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UBC Theses and Dissertations

Aesthetic and engineering analysis of Alouette River crossing Pasicