i l l e t Width (mm.) Figure 12. F i l l e t Width and Tensile Strength Relationship 00 t e n s i l e s t r e n g t h was h i g h l y s i g n i f i c a n t (Figure 13). 5. Facing F a i l u r e and T e n s i l e Strength R e l a t i o n s h i p C o r r e l a t i o n Analysis (Based on data i n Table 9 ). Facing f a i l u r e : X^ T e n s i l e s t r e n g t h : Y SS = 1477.1, SS = 7481.6, SP = 504.4 x 4 Y * 4 y (SP ) 2 2 X 4 y C o e f f i c i e n t of determination : r = ^ ; — g ^ — = 0.023 x4 * y C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.152 2 F = r ( n ~ 2 2 ) = 0.89' n , S * (n = 40) 1 - r n.s. i n d i c a t e s n o n - s i g n i f i c a n c e at the 5% l e v e l . That i s , there was no s i g n i f i c a n t c o r r e l a t i o n between f a c i n g f a i l u r e and t e n s i l e s t r e n g t h . 6. F i l l e t Height and D e f l e c t i o n at Fr a c t u r e R e l a t i o n s h i p Correlation Analysis (Based on data i n Table 9 ) . D e f l e c t i o n : X^ F i l l e t h e i g h t : X.^  41 SS = 3.5140, SS = 22.4962, SP = 3.580 x 3 X l X 1 X 3 (SP ) 2 2 X 1 X 3 C o e f f i c i e n t of determination : r = — — = 0.162 x l x 3 C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.403 2 F = r ( n ~ 2 ) = 7.35 * (n = 40) 1 - r * i n d i c a t e s s i g n i f i c a n c e at the 5% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and d e f l e c t i o n at f r a c t u r e was s i g n i f i c a n t . F l e x u r e Test The r e s u l t s of the f l e x u r e t e s t f o r the four f i l l e t h e i g h t groups, [0.5], [1.0], [1.5], and [2.0] are given i n Tables 10, 11, 12 and 13, r e s p e c t i v e l y . The h o r i z o n t a l shear s t r e s s i n the g l u e l i n e were c a l c u l a t e d by us i n g the equation given i n Appendix 3-a. The types of f a i l u r e of the specimens at the maximum load P were not a l l a l i k e . When the f a i l u r e took place only i n the g l u e l i n e , the l o a d - d e f l e c t i o n curve showed a sudden r e l e a s e of s t r e s s i n the specimen a f t e r reaching the maximum loa d (Figure 14, [0.5]- 3, [1.0]- 14). This type of f a i l u r e was observed mostly i n the s m a l l f i l l e t groups, 42 Figure 14. Selected Load-Deflection Curves in Flexure Tests CF = Core failure GF = Glueline failure CF 0 01 0.2 DEFLECTION (INCH) [0.5] and [1.0]. When the f a i l u r e was due p a r t l y t o the g l u e l i n e f r a c t u r e and p a r t l y t o the core shear or b u c k l i n g , there was no conspicuous change of s t r e s s i n the specimen a f t e r a g l u e l i n e f r a c t u r e was observed, and the d e f l e c t i o n proceeded u n t i l a rupture occurred i n the f a c i n g . In such a case the maximum load was recorded at the f i r s t p o i n t where the g l u e l i n e f a i l u r e was observed even i f the load i n c r e a s e d s l i g h t l y a f t e r t h a t p o i n t (Figure 14, [1.5]- 3). In l a r g e r f i l l e t groups, e s p e c i a l l y i n [2.0] group, most of the specimens f a i l e d i n core shear and/or b u c k l i n g . The g l u e l i n e s of those specimens were considered t o have maintained t h e i r s t r e n g t h up to the maximum core shear s t r e s s , so the f i r s t p o i n t from which the l o a d - d e f l e c t i o n curve became p a r a l l e l t o the d e f l e c t i o n a x i s was chosen f o r determination of P (Figure 14, [2.0]- 6). The measurements of f i l l e t h e i g h t and f i l l e t width were same as those i n the t e n s i l e t e s t . The f a i l u r e types were c l a s s i f i e d i n t o CF f o r core f a i l u r e , GF f o r g l u e l i n e f a i l u r e , and FF f o r f a c i n g f a i l u r e . When a load was a p p l i e d on the sandwich beam and i f any w r i n k l e s appeared on the honeycomb core w a l l s , i t was considered t h a t a f a i l u r e took place i n the core. In most core f a i l u r e s s l a n t i n g w r i n k l e s appeared on the core w a l l s around the n e u t r a l a x i s of the sandwich beam at the outer side s of the l o a d i n g p o i n t s . In some cases core b u c k l i n g , which appeared as s l i g h t f o l d s near the g l u e l i n e , accompanied the core shear f a i l u r e s . 44 The g l u e l i n e f a i l u r e was observed as a s l i d e of the f a c i n g delamination from the core. Minor p e e l i n g damages of the surface of facin g s which sometimes accompanied the delaminations were regarded as a part of the g l u e l i n e f a i l u r e . Facing f a i l u r e s were such t h a t e i t h e r top or bottom f a c i n g was ruptured by bending at or near the center of two lo a d i n g p o i n t s . F i v e specimens from each f i l l e t h e i g h t group except [2.0] were s e l e c t e d f o r the measurement of f r a c t u r e / f i l l e t width r a t i o (Table 14). From [2.0] group the three specimens which f a i l e d i n the g l u e l i n e s were s e l e c t e d f o r the same purpose. The method of measurement was as same as th a t i n the t e n s i l e t e s t specimens. 1. F i l l e t Height and F i l l e t Width R e l a t i o n s h i p Analysis of Variance. Using the data given i n Table 15, the e f f e c t s of f i l l e t h e i g h t treatments on f i l l e t width means were i n v e s t i g a t e d by a n a l y s i s of variance (Appendix 4-a). The high l e v e l of s i g n i f i c a n c e of the F value i n d i c a t e s t h a t the f i l l e t width means were not a l l the same. In order to analyze the r e l a t i o n s h i p s between f i l l e t w i d th means, Duncan's N.M.R. Test was c a r r i e d out (Appendix 4-b) . According to Duncan's N.M.R. Test, f i l l e t width means ranked as: Figure 15. F i l l e t Height and F i l l e t Width Relationship i n Flexure Test Specimens [0 .5 ] < [1 .0 ] < [1 .5 ] < [2 .0 ] at the 1% l e v e l of s i g n i f i c a n c e . C o r r e l a t i o n Analysis (Based on data i n Table 1 5 ) . F i l l e t h eight : X x F i l l e t width : X„ SS = 5 6 . 7 8 2 , SS = 1 9 . 9 3 5 , SP = 2 9 . 7 9 0 x l x 2 X 1 X 2 SP X X b l = s s ' 1 2 = 0 -5246 , b Q = X 2 " b± X = 0 .99 X l Simple r e g r e s s i o n equation : X 2 = 0 .99 + 0 . 52 X^ ( S P x x ) 2 . . 2 1 2 C o e f f i c i e n t of determination : r = g-g ;—g-g = 0 .784 X l x 2 C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0 .886 F = r ( n ~ 2 ) = 2 8 4 * * (n = 80) 1 - r ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , there was a h i g h l y s i g n i f i c a n t l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and f i l l e t width. As the f i l l e t h eight i n c r e a s e d , so d i d the f i l l e t width (Figure 1 5 ) . 2. F i l l e t Height and Shear Strength R e l a t i o n s h i p A n a l y s i s of Variance. Using the data given i n Table 15, the e f f e c t s of f i l l e t h e i g h t treatments on shear s t r e n g t h means were i n v e s t i g a t e d by a n a l y s i s of variance (Appendix 5-a). The s i g n i f i c a n c e of F value i n d i c a t e s t h a t the shear s t r e n g t h means were not a l l the same. In order to analyze the r e l a t i o n s h i p s between shear s t r e n g t h means, Duncan's N.M.R. Test was c a r r i e d out (Appendix 5-b). There was a s i g n i f i c a n t d i f f e r e n c e i n shear s t r e n g t h means between height treatments of [1.0] and [0.5] at the 5% l e v e l according t o Duncan's N.M.R. Test, but i t was not h i g h l y s i g n i f i c a n t at the 1% l e v e l . The d i f f e r e n c e between the two groups, [1.0] and [0.5] as one group, [1.5] and [2.0] as another, was h i g h l y s i g n i f i c a n t a t the 1% l e v e l . C o r r e l a t i o n Analysis (Based on data i n Table 15). F i l l e t h e i g h t : X x Shear s t r e n g t h : Y SS = 56.782, SS = 1487.96, SP = 156.99 y x x y SP b i = ss = 2 - 7 6 5 ' b o = Y - b i x i = 4 6 - 9 x l Simple r e g r e s s i o n equation : Y = 46.9 + 2.77 X^ 2 C o e f f i c i e n t of determination : r = 0.2917 Y = 46.9 + 2.77X1 2 3 X l F i l l e t Height (mm.) Figure l 6 . F i l l e t Height and Shear Strength Relationship C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.540 F = 32.13** (n = 80) ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between f i l l e t h e i g h t and shear st r e n g t h was h i g h l y s i g n i f i c a n t (Figure 16). 3. F i l l e t Width and Shear Strength R e l a t i o n s h i p C o r r e l a t i o n Analysis (Based on data i n Table 15). F i l l e t width : X 2 Shear s t r e n g t h : Y SS = 19.935, SS = 1487.96, SP = 92.61 x 2 y x 2 y SP h1 = = 4. 646 , b Q = Y - b X 2 = 43.6 X2 Simple r e g r e s s i o n equation : Y = 43.0 + 4.65 2 C o e f f i c i e n t of determination : r = 0.2895 C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.538 F = 15.48**' (n = 80) ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between f i l l e t width and shear s t r e n g t h was h i g h l y s i g n i f i c a n t (Figure 17). Y s 43.0 + 4.65X2 2 3 F i l l e t Width (mm.) Figure 17. F i l l e t Width and Shear Strength Relationship 4. D e f l e c t i o n at F r a c t u r e and Shear Strength R e l a t i o n s h i p C o r r e l a t i o n Analysis (Based on data i n Table 15). D e f l e c t i o n at f r a c t u r e : Shear s t r e n g t h : Y SS = 141.889, SS = 1487.96, SP = 280.378 x 3 y x 3 y SP x y b l = ss 3 = 1 - 9 7 6 ' b Q = Y - b x X 3 = 45.8 x 3 Simple r e g r e s s i o n equation : Y = 45.8 + 1.98 X 3 (SP ) 2 2 x 3 y C o e f f i c i e n t of determination : r = : — ^ g — = 0. 3723 x 3 * y C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.61 F = 46.24** (n = 80) ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between d e f l e c t i o n at f r a c t u r e and shear s t r e n g t h was h i g h l y s i g n i f i c a n t . 5. F i l l e t Height and D e f l e c t i o n R e l a t i o n s h i p Analysis of Variance. Using the data given i n Table 15, the e f f e c t s of f i l l e t h e i g h t treatments on d e f l e c t i o n means at f r a c t u r e were i n v e s t i g a t e d by a n a l y s i s of va r i a n c e (Appendix 6-a). The s i g n i f i c a n c e of F value i n d i c a t e s t h a t the d e f l e c t i o n means at f r a c t u r e were not a l l the same. In 52 order t o analyze the r e l a t i o n s h i p s between d e f l e c t i o n means, Duncan's N.M.R. Test was c a r r i e d out (Appendix 6-b). According to Duncan's N.M.R. Test , there was no s i g n i f i c a n t d i f f e r e n c e between the d e f l e c t i o n means of [0.5] group and [1.0] group at the 1% l e v e l . The ranking of the d e f l e c t i o n means was; [0.5], [1.0] < [1.5] < [2.0]. C o r r e l a t i o n Analysis (Based on data i n Table 15). F i l l e t h e i g h t : X1 D e f l e c t i o n : SS = 56.782, SS = 141.889, SP = 74.222 x l x 3 X 1 X 3 SP X X b. = r._ 1 3 = 1. 307, b_ = X- - b1 X, = 0.6838 1 bb (J J 1 1 X l Simple r e g r e s s i o n equation : X^ = 0.73 + 1.307 X^ 2 C o e f f i c e i n t of determination : r = 0.6 838 C o e f f i c i e n t of l i n e a r c o r r e l a t i o n : r = 0.827 F = 168.68 (n = 80) ** i n d i c a t e s s i g n i f i c a n c e at the 1% l e v e l . That i s , the l i n e a r r e l a t i o n s h i p between d e f l e c t i o n and f i l l e t h e i g h t was h i g h l y s i g n i f i c a n t (Figure 18). a a a 1 2 3 X l F i l l e t Height (mm.) Figure 18. F i l l e t Height and Deflection Relationship i n Flexure Test Specimens w 54 D ISCUSSION F i l l e t G e o m e t r y F o r t h e t e n s i l e t e s t s p e c i m e n s , t h e r e was no s i g n i f i -c a n t d i f f e r e n c e i n f i l l e t w i d t h b e t w e e n t h e f i l l e t h e i g h t t r e a t m e n t s o f [ 1 . 5 ] and [ 2 . 0 ] , F o r t h e f l e x u r e t e s t s p e c i m e n s , h o w e v e r , e a c h o f t h e f o u r h e i g h t t r e a t m e n t s was s i g n i f i c a n t l y d i f f e r e n t i n f i l l e t w i d t h . C o n s i d e r i n g t h e f a c t t h a t t h e t e n s i l e t e s t s p e c i m e n s o f one f i l l e t h e i g h t g r o u p w e r e c u t f r o m o n l y t w o o r i g i n a l s a n d w i c h p a n e l s , w h i l e t h e f l e x u r e t e s t s p e c i m e n s o f one f i l l e t h e i g h t g r o u p w e r e made f r o m t w e n t y d i f f e r e n t s a n d w i c h p a n e l s , t h e i n f e r e n c e b a s e d on t h e f l e x u r e t e s t s p e c i m e n s w i l l b e more r e l i a b l e a s f a r a s g e n e r a l d i s c u s s i o n o n f i l l e t h e i g h t a n d f i l l e t w i d t h r e l a t i o n s h i p i s c o n c e r n e d . A s was shown i n t h e p r e v i o u s c h a p t e r , t h e r e was a h i g h l y s i g n i f i c a n t l i n e a r c o r r e l a t i o n b e t w e e n f i l l e t h e i g h t a n d f i l l e t w i d t h i n "both t y p e s o f s p e c i m e n when a l l t h e o b s e r v a t i o n s w e r e c o n s i d e r e d t o be i n d e p e n d e n t . H o w e v e r , i f t h e t r e a t m e n t means o f f i l l e t h e i g h t a n d f i l l e t w i d t h i n t h e f l e x u r e t e s t s p e c i m e n s a r e t a k e n i n t o c o n s i d e r a t i o n , a p a r a b o l i c c u r v e X1 = - 0.06 X 2 + ° ' 5 ( X 2 " fc> , 0.8 < X 2 _< 2.9 can be f i t t e d , where and X^ denote the f i l l e t h e i g h t and the f i l l e t width, r e s p e c t i v e l y , and t denotes the t h i c k n e s s of the honeycomb paper. The boundary c o n d i t i o n s of X^ were obtained by extending the sequence of experimental data of X 2 1 s t o both l i m i t s (Appendix 7). The minimum f i l l e t width (X^ = 0.80) and height (X^ = 0.30) given i n Appendix 7 are e x p l a i n e d i n the f o l l o w i n g d i s c u s s i o n . When a honeycomb c e l l w a l l edge i s placed on a l i q u i d glue surface (glue depth = 0.00), the glue w i l l be p u l l e d up on the c e l l w a l l by the surface f r e e energy u n t i l the e q u i l i b r i u m i n l i q u i d - s o l i d system i s reached. This h e i g h t w i l l be 0.3 mm. When t h i s c e l l w a l l i s placed on the pre-wetted plywood, the glue attached around the c e l l w a l l edge w i l l flow sideways by the surface t e n s i o n and the mechanical f o r c e of the c e l l w a l l movement toward the f a c i n g . The t o t a l width of these flows on both s i d e s of the c e l l w a l l w i l l be 0.8 mm. Then, the f i l l e t width on one s i d e of the c e l l w a l l e x c l u d i n g the c e l l w a l l t h i c k n e s s i s 0.3 mm. I f the c e l l w a l l i s dipped into the glue for 1.40 mm. f o r example, the c e l l w a l l becomes wetted t o a height of 1.40 + 0.30 = 1.70 mm. The f i l l e t width i n t h a t case w i l l be 1.90 mm. S i m i l a r l y , the maximum width of the f i l l e t can be estimated as X^ = 2.90 by extending the sequence to the upper l i m i t . As t h i s p o i n t the f i l l e t height w i l l be 4.5 mm. or higher. This means t h a t the f i l l e t width w i l l not become l a r g e r than 2.9 mm. even though the f i l l e t h e i g h t may be l a r g e r than 4.5 mm. 56 Grimes (16) suggested t h a t a l a r g e f i l l e t i s d e f i n e d as one whose width i s equal to r/2, where r i s the core c e l l s i z e ; s i m i l a r l y the width of medium f i l l e t i s r/3, and the width of s m a l l f i l l e t i s r/4. Since the ra d i u s of honeycomb c e l l used i n t h i s t h e s i s i s 3/8 i n c h , or 4.7 mm., l a r g e f i l l e t width becomes r/2 = 2.4 mm., medium f i l l e t width i s r/3 = 1.6 mm., and s m a l l f i l l e t width i s r/4 = 1.2 mm. The f i l l e t width on one side of the c e l l w a l l , i . e . (X 2 -0.25)/2, f o r the four f i l l e t h e i g h t groups are; [0.5] i (1. 37 -- 0 .25)/2 = 0.56 [1.0] (2. 58 -- 0 .25)/2 = 1.17 [1.5] : (3. 80 -- 0 .2 5)/2 = 1.78 [2.0] : (3. 84 -- 0 .25)/2 = 1.80 Therefore, according t o the c l a s s i f i c a t i o n by Grimes, the f i l l e t s i n [1.5] and [2.0] belong t o the medium f i l l e t group, w h i l e [1.0] belongs t o the small f i l l e t . The f i l l e t width i n [0.5] group i s approximately one-half of the s m a l l f i l l e t w i d th. F i l l e t geometry at a j o i n t of honeycomb and plywood cannot be determined by the f i l l e t h eight and width o n l y . The shape of f i l l e t i s a l s o an important f a c t o r . When a g l u e - t r e a t e d honeycomb was placed on a plywood surface the f i l l e t s urface was convex at f i r s t , but i t changed i n t o concave w i t h the passage of time. This may be p a r t l y due t o the change of surface tensions between the l i q u i d and s o l i d s t h a t was induced by the glue d i f f u s i o n i n t o the honey comb w a l l and plywood. The shrinkage of the glue body which took place as a r e s u l t of glue s o l i d i f i c a t i o n i s probably c o n t r i b u t i n g to the change of surface shape, too. Although no numerical measurement was made f o r determining the curve of f i l l e t s u r f a c e s , i t was assumed f o r f u r t h e r a n a l y s i s t h a t every concave curve was forming a part of a c i r c l e as i l l u s t r a t e d i n Figure 19 - (A). The type of adhesive used i n t h i s experiment was a modified p h e n o l i c - r e s o r c i n o l r e s i n as was mentioned e a r l i e This was a commercially blended adhesive and no d e t a i l of the formula was o b t a i n a b l e , n e v e r t h e l e s s i t i s assumed t h a t the adhesive c o n s i s t e d of a r e s o l e based p h e n o l i c and r e s o r c i n o l formaldehyde r e s i n s from i t s property of water s o l u b i l i t y (43, 54). I f so, the glue should c o n t a i n some water f o r a d i s p e r s i n g agent. A small amount of water i s a l s o r e l e a s e d by the condensation p o l y m e r i s a t i o n r e a c t i o n i n both p h e n o l i c and r e s o r c i n o l r e s i n s (32). Only scant experimental proof e x i s t s f o r the reason of bubble or v o i d formation i n a s o l i d i f i e d glue of any type (8), but water i s one of the l i k e l y main causes of v o i d formation. Some f i l l e t s i n the specimens of [2.0] group had a r e l a t i v e l y l a r g e c a v i t y beneath the t h i n glue s k i n which was forming the outward surface of the f i l l e t . This f a c t may e x p l a i n the reason why f i l l e t shear s t r e n g t h of [2.0] F i g u r e 1 9 . D i m e n s i o n a l N o m e n c l a t u r e on F i l l e t S e c t i o n a n d S h e a r S t r e s s D i s t r i b u t i o n 59 was not l a r g e r than t h a t of [1.5] i n s p i t e of the l a r g e r s i z e i n f i l l e t h eight and w i d t h , f o r voids and bubbles i n a s o l i d i f i e d adhesive l a y e r are the major f a c t o r s which cause weakening of t o t a l g l u e l i n e s t r e n g t h (8). T e n s i l e Strength A s i g n i f i c a n t d i f f e r e n c e i n t e n s i l e s t r e n g t h was found between the low f i l l e t groups of [0.5], [1.0] and the high f i l l e t groups of [1.5], [2.0], as s t a t e d e a r l i e r . Between [1.5] and [2.0], there was no s i g n i f i c a n t d i f f e r e n c e i n e i t h e r f i l l e t width or t e n s i l e s t r e n g t h . Hence, these two can be t r e a t e d as one group. In s p i t e of the s i g n i f i c a n t d i f f e r e n c e i n f i l l e t width between [0.5] and [1.0], there was no s i g n i f i c a n t d i f f e r e n c e i n t e n s i l e s t r e n g t h between them. By observing the f r a c t u r e l i n e s i n the specimens a f t e r the t e n s i l e t e s t , i t was found t h a t most of the f r a c t u r e took place by t e n s i l e f a i l u r e i n the j o i n t of paper honeycomb and plywood plus shear f a i l u r e i n the f i l l e t . The shear f r a c t u r e was approximately p e r p e n d i c u l a r to the f a c i n g . In order to examine how f i l l e t s are c o n t r i b u t i n g to the t o t a l g l u e l i n e s t r e n g t h the s t r e s s d i s t r i b u t i o n and rupture p o i n t should be known. F i l l e t shape i s assumed to be symmetrical with respect to the c e l l w a l l , and a n a l y s i s w i l l be c a r r i e d out f o r f i l l e t on one s i d e of the c e l l w a l l . For the purpose of mathematical e x p r e s s i o n , the f a c i n g surface i s taken as X-axis and the c e l l w a l l i s taken as Y-axis (Figure 19 - A). I f a t e n s i l e l o ad P per u n i t f i l l e t l e ngth i s a p p l i e d to the c e l l w a l l , the g l u e l i n e OA w i l l be subjected to the t e n s i l e s t r e s s : X 1 P ° = 2iqTt •••• [ 1 ] At the same time v e r t i c a l shear s t r e s s i s d i s t r i b u t e d i n the f i l l e t as shown i n Figu r e 19 - ( B ) . The magnitude of the shear s t r e s s at p o i n t B, x-distance from 0, i s p x, x x = £. . _ r 21 B 2 x n "* * ' I f the concave face of a f i l l e t i s assumed to be a quar t e r p o r t i o n of a c i r c l e w i t h r a d i u s x^ then the f i l l e t h e i g h t y at B i s expressed by: y = x 1 - /2x 1x - x^ .... [3] Let R be the r a t i o of f r a c t u r e width* X f t o the f i l l e t width X w, then x = (R X 2 - t ) / 2 [4] and x± = (X 2 - t ) / 2 [5] * The d i s t a n c e between the shear f a i l u r e p o i n t s , B and D (Figure 19 - A). S u b s t i t u t i n g the values of R (Table 7) and X^ (Table 8) i n t o [4] and c a l c u l a t i n g the r a t i o , x/x^, i t i s found t h a t x/x^ becomes constant f o r a l l f i l l e t h e i g h t groups; i . e . x = 0 . 3 x 1 . . . . [ 6 ] S u b s t i t u t i n g [6] i n t o [ 3 ] , i t i s determined t h a t y = 0.3 x x y = x .... [7] This r e s u l t shows th a t the shear f a i l u r e p o i n t on the f i l l e t s u r face was the center of the concave (the p o i n t C i n Figur e 19 - A). S u b s t i t u t i n g [6] i n t o [ 2 ] , x = 0.35 P J3 Since P i s p r o p o r t i o n a l to Y, T_, i s p r o p o r t i o n a l t o Y, too. Therefore, x can be expressed as: TB = kY [8] where k i s a constant. In order to examine whether or not the shear s t r e n g t h of f i l l e t i s p r o p o r t i o n a l to y, the 62 hypothesis x_, = my, where m i s a constant, w i l l be t e s t e d . o From [ 8 ] , Td = my = kY , JO then y = — Y , 1 m ' or ^ = c , where c i s a constant. Y But, the r e s u l t s of c a l c u l a t i o n of — x 100 f o r [ 0 . 5 ] , [ 1 . 0 ] , Y [ 1 .5 ] and [ 2 .0 ] were 0 . 3 4 4 , 0 . 6 3 2 , 0 .731 and 0 . 7 9 5 , respec-t i v e l y . That i s , Y then T_, 7^  my or, the shear s t r e n g t h of the f i l l e t at p o i n t B was not pro-p o r t i o n a l t o the f i l l e t h e i g h t at B. Moreover, ^ in c r e a s e d Y as e i t h e r f i l l e t width or f i l l e t h e i g h t i n c r e a s e d . The value ^ x 100 i s a parameter which i n d i c a t e s the weakness of Y f i l l e t under the v e r t i c a l shear s t r e s s . Although the shear s t r e n g t h was not d i r e c t l y propor-t i o n a l t o y, i t d i d not i n d i c a t e the l a c k of l i n e a r r e l a t i o n -s h i p between the shear s t r e n g t h and y. Suppose there i s a l i n e a r r e l a t i o n s h i p between them, then T b = m y + d . . . . [9] where d i s a constant. S u b s t i t u t i n g [9] i n t o [ 8 ] , 63 k Y m Taking — = 0.22* and s u b s t i t u t i n g the values of Y and y f o r each f i l l e t h e i g h t group, the values of — are found t o be n e a r l y constant (Appendix 8). This s u b s t a n t i a t e s the hypothesis [ 9 ] . These r e s u l t s r e v e a l t h a t , when a t e n s i l e l o ad normal to a sandwich f a c i n g i s g i v e n , a f i l l e t rupture occurs i n v e r t i c a l shear at the center of the f i l l e t concave face and i n t e n s i o n at or near the j o i n t between adhesive and the f a c i n g , and t h a t the shear s t r e n g t h of the f i l l e t i n c r e a s e s as the f i l l e t h e i g h t i n c r e a s e s under the r e l a t i o n s h i p : The absence of s i g n i f i c a n t d i f f e r e n c e i n t e n s i l e s t r e n g t h between [1.5] and [2.0] may be owing t o the la c k of s i g n i f i c a n t d i f f e r e n c e i n f i l l e t s i z e between them. The m k T = my + d, where 0 < m < 1 and d > 0 absence of s i g n i f i c a n t d i f f e r e n c e i n t e n s i l e s t r e n g t h between [0.5] and [1.0] cannot be e x p l a i n e d . * From [1.0] and [1.5], 0.348 + d/m 0.531 + d/m t • 54.9 72.6 d/m = 0.22 Although there was a h i g h l y s i g n i f i c a n t c o r r e l a t i o n between d e f l e c t i o n at f rac ture and t e n s i l e s trength , glue f i l l e t s are not considered as the main fac tor c o n t r i b u t i n g to the d e f l e c t i o n . The e longat ion i n the composite of plywood and paper honeycomb may be the main f a c t o r . The proposed reasons are: (a) The magnitude of d e f l e c t i o n was greater than the f i l l e t he ight . The f i l l e t cannot elongate so much as i t s he ight , s ince i t i s so b r i t t l e that i t breaks by shear before i t elongates that much. (b) I t i s supposed that s tresses i n e i t h e r plywood or honeycomb d i d not exceed the p r o p o r t i o n a l l i m i t . That i s , the d e f l e c t i o n of plywood or honeycomb was p r o p o r t i o n a l to the t e n s i l e l o a d . Hence the l i n e a r c o r r e l a t i o n between the t e n s i l e strength and the d e f l e c t i o n of the specimen was h i g h l y s i g n i f i c a n t . The type of fac ing f a i l u r e was such that the plywood edge s p l i t p a r a l l e l to the gra in to the depth of the inner face p l y . The average percentages of fac ing f a i l u r e were 1.2% for [0.5] as the lowest and 9.2% for [1.0] as the h ighes t . Since these values are comparatively low, i . e . l e s s than 10%, the fac ing f a i l u r e i s not considered as a s i g n i f i c a n t fac tor for the ana lys i s of f i l l e t funct ions . This fac t i s a l so supported by the c o r r e l a t i o n a n a l y s i s . Shear Strength According t o the data p u b l i s h e d by Hexcel, Inc. the shear s t r e n g t h of the honeycomb used f o r t h i s t h e s i s was 70 p s i . (perpendicular t o ribbon d i r e c t i o n ) . By using the formula f o r determination of core shear s t r e s s ( 4 ) , the maximum load f o r f l e x u r e t e s t i s approximated as f o l l o w s i s . P i , (h + c)b where S = 70 p s i . , h = 1.5 i n c h , c = 1.0 i n c h , b = 3.75 in c h and = load i n l b s . by mid-span l o a d i n g . P x = S(h + c)b = 656.25 (lbs.) . This means t h a t the sandwich panel specimen w i l l f a i l by core shear i f the f l e x u r e l o ad exceeds 656 l b s . by mid-span l o a d -i n g . The value of P w i l l i n c r e a s e t o some extent (P 2 = 685) under the l o a d i n g method p r a c t i s e d i n t h i s t h e s i s (Appendix 9). As the data show (Tables 10, 11, 12, 13) no f l e x u r e load exceeded 600 l b s , n e v e r t h e l e s s most of the specimens of l a r g e r f i l l e t groups, i . e . [1.5] and [2.0], f a i l e d i n core shear before g l u e l i n e f a i l u r e took p l a c e . This might be due to the lack of e x t r a c a u t i o n taken during pressure c o n t r o l f o r the higher f i l l e t groups. When paper honeycomb i s wetted by glue i t becomes much s o f t e r than i n the dry c o n d i t i o n . The paper honeycomb t r e a t e d w i t h t h e d e e p e r g l u e s p r e a d h a d a l a r g e r w e t a n d s o f t p o r t i o n t h a n t h o s e t r e a t e d w i t h s h a l l o w e r s p r e a d s . T h e r e -f o r e , t h e h i g h e r f i l l e t g r o u p s h a d a g r e a t e r c h a n c e f o r b u c k l i n g i f t h e same p r e s s i n g l o a d i s g i v e n t o t h e a l l f i l l e t g r o u p s d u r i n g t h e c u r i n g p r o c e s s . The p r e s s u r e was a p p r o x -i m a t e l y 50 p s i . r e g a r d l e s s o f t h e g l u e h e i g h t g r o u p . How-e v e r , t h e p r e s s u r e g a u g e was n o t s u f f i c i e n t l y s e n s i t i v e i n c o n t r o l b e l o w 100 p s i . , h e n c e t h e s a n d w i c h p a n e l s o f t h e h i g h e r f i l l e t g r o u p s m i g h t h a v e b e e n o v e r p r e s s e d b e y o n d t h e i r p r o p o r t i o n a l l i m i t s i n t h e w e t c o n d i t i o n . E v e n t h o u g h t h e f a i l u r e w e r e i n v i s i b l e , o n c e t h e p a p e r honeycomb was o v e r -p r e s s e d i t w o u l d n o t b e a b l e t o show i t s i n h e r e n t s t r e n g t h when a s h e a r o r c o m p r e s s i v e l o a d was s u b s e q u e n t l y a p p l i e d . I n s p i t e o f t h e c o r e f a i l u r e s i n t h e h i g h e r f i l l e t g r o u p s , h i g h l y s i g n i f i c a n t c o r r e l a t i o n s w e r e f o u n d b e t w e e n f i l l e t h e i g h t a n d s h e a r s t r e n g t h , a n d b e t w e e n f i l l e t w i d t h a n d s h e a r s t r e n g t h . The mean s h e a r s t r e n g t h o f [ 1 . 0 ] was l e s s t h a n t h a t o f [ 0 . 5 ] a t t h e 5% l e v e l o f s i g n i f i c a n c e . The c a u s e f o r t h i s p a r t i c u l a r c a s e i s unknown. I f t h e f i l l e t h e i g h t g r o u p s a r e c l a s s i f i e d i n t o s m a l l a n d medium f i l l e t , a s d i s c u s s e d i n t h e f i r s t s e c t i o n o f t h i s c h a p t e r , t h e r e r e m a i n s no d i f f i c u l t y i n t h e i n t e r p r e t a t i o n o f t h e s t a t i s t i c a l d a t a . T h a t i s , t h e h o r i z o n t a l s h e a r s t r e n g t h i n s a n d w i c h c o n s t r u c t i o n i s a f f e c t e d b y t h e f i l l e t s i z e . The l a r g e r f i l l e t c a r r i e s more s h e a r s t r e s s t h a n d o e s t h e s m a l l e r f i l l e t . 67 The appearance of the f a i l u r e i n the g l u e l i n e was s i m i l a r to that i n the t e n s i l e t e s t . The r a t i o x / x 1 f o r the f i l l e t h eight groups of [0.5], [1.0], [1.5] and [2.0] '.are c a l c u l a t e d as 0.24, 0.27, 0.28 and 0.27, r e s p e c t i v e l y . I f i t i s assumed t h a t the concave face of the f i l l e t was the q u a r t e r p o r t i o n of a c i r c l e w i t h r a d i u s xx, then the f r a c t u r e i s considered to have taken place by breaking the f i l l e t v e r t i c a l l y at the middle p o i n t s of the concave face on both s i d e s of the c e l l w a l l and the glue-plywood j o i n t between them. The l a t t e r was due t o the shear f o r c e , w h i l e the former was regarded as a r e s u l t of the combination of compression, t e n s i o n and shear f o r c e s . More a c c u r a t e l y , the glue-plywood j o i n t was a l s o c a r r y i n g t e n s i l e s t r e s s because of the d e f l e c t i o n (14). 68 SUMMARY AND CONCLUSION When the modified phenolic-resorcinol r e s i n glue was used f o r bonding k r a f t paper honeycomb to plywood to make a sandwich construction, f i l l e t s were formed around the j o i n t s of honeycomb and plywood. F i l l e t s i z e was measured i n terms of i t s height and width. I t was found that the cores treated with heavier glue spread produced higher and wider f i l l e t s , and the c o r r e l a t i o n between f i l l e t height and width was highly s i g n i f i c a n t . The surface shape of f i l l e t was convex at f i r s t , but i t changed into concave as glue s o l i d i f i -cation proceeded. This phenomenon was true regardless of f i l l e t s i z e . However, some f i l l e t s i n large f i l l e t groups, e s p e c i a l l y i n [2.0] group, had a r e l a t i v e l y large void underneath a t h i n glue surface. I t i s well known that voids i n a s o l i d i f i e d adhesive layer are one of the major factors to decrease the t o t a l glueline strength. This f a c t w i l l probably apply to f i l l e t as w e l l . Hence a too large f i l l e t may s u f f e r a weakening e f f e c t from void formation. In the t e n s i l e t e s t most of the fractures were observed at the glue-plywood j o i n t by the t e n s i l e f a i l u r e and at the middle of the f i l l e t concave face by the v e r t i c a l shear. This tendency was encountered regardless of the f i l l e t height group. 69 The v e r t i c a l shear stre n g t h at the f r a c t u r e l i n e i n a f i l l e t can be expressed as: T f i = my + d , where i s the shear stre n g t h at the f r a c t u r e p o i n t B, y i s the f i l l e t height at B, m and d are constants. This means t h a t the v e r t i c a l shear stre n g t h of a f i l l e t at the f r a c t u r e p o i n t B increases as the f i l l e t h e i g h t at B incr e a s e s by the r a t i o of m. The value of m, which i s grea t e r than zero and l e s s than one, can be obtained e m p i r i c a l l y . The value of d i s approximately equal t o 0.22 x m. I f there e x i s t s a v o i d i n the f i l l e t , however, m w i l l assume a much sma l l e r value than the c a l c u l a t e d value based on the a n a l y s i s . I t was a l s o noted t h a t , i n the use of paper honeycomb as the core f o r a s t r u c t u r a l sandwich con-s t r u c t i o n , the r i g h t pressure f o r the assembly should be c a r e f u l l y s t u d i e d s i n c e the core, when i t i s wet w i t h g l u e , tends to f a i l i n shear or compressive b u c k l i n g more e a s i l y than when i t i s dry. In g e n e r a l , a l a r g e r f i l l e t withstands bigger l o a d . But, as f a r as the adhesive used i n t h i s t h e s i s i s concerned, the r a t e of increase of f i l l e t s t r e n g t h decreases as the f i l l e t s i z e i n c r e a s e s . I t was p r e v i o u s l y pointed out t h a t too l a r g e a f i l l e t i s apt t o produce voids w i t h i n i t , r e s u l t i n g i n lowering s t r e n g t h values. Such a f i l l e t 70 dimi n i s h e s the c h a r a c t e r i s t i c s t r e n g t h of i t s s i z e . There-f o r e , too l a r g e a f i l l e t i s not e f f i c i e n t f o r good bonding, not only f o r economical reasons, but a l s o by t e c h n i c a l i n t e r f e r e n c e . 71 BIBLIOGRAPHY 1. Anderson, L.O. 1964. A review of FPL s t u d i e s on s t r e s s e d - s k i n and sandwich-panel u n i t s . For. Prod. J . 14 (5) : 192-194. 2. (Anonymous). 1969. P a i n t t h i c k n e s s . J o u r n a l of P a i n t Technology. V o l . 41. No. 533. June: 375pp. 3. ASTM Committee. 1963. Adhesion of coatings of p a i n t , v a r n i s h , l a c q u e r , and r e l a t e d products. ASTM Designation: D2197-63. 4. . 1961. Flexure t e s t of f l a t sandwich c o n s t r u c t i o n s . ASTM Designation: C39 3-62. 1961. Standard d e f i n i t i o n s of terms r e -l a t i n g t o s t r u c t u r a l sandwich c o n s t r u c t i o n s . ASTM Des i g n a t i o n : C274-53. 1965. Standard methods of producing f i l m s of uniform t h i c k n e s s of p a i n t , v a r n i s h , l a c q u e r , and r e l a t e d products on t e s t panels. ASTM Des i g n a t i o n : D823-53. . 1961. Shear t e s t i n f l a t w i s e plane of f l a t sandwich c o n s t r u c t i o n s or sandwich cores. ASTM Des i g n a t i o n : C273-61. 1961. Tension t e s t of f l a t sandwich con-s t r u c t i o n s i n f l a t w i s e plane. ASTM Designation: C297-61. 9. Bikerman, J . J . 1961. The Science of Adhesive J o i n t s . Academic Pr e s s , New York, pp. 128-133. 10. B u i l d i n g Research I n s t i t u t e . 1958. Adhesives and Sealants i n B u i l d i n g . N a t i o n a l Research C o u n c i l , Washington, D.C, 12 3pp. 11. Cagle, C V . 1968. Honeycomb and sandwich c o n s t r u c t i o n . Adhesive Bonding. McGraw-Hill, New York, pp. 70-84. 12. D i e t z , A.G.H. 1969. Composite Engineering Laminates. The M.I.T. Pre s s , Cambridge, Massachusetts, 70pp. 13. E i c k n e r , H.W. 1947. D u r a b i l i t y of glued j o i n t s between aluminum and end-grain b a l s a . U.S. For. Prod. Lab. Rep. 1566. 72 14. Gray, V.R. 1962. The w e t t a b i l i t y of wood. For. Prod. J . 12(9): 452-461. 15. Grimes, G.C. .1966. The adhesive-honeycomb r e l a t i o n -s h i p . A p p l i e d Polymer Symposia No. 3. S t r u c t u r a l Adhesives Bonding. I n t e r s c i e n c e P u b l i s h e r s , New York, pp. 157-190. 16. Heebink, B.G., and Mohaupt, A.A. 1947. I n v e s t i g a t i o n of methods of i n s p e c t i n g bonds between cores and faces of sandwich panels of the a i r c r a f t type. U.S. For. Prod. Lab. Rep. 1569. 17. Heebink, B.G. 1950. M o i s t u r e - e x c l u d i n g e f f e c t i v e -ness of edge se a l s f o r a i r c r a f t sandwich panels. U.S. For. Prod. Lab. Rep. 1822. 18. Hexcel, Inc. 1970. Non-combustible k r a f t paper honey-comb. S p e c i f i c a t i o n Grade D.S. 1007 (1970). Hexcel, Inc., Long Beach, C a l i f o r n i a . 19. Houwink, R., and Salmon, G. 1967. Adhesion and Adhesives. V o l . 2. E l s e v i e r P u b l i s h i n g Co. , Amsterdam, pp. 361-362, and pp. 533-536. 20. Humke, R.K. 1958. S e l e c t i o n guide f o r sandwich-panel core m a t e r i a l s . Product Engineering. January 20: 70-75. 21. . 1958. S e l e c t i o n guide f o r sandwich-panel adhesives. Product Engineering. May 26: 56-60. 22. Hunt, W.D. 1958. The Contemporary C u r t a i n W a l l . F.W. Dodge C o r p o r a t i o n , pp. 309-335. 23. Japanese Government Forest Experiment S t a t i o n . 1960. Handbook of Wood Industry. Maruzen P u b l i s h i n g Co., Tokyo, pp. 357-420. 24. Kommers, W.J. 1944. The f l e x u r a l r e s i d i t y of a r e c t a n g u l a r s t r i p of sandwich c o n s t r u c t i o n . U.S. For. Prod. Lab. Rep. 1505-A. 25. Kuenzi, E.W. 1966. A n i s o t r o p i c Sandwich C o n s t r u c t i o n s . ASTM STP" 40 5 : 14pp. 26. . 1949 . E f f e c t of e l e v a t e d temperatures on the strengths of small specimens of sandwich con-s t r u c t i o n of the a i r c r a f t type. U.S. For. Prod. Lab. Rep. 1804. 27. . 1951. Flexure of s t r u c t u r a l sandwich c o n s t r u c t i o n . U.S. For. Prod. Lab. Rep. 1829. 73 28. Lewis , W.C. 1 9 4 6 . Fatigue of sandwich construct ions for a i r c r a f t . U .S . F o r . Prod. Lab. Rep. 1559. 29. Muto, K . , T s u j i i , S . , and Umemura, T . 1959. Kenchiku Kozo Rikigaku (S truc tura l Mechanics i n A r c h i t e c t u r e ) . Ohm C o . , Tokyo. 30. Panek, E . , and Heebink, B . G . 1948. Repair of a i r c r a f t sandwich cons truc t ions . U . S . F o r . Prod. Lab. Rep. 1 5 8 4 . 31. Parker , R . S . R . , and T a y l o r , P. 1966. Adhesion and Adhesives . Pergamon Press , Oxford, pp. 76-92. 32. Patton, T . C . 1964. Paint Flow and Pigment D i s p e r s i o n . Intersc ience P u b l i s h e r s , New York, pp. 435-415. 33. P i e r c e , P . E . 1969. Rheology of coat ings . Journa l of Paint Technology. V o l . 41, No. 533, June: 383pp. 34. Plantema, F . F . 1966. Sandwich Cons truc t ion . John Wiley & Sons, I n c . , New York, pp. 55-77. 35. Plywood Manufacturers A s s o c i a t i o n of B . C . (Undated). Plywood design fundamentals. F i r Plywood Reference Manual. Plywood Manufacturers A s s o c i -a t ion of B . C . , Vancouver. 36. S c o f i e l d , W . F . , and O ' B r i e n , W.H. 1 9 6 3 . Modern Timber Engineer ing . Southern Pine A s s o c i a t i o n . New Orleans , pp. 88-94. 37. Timoshenko, S . , and Goodier, J . N . 1951. Theory of E l a s t i c i t y . 2nd E d . Kogakusha Co.,Tokyo/ pp. 140-142. 38. U . S . Forest Products Laboratory . 19 50. Methods for conducting mechanical tes ts of sandwich construc-t ions at normal temperature. U . S . F o r . Prod. Lab. Rep. 1556 (Revised). 39. . 1955. S t r u c t u r a l design of sandwich construc-t i o n . Wood Handbook. A g r i c u l t u r e Handbook No. 72? 291-298. 40. Weibel , E . E . 1 9 3 4 . American Society of Mechanical Engineers - Transac t ions . V o l . 56. 41. Weiss, P . , Berry , J . P . , and Bueche, A . M . 1962. Adhesion and Cohesion. E l s e v i e r Publ i sh ing C o . , New York, i pp. 18-35. 42. Wood, L.W. 1 9 5 8 . Sandwich panels for b u i l d i n g construc-t i o n . U . S . F o r . Prod. Lab. Rep. 2121. 74 TABLES Table 1. Partial Results of Preliminary Test for Determination of Loading System F i l l e t Height [2.0] Blank flax. Load Failure Max. Load Failure Two-Point Loading I = l A 5^7 lbs. Glueline shear 563 lbs. Facing tension Mid-Span Loading i ' = o 457 lbs. Facing tension 380 lbs. Facing tension Table 2 . Results of Tensile Test for F i l l e t Height Group [ 0 . 5 ] Sample Tensile Strength p s i . Deflec-tion mm. F i l l e t Height mm. F i l l e t Width mm. F.F. No. 1 2 3 4 Mean 1 2 3 4 Mean % 1 3 9 0 . 2 3 1 . 2 0 1.40 1.40 1 . 0 5 1 . 2 6 1 . 4 5 1 . 1 0 1 . 1 5 0 . 9 5 1 . 1 6 0 2 40 0 . 2 5 0 . 9 5 1 . 4 5 1 . 5 0 1 . 2 5 1 . 2 9 1 . 3 0 1 . 2 0 1 . 5 0 1.40 1 . 3 5 0 3 46 0 . 2 0 1 . 1 0 1 . 3 5 1 . 2 0 1 . 1 0 1 . 1 9 1 . 1 0 1 . 2 5 1 . 2 5 1 . 2 0 1 . 2 0 0 4 5 1 0.48 0 . 9 0 1 . 5 5 1 . 2 5 1 . 3 0 1 . 2 5 1 . 3 5 1 . 5 0 1 . 3 0 1 . 2 0 1 . 3 ^ 0 5 46 O . 3 6 1 . 4 5 1 . 4 5 1 . 4 5 1.40 1 . 4 4 1 . 7 5 1 . 7 5 1 . 6 0 1 . 6 5 1 . 6 9 0 6 4 3 0 . 6 3 1 . 4 5 1 . 1 5 1 . 0 0 1 . 1 5 1 . 1 9 1.40 1 . 1 0 1 . 2 5 1 . 3 0 1 . 2 6 0 7 5 2 0 . 5 6 1 . 4 5 1 . 3 5 1 . 2 5 1 . 1 0 1 . 2 9 1 . 3 0 1 . 2 5 1 . 6 0 1.40 1 . 3 9 0 8 5 2 1 . 0 2 1 . 3 0 1 . 5 0 1 . 7 0 1 . 3 0 1 . 4 5 1 . 5 5 1 . 5 0 1 . 7 0 1 . 6 5 1 . 6 0 0 9 6 2 0 . 5 1 0 . 9 5 1 . 3 0 1 . 2 0 • 1 . 1 5 1 . 1 5 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 . 2 0 1 2 1 0 5 4 0 . 3 8 1 . 2 0 1.40 1 . 3 5 1 . 0 0 1.24 1 . 4 5 1 . 5 0 1 . 3 5 1 . 6 0 1.48 0 Mean 48 . 5 0 . 4 6 2 1 . 2 7 5 1 . 3 6 7 1 . 2 F.F. = Facing Failure Table 3. Results of Tensile Test f o r F i l l e t Height Group [1.0] Sample Tensile Strength p s i . Deflec-t i o n mm. F i l l e t Height mm. F i l l e t Width mm. F.F. No. 1 2 3 4 Mean 1 2 3 4 Mean % 1 77 0.53 2.00 2.20 2.20 2.00 2.10 4.60 3.20 3.35 2.80 3.^9 8 2 65 1.22 2.00 2.25 2.20 1.95 2.10 1.85 2.35 1.80 2.05 2.01 10 3 50 0.81 1.80 2.15 2.20 2.45 1.90 2.50 2.40 2.55 2.60 2.51 12 4 41 0.33 1.80 1.60 2.00 1.50 1.73 2.20 2.00 2.05 2.05 2.08 24 5 60 0.74 2.20 1.85 1.95 1.95 1.99 2.80 2.40 2.35 2.30 2.46 8 6 61 1.17 1.90 1.75 2.00 2.10 1.94 2.50 2.40 2.10 2.25 2.31 6 7 49 0.56 2.15 2.30 1.90 1.90 2.06 2.90 3.25 2.85 2.80 2.95 12 8 53 0.76 1.85 2.00 1.80 1.80 1.86 2.55 2.25 2.00 2.60 2.35 8 9 55 0.51 1.75 2.50 2.20 2.50 2.24 2.95 2.65 2.90 2.55 2.76 0 10 38 0.33 2.50 2.50 2.20 2.30 2.38 3.05 3.00 2.40 2.85 2.83 4 Mean 5^.9 O.696 2.030 2.575 9.2 F.F. = Facing Failure Table 4 . Results of Tensile Test for F i l l e t Height Group [ 1 . 5 ] Sample Tensile Strength psi. Deflec-tion mm. F i l l e t Height mm. F i l l e t Width mm. F.F. No. 1 2 3 4 Mean 1 2 3 4 Mean % 1 66 0 . 7 9 2 . 3 5 2 . 5 5 2 . 6 0 2 . 3 5 2.46 3 . 6 0 3 . 2 5 3.70 2 . 9 5 3 - 3 8 0 2 63 1 .15 2 . 6 5 2 . 9 5 2 . 9 0 2 . 9 5 2 . 8 6 3.80 3 . 5 0 3 .^5 3 . 7 0 3 . 6 1 12 3 69 0 . 9 9 2 . 9 5 2 . 9 5 2 . 6 0 2.40 2 . 7 3 3 . 2 5 3 . 6 5 4 . 2 0 3.40 3 . 6 3 14 4 49 0 . 3 8 2 . 5 0 2.80 2 . 9 5 2 . 5 5 2 . 7 0 3 . 9 5 3 . 3 0 3 . 3 0 3-75 3 . 5 8 0 5 72 0 . 9 7 3 . 0 0 2 . 9 5 2.40 2 . 7 0 2 . 7 6 3 . 8 5 3 . 8 0 4 . 5 0 *K35 4 . 1 3 12 6 79 0 . 9 9 2 . 5 5 2 . 8 5 3 . 10 2 . 7 5 2.81 3 . 7 5 3 . 7 0 4 . 3 0 5 . 0 0 4 . 1 9 8 7 79 1 .07 2 . 5 0 2 . 3 5 2 . 5 0 2 . 4 5 2 . 4 5 4 . 4 5 4 . 4 5 3 . 6 5 4.40 4.24 0 8 93 1 . 0 2 2 . 5 0 2 . 3 5 2 . 3 5 2 . 7 0 2.48 4 . 0 5 3.40 3 . 2 0 3.80 3.61 12 9 84 0 . 9 9 2 . 5 0 2 . 6 5 2 . 7 0 2 . 6 5 2 . 6 3 3 . 5 5 4 . 0 0 ^ . 3 5 4 . 0 5 3-99 16 10 72 1 . 0 2 2 . 7 0 2.40 2 . 6 0 2 . 3 5 2 .51 3 . 6 0 3 . 7 0 3 . 3 5 3 . 7 0 3 . 5 9 0 Mean 7 2 . 6 0 .937 2 . 6 3 9 3 . 7 9 5 7.* F.F. = Facing Failure CO Table 5. Results of Tensile Test for F i l l e t Height Group [2.0] Sample Tensile Strength psi. Deflec-tion mm. F i l l e t Height mm. F i l l e t Width mm. F.F. No. 1 2 3 4 Mean 1 2 3 4 Mean % 1 83 1.07 3.15 2.60 2.50 2.90 2.79 4.20 4.00 3.55 4.45 4.05 0 2 75 0.71 3.45 3.20 3.^5 2.95 3.26 3.95 3.65 3.85 3.85 3.83 0 3 70 0.58 3.20 3.20 3.50 3.25 3.29 3.95 4.00 3.80 3.80 3.89 8 4 79 0.86 2.85 3.00 3.20 2.70 2.94 3.90 4.25 3.70 4.20 4.01 0 5 59 0.51 3.40 3.80 3.90 3.20 3.58 3.95 3.80 3.60 3.80 3.79 14 6 69 1.25 3.30 3.15 3.40 3.20 3.26 3.45 3.25 3.05 3.70 3.36 0 7 61 0.51 3.55 3.60 3.15 3.20 3.38 3.10 3.20 4.35 4.60 3.81 4 8 55 0.61 3.50 3.25 3.20 3.45 3.35 4.00 3.85 3.40 4.40 3-91 3 9 58 0.64 3.60 3.35 3.50 3.00 3.36 3.80 4.25 3.65 3.70 3.85 1 10 67 0.64 3.40 3.25 3.35 3.15 3.29 4.25 3.60 4.10 3.60 3.89 6 Mean 67.6 0.738 3.250 3-839 3.6 F.F. = Facing Failure Table 6. Glue Depth and F i l l e t Height i n Tensile Test Specimens F i l l e t Height Group Glue Depth F i l l e t Height Difference [0.5] 0.7 mm. 1.28 mm. 0.58 ram. [1 . 0 ] 1.4 2.03 O.63 [1.5] 2.1 • 2.64 0.54 [2.0] 2.8 3.25 0.45 T a b l e 7. F r a c t u r e / F i l l e t - W i d t h R a t i o i n S e l e c t e d T e n s i l e T e s t S p e c i m e n s No. 1 2 3 4 Mean X w X f x f / x w X w X f x f / x w x w x f x f / x w X w X f x f / x w R = X f / X w [0. 5] 1 55 17 0.310 55 20 0.364 54 24 0.444 40 24 0.600 0.430 2 56 21 0.374 47 20 0.425 54 24 0.444 56 25 0.446 0.422 3 60 28 0.466 76 28 0.369 54 23 0.426 50 26 0.520 0.445 5 70 25 0.357 65 32 0.494 65 27 0.414 71 30 0.423 0.421 6 40 20 0.500 50 21 0.420 54 20 0.371 47 22 0.469 0.440 Mean 0.432 [1. 0] 1 130 30 0.231 137 40 0.292 105 32 0.306 105 45 0.428 0.314 3 110 42 0.382 108 45 0.416 105 35 O.368 115 42 0.365 0.383 6 88 30 0.341 80 30 0.375 93 35 0.376 89 45 0.393 0.371 7 113 35 0.310 109 32 0.294 125 45 O.360 119 30 0.252 0.304 8 90 29 0.322 95 32 0.338 100 28 0.280 97 36 0.372 0.328 Mean 0.340 [1- 5] 3 145 41 0.282 145 40 0.276 142 50 0.352 137 41 0.300 0.302 174 52 0.300 156 54 0.346 121 40 0.330 145 53 O.366 0.336 5 158 56 0.354 137 64 0.466 143 60 0.420 158 49 0.310 0.387 6 165 45 0.273 150 49 0.327 131 54 0.414 125 41 0.328 0.336 10 125 47 0.375 119 44 0.470 136 49 0.360 144 50 0.347 0.388 Mean 0.350 [2. 0] 1 163 53 0.325 140 42 0.300 165 49 0.297 128 40 0.312 0.309 2 138 50 O.362 133 45 0.345 157 50 0.339 129 57 0.442 0.372 3 138 50 O.362 148 4o O.270 150 43 0.286 141 50 0.354 O.318 4 168 54 0.321 158 45 0.285 165 53 0.321 175 49 0.280 O.302 8 140 56 0.400 140 55 0.393 130 51 0.392 145 56 O.386 0.417 Mean 0.344 N o t e : X w = F i l l e t w i d t h i n 1/1000 i n c h X f = W i d t h o f f r a c t u r e i n f i l l e t i n 1/1000 i n c h . Table 8. A u x i l i a r y Table for S t a t i s t i c a l Analysis of Tensile Test Results - (A) F i l l e t Height X^ F i l l e t Width X 2 Deflection x 3 Facing Failure X^ Tensile Strength Y. df [0.5] £X 12.75 13.67 4.62 12 485 z x 2 16.3467 18.9699 2.6708 144 239.71 ( s x ) 2 162.5625 186.8689 21.3444 144 235225 ss 0.0904 0.2830 0.5364 129.6 448.5 s 0.10 0.18 0.24 3.8 7.1 9 X 1.275 1.367 0.46 1.2 48.5 [ l . o ] EX 20.03 25.75 6.96 92 5^9 2 ZX^ 41.5318 68.0859 5.7H0 1208 31335 (SX) 2 412.0900 663.0625 48.4416 8464 301401 SS 0.3228 1.7796 0.8668 361.6 1194.9 s 0.19 0.44 0.31 6.3 11.5 9 X 2.030 2.575 0.696 9.2 5^.9 [1 .5 ] s x 26.39 37-95 9.37 726 zxc 69.8577 144.8807 9.1979 948 54042 CO Table 8. (Continued) x l X 2 X 3 X 4 Y df 696.4321 1440.2025 87.7969 5476 527076 ss 0.2145 0.8604 0.4182 400 .4 133^.^ s 0.15 0.31 0.22 6.7 12.2 9 X 2.639 3-795 0.937 7.4 72.6 sx 32.50 38.39 7.38 36 676 2 HIT 106.0840 147.6961 5.9990 322 46496 ( E X ) 2 1056.2500 1473.7921 54.4644 1296 456976 SS 0.4590 0.3169 0.5526 192.4 798.4 s 0.23 0.19 0.25 4.6 9.4 9 X 3.250 3.839 0.74 3-6 67.6 Total. ZX 91.94 115.76 28.33 214 2436 Z X 2 233.8202 379.6326 23.5787 2622 155844 CF 211.3240 312.2574 20.0647 1144.9 148352.4 SS 22.4962 67.3752 3.51^0 1477.1 7^81.6 S 0.79 1.37 0.31 6.41 14.42 36 X 2.30 2.89 0.71 5-35 60.90 Note: SS = Sum of squares, S = Standard deviation, CF = Correction factor = (£X) /40 CO Table 9 . Auxiliary Table for Statistical Analysis of Tensile Test Results - ( X^Xg "^ 1^ 3 ^1^ ^2^" X^Y X/^Y [0.5] 17.5674 5-9775 617.38 664.50 230.60 744 [1.0] 52.6600 14.0223 1115.03 1427.11 398.22 4860 [1.5] 100.233^ 24.7352 1909.75 2769.IO 695.56 5678 [2.0] 124.6050 23.9656 2180.53 2599.33 5H.60 2255 Total 295.0658 68.7006 5822.69 7460.04 1835.98 13537 GP 2 ) 266.07 65.117 5599.146 7049.78 1725.29 13032.6 SP 3 ) 28.99 3.580 223.5^ 410.26 110.69 504.4 Note: 1) Symbols from Table 8 2) Correction factor 3) Sum of products T a b l e 10. R e s u l t s o f F l e x u r e T e s t f o r F i l l e t H e i g h t G r o u p [0.5] No. Max. S h e a r D e f l e c -L o a d S t r e n g t h t i o n l b s . p s i . nun. F i l l e t H e i g h t (mm.) F i l l e t W i d t h (mm.) Type o f F a i l u r e Mean Mean 1 540 56.9 2 475 50.0 3 496 52.2 4 500 52.6 5 443 46 .6 6 485 51.1 7 455 47.9 8 475 50.0 9 495 52.1 10 482 50.7 11 535 56.3 12 466 49.1 13 518 54.5 14 493 51.9 15 492 51.8 16 445 46 .8 17 439 46 .2 18 490 51.6 19 446 46 .9 20 500 52.6 2.54 1.91 2.29 2.87 1.83 2.16 2.03 2.80 2.03 I . 6 3 2.46 2.03 1.98 2.11 2.03 1.91 2.80 2.80 2.03 1.65 1.30 0.60 1.05 0.90 0.60 0.85 0.95 0.70 0.70 1.00 0.80 1.00 1.35 0.95 0.90 0.70 0.80 0.65 0.80 0.60 1.45 0.70 1.00 1.00 0.70 0.50 0.80 0.75 0.80 1.10 1.00 0.95 1.15 0.95 0.60 0.70 0.85 1.00 0.70 0.85 1.40 0.65 1 .25 0.95 O.65 0.80 0.60 0 .90 0.75 1.00 0.95 0.95 1.15 1 .25 1.00 0.70 1.00 1.00 0.80 0.85 1.70 0.80 1.25 0.85 0.70 0.70 0.75 0.80 0.75 1.10 1.10 1.00 0.95 1.15 0.95 0.60 1.10 1.10 0.70 0.85 1.46 0.69 1.14 0.93 0.66 0.71 0.78 0.79 0.75 I . 0 5 0.96 0.98 1.15 1.08 0.86 0.68 0.94 0.94 0.75 0.79 1.85 2.00 1.15 1.25 1.60 1.45 1.30 1.35 1.30 1.45 1.45 1.10 1.70 1.45 1.25 1.10 1.05 1.45 0.95 1.45 1.65 2.00 1.00 1.60 1.70 1.60 1.30 1.60 1.30 1.10 1.45 1.20 1.70 1.35 1.30 1.20 0.85 1.50 1.10 1.35 1.75 1.40 1.55 1.20 1.65 1.45 1.45 1.35 1.65 0.75 1.25 0.90 1.70 1.20 1.45 1.15 1.00 1.50 1.00 1.45 1.40 1.55 1.00 1.70 1.40 1.60 1.35 1.35 1.60 0.80 1.45 1.00 1.45 1.25 1.70 1.25 0.90 1.45 1.20 1.40 1.66 1.74 1.18 1.44 1-59 1.53 1.35 1.43 1.46 1 .03 1.40 1 .05 1.64 1.31 1.43 1.19 0.95 1.48 1.06 1.41 GF GF GP GF GP GF+CP GF GF+CF GP GP GP GF GF+CP GF+CF GP GP GP GP+CP GP GP Mean 483.5 50-89 2.19 0.90 1.37 N o t e : CP = C o r e f a i l u r e GF = G l u e l i n e f a i l u r e FF = F a c i n g f a i l u r e . CO T a b l e 11. R e s u l t s o f F l e x u r e T e s t f o r F i l l e t H e i g h t G r o u p [1.0] No. Max. S h e a r D e f l e e L o a d S t r e n g t h t i o n l b s . p s i . mm. F i l l e t H e i g h t (mm.) F i l l e t W i d t h (mm.) Type o f Mean Mean F a i l u r e 1 467 49.2 2.16 1.50 2 469 49.4 3-81 1.80 3 470 49.5 2.82 • 1.60 4 441 46.4 1.53 1.90 5 480 50.5 2.04 1.85 6 424 44.6 1.78 1.20 7 485 51.1 2.42 I.65 8 453 47.7 2.80 2.30 9 480 50.5 2.04 1.85 10 447 47.1 2.28 1.40 11 478 50.3 2.04 2.00 12 464 48.9 2.67 1.80 13 402 42.3 1.83 1.50 14 455 47.9 2.80 1.80 15 480 50.5 2.04 1.90 16 422 44.4 2.54 1.60 17 460 48.4 4.82 1.10 18 470 49.5 2.04 1.00 19 540 56.8 3.05 1.35 20 425 44.7 3.56 1.30 Mean 460.6 48.48 2.55 1.75 1.90 2.10 1.75 1.90 1.80 1.65 1.90 1.85 1.70 2.25 1.80 1.45 1.70 1.85 1.95 1.40 0.80 1.10 1.25 1.50 1.95 2.00 1.50 1.85 1.60 1.60 1.90 1.90 1.45 2.25 1.65 1.65 1.90 1.90 1.65 1.30 1.60 1.60 1.35 1.65 1.80 1.85 1.60 1.90 1.80 1.85 1.80 2.00 1-55 2.30 2.00 1.80 2.00 1.80 1.95 1.40 1.35 1.40 1.45 1.60 1.86 1.89 I.69 1.88 1.60 I.69 1.98 1.90 1-53 2.20 1.81 1.60 1.85 1.86 1.79 1.30 1.19 I.36 1.34 1.35 2.35 1.75 1.25 2.00 I.65 2.15 2.40 2.00 1.80 2.15 1.30 I.65 1.80 1.90 1.75 1.75 I.85 2.00 2.15 1.70 1.90 1.80 1.95 1.90 1.70 2.15 2.15 2.10 2.20 2.15 1.55 1.60 2.70 1.85 2.00 2.05 1.60 2.05 1.90 1.85 1.70 1.30 1.70 2.00 2.15 2.35 2.10 2.05 I.65 2.05 1.80 2.05 2.00 1.95 2.00 2.15 I.65 2.15 2.00 1.70 2.10 1.45 1.80 1.90 1.65 2.25 1.95 2.00 2.15 2.00 1.70 1.45 1.70 2.00 2.00 2.20 1.65 1.95 2.00 1.65 2.01 1.58 1.68 1.95 1.79 2.23 2.15 2.04 1.95 2.09 1.59 I.69 1.88 1.93 1.94 2.04 I.69 2.04 2.01 GF GF+CF CF GF GF GF GF+CF GF GF GF GF GF GF GF GF GF+CF CF+FF GF+CF GF CF 1.70 1.90 N o t e : CF = C o r e f a i l u r e GF = G l u e l i n e f a i l u r e FF » F a c i n g f a i l u r e . CO T a b l e 12. R e s u l t s o f F l e x u r e T e s t f o r F i l l e t H e i g h t G r o u p [1.5] No. Max. L o a d l b s . S h e a r S t r e n g t h p s i . D e f l e c -t i o n mm. F i l l e t H e i g h t (mm.) F i l l e t W i d t h (mm.) Type o f F a i l u r e 1 2 3 4 Mean 1 2 3 4 Mean 1 502 52.8 2.92 2.15 2.40 2.35 2.50 2.35 2.40 2.20 2.65 2.65 2.48 GF 2 518 54.5 2.54 2.00 2.45 1.80 1.80 2.01 2.35 2.55 2.30 2.75 2.49 GF 3 517 54.4 3-81 2.00 2.15 2.35 2.50 2.25 2.80 2.50 2.00 2.25 2.39 GF+CF 4 555 58.4 3-81 1.90 2.15 2.40 2.60 2.26 2.30 2.45 2.25 2.35 2.34 GF+CF 5 5^5 57.^ 3.56 1.90 2.40 2.35 2.35 2.25 2.30 2.65 2.25 2.60 2.45 GF+CF 6 519 54.6 3.04 2.35 2.60 2.05 2.20 2.30 2.30 2.00 2.30 2.60 2.30 GF+CF 7 54? 57.6 3.81 2.70 2.40 2.20 2.35 2.41 2.55 2.40 2.40 2.15 2.38 CF 8 472 49-7 3.81 2.50 2.25 2.60 2.65 2.50 2.45 2 30 2.60 2.45 2.45 GF+CF 9 548 57.7 3.04 2.15 2.20 2.45 2.55 2.34 2.60 2.15 2.40 2.35 2.38 GF+CF 10 541 56.9 3-81 2.30 2.25 2.30 2.80 2.41 2.10 2.10 2.20 2.15 2.14 GF+CF 11 500 52.6 3-91 2.35 2.40 2.85 2.85 2.61 2.20 2.25 2.40 2.40 2.31 GF+CF 12 550 57.9 3-94 2.65 2.50 2.45 2.50 2.53 2.10 2.05 2.10 2.20 2.11 CF 13 514 54.1 3.30 2.45 2.35 2.20 2.25 2.31 2 25 2.40 2.45 2.20 2.33 CF 15 495 52.1 3.81 2.30 2.75 2.25 2.50 2.45 2.45 2.20 2.25 2.50 2.35 CF 16 505 53-2 3.68 2.60 2.75 2.55 2.50 2.60 2.20 2.45 2.40 2.35 2.35 GF+CF 17 527 55.5 3.81 2.3Q 2.30 2.10 2.35 2.26 2.40 2.30 3.00 2.60 2.58 CF 18 510 53.7 3.56 2.60 2.30 2.50 2.45 2.46 2.45 2.35 2.80 2.30 2.48 CF 19 495 52.1 3.30 2.60 2.70 2.45 2.25 2.50 2.05 2.30 2.45 1.95 2.19 CF 20 493 51.9 4.06 2.85 2.75 2.50 2.65 2.69 2.45 1.95 1.85 2.15 2.10 GF Mean 518.2 54.54 3.54 2.39 2.34 N o t e : CF = C o r e f a i l u r e GF = G l u e l i n e f a i l u r e FF = F a c i n g F a i l u r e . CO T a b l e 1 3 . R e s u l t s o f F l e x u r e T e s t f o r F i l l e t H e i g h t G r o u p [2.0] No. Max. S h e a r D e f l e c - F i l l e t H e i g h t (mm.) F i l l e t W i d t h (ram.) Type o f F a i l u r e l b s . p s i . mm. 1 2 3 4 1 5 9 5 6 2 . 6 6 . 3 5 2 . 9 5 3 . 0 5 2 . 5 5 2 . 6 5 2 4 8 2 5 0 . 7 3.81 2 . 9 5 3 . 1 5 3 . 3 0 3 . 0 5 3 5 9 0 6 2 . 1 6 . 3 5 3 . 0 0 3 . 0 0 3 . 8 5 3 . 0 5 4 5 0 0 5 2 . 6 3 - 7 9 2 . 6 0 2 . 5 5 2 . 6 5 2 . 8 5 5 5 7 5 6 0 . 5 5 . 8 5 3 . 2 0 3 . 1 5 3 . 0 5 3 . 2 0 6 5 6 0 5 8 . 9 5 - 8 5 3 . 2 0 3 . 8 0 2 . 5 5 2 . 9 0 7 5 1 7 5 4 . 4 5 . 8 5 3 . 2 0 3 . 1 0 2 . 8 5 3 . 4 5 8 5 0 8 5 3 - 5 3.81 3 - 0 5 2 . 6 0 2 . 4 0 2 . 5 0 9 5 2 6 5 5 . 4 5 . 0 8 2 . 2 5 2 . 9 0 3 . 0 0 3 . 1 0 1 0 5 3 9 5 6 . 7 6 . 3 5 3 . 0 5 3 . 0 0 2 . 8 5 2 . 9 0 1 1 5 0 0 5 2 . 6 5 - 5 9 2 . 6 5 3 . 4 5 2 . 7 0 2 . 4 5 1 2 5 6 0 5 8 . 9 4 . 3 2 2 . 5 5 2 . 8 0 2 . 9 5 2 . 9 0 1 3 5 5 0 5 7 . 9 5 . 8 5 3 . 5 0 3 . 5 0 3 . 6 5 3 . 6 0 14 5 3 6 5 6 . 4 4 . 3 2 3.40 3 . 1 0 3.40 3 . 4 0 1 5 5 9 5 6 2 . 6 4 . 5 7 2 . 7 5 2 . 8 0 2 . 6 0 3 . 0 0 1 6 5 1 5 5 4 . 2 5 . 0 8 3 . 2 0 3 . 3 5 3.40 3 . 5 0 1 7 4 7 0 4 9 . 5 5 . 9 6 3 . 8 5 3 . 7 0 3 . 9 0 3.40 1 8 5 3 0 5 5 - 8 5 . 0 4 3 . 5 5 3 . 7 5 3 . 2 0 3 . 2 0 1 9 5 0 5 5 3 . 2 5.40 3 . 6 0 2.80 3 . 2 0 3 . 4 5 2 0 5 3 0 5 5 . 8 5 . 0 8 2 . 9 5 2 . 9 0 2 . 9 0 2 . 7 0 Mean Mean 2 . 8 0 3 . U 3 . 2 3 2 . 6 6 3 . 1 5 3 . 1 1 3 . 1 5 2.64 2 . 8 1 2 . 9 5 3 . 0 6 2.80 3 . 5 6 3 . 3 3 2 . 7 9 3 . 3 6 3-71 3 . 4 3 3 . 2 6 2 . 8 6 2 . 5 0 2 . 2 5 2 . 0 0 3 . 0 0 2 . 3 5 2 . 3 5 2 . 6 0 2 . 1 5 2 . 0 5 2 . 8 5 2 . 1 5 2 . 6 5 2 . 6 5 2 . 4 5 2 . 6 0 3 . 0 0 2 . 3 5 2 . 3 5 2 . 6 0 2 . 7 0 2 . 4 5 2 . 4 5 2 . 5 0 2 . 6 0 2 . 7 0 2 . 0 5 2 . 7 0 2 . 2 0 2 . 7 5 2 . 7 5 2 . 8 5 2 . 7 0 2 . 8 0 2.40 2 . 8 0 2 . 9 0 3 . 3 0 1 . 6 0 3 - 1 0 3 . 0 0 2 . 8 0 2 . 8 5 2 . 5 0 2 . 9 0 2 . 6 5 2 . 3 5 2 . 6 0 2 . 5 5 2 . 7 0 2 . 9 0 2 . 9 5 2 . 4 5 2 . 6 5 2 . 2 5 2 . 7 5 3 . 2 0 2 . 7 0 2 . 8 0 2 . 9 0 2 . 7 5 2.55 2.40 2.80 2.60 2 . 6 0 2.70 2.75 2.35 2.20 2.20 2 . 1 5 2.35 2.20 2.40 2.40 2.80 2 . 3 0 2.40 3.10 2.85 2.58 2.49 2.45 2.78 2.58 2 . 3 6 2.66 2 . 3 1 2.43 2.68 2.53 2 54 2.58 2.38 2.64 2.98 2.66 2.29 2.93 2.83 CF CP CF GP+CF CP CP CF GP+CP GP+CF CF CF CF CP CP CF CP CF CF+FF CP CP+FP Mean 534.2 56.22 5.22 3 . 0 9 2 . 5 8 N o t e : CF = C o r e f a i l u r e GP = G l u e l i n e f a i l u r e FF = F a c i n g f a i l u r e . CO OO T a b l e 14. F r a c t u r e / F i l l e t - W i d t h R a t i o i n S e l e c t e d F l e x u r e T e s t S p e c i m e n s [0.5] [ i . o ] [1.5] [2.0] No. l 2 3 4 Mean x w x f x f / x w X w X f x^/x^ X w x f x f / x w X w X f X^/Xw x77xw 4 63 23 0.37 75 30 0.40 57 24 0.42 55 2<? 0.45 0.41 5 50 23 0.46 49 21 0.43 53 25 0.47 49 24 0.49 0.46 9 65 19 0.29 65 22 0.34 65 20 0.31 65 24 0.37 0.33 2 70 25 0.33 81 35 0.43 65 25 0.39 50 20 0.40 0.39 1 75 28 0.37 65 22 0.34 69 25 0.37 75 25 0.33 0.37 0.39 4 76 26 0.34 75 30 0.40 80 30 0.38 80 25 0.31 0.36 11 70 27 0.39 68 25 0.37 70 18 0.26 73 25 0.34 0.34 12 73 24 O.33 75 28 0.37 70 25 O.36 75 20 0.27 0.34 13 70 24 0.34 80 30 O.38 76 30 0.40 70 27 0.39 O.38 14 79 3^ 0.43 80 40 0.50 75 32 0.43 85 40 0.47 0.46 O.38 1 110 40 0.36 99 37 0.37 97 ^5 0.46 100 36 O.36 0.39 2 102 38 0.37 95 38 0.40 99 45 0.45 100 40 0.40 0.41 6 90 25 0.28 125 43 0.34 100 35 0.35 95 29 0.31 0.32 9 97 ^5 0.46 112 ^5 0.40 95 34 O.36 116 33 0.29 O.38 10 121 35 0.29 125 30 0.24 85 32 O.38 120 42 0.35 0.32 O.36 4 200 70 0.35 170 37 0.22 195 50 0.26 139 48 0.35 0.30 8 100 4o 0.40 128 30 0.23 145 50 0.35 110 46 0.42 0.35 9 75 27 O.36 163 62 0.38 150 ^5 0.30 93 37 0.40 0.35 0.34 N o t e : X w = F i l l e t w i d t h i n 1/1000 i n c h X f = W i d t h o f f r a c t u r e i n f i l l e t i n 1/1000 i n c h . CO Table 15. Auxiliary Table for Statistical Analysis of Flexure Test Results F i l l e t Height X x F i l l e t Width X 2 Deflection x 3 Shear Strength Y df [0.5] £X 18.09 27.33 48 . 8 9 1 0 1 7 . 8 s x 2 1 7 . 1 3 6 1 3 8 . 3 1 1 9 9 9 . 1 7 1 3 5 1 9 7 2 . 5 0 ( s x ) 2 327.2481 746 . 9 2 8 9 1 9 2 6 . 3 3 2 1 1 0 3 5 9 1 6.84 ss 0 . 7 7 3 7 0.9655 2 . 8 5 4 7 1 7 6 . 6 6 s 0 . 2 0 0 . 2 3 0 . 3 9 3 .05 1 9 X 0 . 9 0 1 . 3 7 2 . 1 9 5 0 . 9 [ 1 . 0 ] z x 3 3 . 9 2 3 7 . 9 3 5 1 . 0 7 9 6 9 . 7 s x 2 5 8 . 7 8 3 2 72.6421 142 . 3 2 4 1 4 7 2 0 2 . 5 3 ( s x ) 2 1 1 5 0 . 5 6 6 4 1438.6849 2608.1449 940318.09 ss 1 . 2 5 4 9 0 . 7 0 7 9 1 1 . 9 1 6 9 I 8 6 . 6 3 s 0 . 2 6 0 . 1 9 0 . 7 9 3 . 1 3 1 9 X 1 . 7 0 1 . 9 0 2.55 48.5 Ci .53 nx 47.82 46 . 8 3 7 0 . 7 0 1 0 9 0 . 8 S x 2 114.8128 1 0 9 . 9 8 9 5 253.1512 5 9 6 0 4 . 9 6 VD O Table 15. (Continued) X l X 2 x 3 Y df C1.5J (six)2 2286.7524 2193.0489 4998.49 1189844.64 SS 0.4752 0.3371 3.1267 112.73 S 0.16 0.13 0.41 2.44 19 X 2.39 2.34 3.54 54.5 [2.0] HX 61.77 51.68 104.30 1124.3 z x 2 192.4819 134.2492 558.2140 63481.05 (ZX) 3815.5329 2670.8224 10878.49 1264050.49 s s 1.7053 0.7081 14.7895 278.53 s O.30 0.19 0.88 3.83 19 X 3.09 2.58 5.22 56.2 Total EX X2 (rx)2 SS s X 161.60 383.2140 26114.5600 56.7820 0.86 2.02 163.77 355.1929 26820.6129 19.9351 0.51 2.05 269.96 1052.8686 72878.4016 141.889 1.37 3-37 4202.6 222261.04 17661846.76 1487.96 4.42 52.5 76 Note: SS = Sura of squares, S = Standard deviation 92 APPENDICES APPENDIX 1 93 Tables of Analysis of Variance and Duncan's New Multiple Range Test for F i l l e t Width means in Tensile Test Specimens a. Analysis of Variance Source df ss MS F Height Treatment 3 64 • 135 21.378 237.53** Error 36 3 .240 0.090 Total 39 67 • 375 ** indicates significance at the 1% level. b. Duncan's New Multiple Range Test Tr. X 2 T V t Q 5 S3R > Q 5 ^ D 2 ^ W > Q 1 S5R < Q 1 D l [2.0] 3-839 3-114 0.2958 + 4.126 0.3919 + [1-5] 3-795 3-018 0.2863 + + 4.015 0.3814 + + [1.0] 2.575 2.870 0.2762 - + + 3.851 O.3658 - + + [0.5] 1.367  [0.5] [1.0] [1.5] [2.0] 1.367 2.575 3.795 3.839 Means underlined by the same line did not d i f f e r significantly(P = .01) . APPENDIX 2 94 T a b l e s o f A n a l y s i s o f V a r i a n c e a n d D u n c a n ' s New M u l t i p l e Range T e s t f o r T e n s i l e S t r e n g t h Means i n T e n s i l e T e s t S p e c i m e n s a . A n a l y s i s o f V a r i a n c e S o u r c e d f SS MS ? H e i g h t T r e a t m e n t 3 3715-4 1238. 5 11.81** E r r o r 36 3776.2 104. 9 T o t a l 39 7491.6 ** i n d i c a t e s s i g n i f i c a n c e a t t h e 1% l e v e l . b. D u n c a n ' s New M u l t i p l e Range T e s t T r . w . 0 5 S S R . 0 5 D l D 2 D 3 W . 0 1 S S R > 0 1 D 2 D-j [1.5] 72.6 3.114 10.09 + 4.126 13.36 + [2.0] 67.6 3.018 9.78 + + 4.015 13.00 + + [1.0] 54.9 2.870 9.30 + 3.851 12.47 - + -[0.5] 48 .5 / EMS n = 10, =\/- n- = 3.239 [0.53 [1.0] [2.0] [ 1 . 5 ] 48.5 54.9 67.6 72 .6 Means u n d e r l i n e d b y t h e same l i n e d i d n o t d i f f e r s i g n i f i c a n t l y (P = .01). APPENDIX 3 95 Basic Equations a. Modulus of Rupture of Pacing in Bending ( 3 0 ) M y b ~ I M =TT ( i -/) T _ ^ ( " 3 - o 3) 1 " 12 = j P i - I') »h == 3Ph(i -1')  ( r b b h3 - 03 — 2b(h3 - o J ) where crb : modulus of rupture in bending (psi.) M I bending moment (in. lb.) 4. moment of Inertia (in. ) b : width of beam (in.) P : load (lbs.) -h C J L •4\ £P 4P APPENDIX 3 (Continued) b. Horizontal Shear Stress in Glueline (37) Q - ~ t>(h 2 - c 2 ) 8 3P(h 2 - o 2) 4b(h 3 - c 3) where : horizontal shear stress (psi.) V : total shear at the section (lbs.) Q : st a t i c a l moment of the area above the plane upon which the unit shear i s computed, taken 3 about the neutral axis of the beam (in. ). VQ lb £?(b / 8)(h 2 - c 2) b(h 3 - c 3) h 12 97 APPENDIX 4 T a b l e s o f A n a l y s i s o f V a r i a n c e a n d Duncan's New M u l t i p l e Range T e s t f o r F i l l e t W i d t h Means i n F l e x u r e T e s t S p e c i m e n s a . A n a l y s i s o f V a r i a n c e S o u r c e d f SS MS F H e i g h t T r e a t m e n t 3 1 7 . 2 1 6 5 . 7 3 9 1 6 0 . 3 * * E r r o r 76 2 . 7 1 9 0 . 0 3 5 8 T o t a l 79 1 9 . 9 3 5 ** i n d i c a t e s s i g n i f i c a n c e a t t h e 1% l e v e l . b . D u n c a n ' s New M u l t i p l e Range T e s t T r . x 2 T V . 0 5 S S R . 0 5 D l D 2 D 3 TV .01 3 S R . 0 1 D l D 2 D 3 [ 2 . 0 ] 2 . 5 8 3 . 0 6 6 0.129 + 4 . 0 1 3 0 . 1 6 9 + [1 • 51 2 . 3 4 2 . 9 6 9 0 . 1 2 5 + + 3 . 9 0 5 0 . 1 6 4 + + [ 1 . 0 ] 1 . 9 0 2.821 0.118 + + + 3-746 0 . 1 5 7 + + + [ 0 . 5 ] 1 .37 n = 2 0 , S= = 1 / ^ = 0.042 2 v n A c c o r d i n g t o D u n c a n ' s N.M.R. T e s t , f i l l e t w i d t h means r a n k e d a s : [ 0 . 5 ] < [ 1 . 0 ] < [ 1 . 5 J < [ 2 . 0 ] a t t h e 1% l e v e l o f s i g n i f i c a n c e . APPENDIX 5 98 T a b l e s o f A n a l y s i s o f V a r i a n c e a n d D u n c a n ' s New M u l t i p l e Range T e s t f o r S h e a r S t r e n g t h Means i n f l e x u r e T e s t S p e c i m e n s a . A n a l y s i s o f V a r i a n c e S o u r c e d f ss MS F H e i g h t T r e a t m e n t 3 733.42 244.47 24.62** E r r o r 76 755-54 9.93 T o t a l 79 1487-96 ** i n d i c a t e s s i g n i f i c a n c e a t t h e 1% l e v e l . b . D u n c a n ' s New M u l t i p l e Range T e s t T r . 1 T V t Q 5 S S R > Q $ ^ Dg D3 T V < Q 1 S S B > 0 1 D 1 D 2 D3 [2.0] 56.22 3.066 2.160 + 4.013 2.827 + [1.5] 54.54 2.969 2.092 + + 3.905 2.751 + + [0.5] 50.89 2.821 1.987 - + + 3.746 2.639 - + -[1.0] 48.48 [1.0] [0.5] [1.5] [2.0] 48.5 50.9 54•5 56.2 [l . o ] [0.5] [1.5] [2.0] 48.5 50.9 54.5 56.2 l i n e d i d n o t d i f f e r / EMS n = 20, S Y =\j - g - = 0.7045 A t t h e 5% l e v e l o f s i g n i f i c a n c e ; A t t h e 1% l e v e l o f s i g n i f i c a n c e ; Means u n d e r l i n e d b y t h e same s i g n i f i c a n t l y . APPENDIX 6 99 T a b l e s o f A n a l y s i s o f V a r i a n c e a n d Dunca n ' s New M u l t i p l e Range T e s t f o r D e f l e c t i o n Means i n F l e x u r e T e s t S p e c i m e n s a . A n a l y s i s o f V a r i a n c e S o u r c e d f SS MS F H e i g h t T r e a t m e n t 3 109. 59 36.53 85.95** E r r o r 76 32. 30 0.425 T o t a l 79 141. 89 ** i n d i c a t e s s i g n i f i c a n c e a t t h e 1% l e v e l . b . D u n c a n ' s New M u l t i p l e Range T e s t T r . x 3 T V . o 5 S S R . 0 5 D l D2 D 3 T V.01 3 S R . 0 1 D l D2 D 3 [2.0] 5.22 3.066 0.448 + 4.013 0.585 + [1.5J 3.54 2.969 0.433 + + 3.905 0.570 + + [1.0] 2.55 2.821 0.412 + + - 3.746 0.546 + + -[0.5] 2.19 n = 20, S^ =^ jp = 0.146 [0.5] [1.0] [1.5] C2.0] 2.19 2.55 3.54 5-22 Means u n d e r l i n e d by t h e same l i n e d i d n o t d i f f e r s i g n i f i c a n t l y ( P = .01). 100 APPENDIX 7 Sequences of F i l l e t Width Means (Unit : mm.) Ext. E m p i r i c a l Ext. Glue Depth 0.00 0. 70 1.40 2. 10 2. 80 3.50 4.20 0.30 0. 90 1.70 2. 39 3. 09 3.80 4.50 h 0.80 1. 37 1.90 2. 34 2. 58 2.80 2.90 h - t ~2 0.30 0. 60 0.85 1. 05 1. 20 1.30 1.35 1 s t d i f f e r e n c e 0 . 3 0 0.25 0 . 2 0 0 . 1 5 0 . 1 0 0.05 2nd d i f f e r e n c e 0.05 0.05 0.05 0.05 0.05 X 1 = F i l l e t height X 2 = F i l l e t width t = Honeycomb c e l l wall thickness (0.2 mm.) Ext. = Extrapolated APPENDIX 8 Yalues of k/m f o r the Four F i l l e t Height Groups Y x 1 = (X 2 - t)/2 y = 0.3*1 1 0 0 k / m [0.5] 48.5 0.557 0.167 0.81 [1.0] 54.9 1.161 0.348 1.03 [1.5] 72.6 1.771 0 . 5 3 1 1.04 [2.0] 67.6 1.793 0.538 1 . 1 3 Jc_ _ y +_0.22 m " Y APPENDIX 9 101 Gore Shear Stress under Two-Point Loading When two loading points are located at a distance of 3/8-span from each support, core shear stress is calculated as follows (.4): h = sandwich thickness = 1.5 inch c = core thickness = 1 inch b = sandwich width = 0.375 inch P 2 = flexure load (lbs.) —3 k = 1 - e , and f = facing thickness = 0.25 inch E = modulus e l a s t i c i t y of the facing = 1,800,000 psi.(36) G = effective core shear modulus = 8,000 psi. S = (h + c)b k where core shear stress (psi.) If S = 70 psi • » then P 2 = 70 (1.5 + 1) x 3.75 x 0.958 = 685 lbs. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            data-media="{[{embed.selectedMedia}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
https://iiif.library.ubc.ca/presentation/dsp.831.1-0101667/manifest

Comment

Related Items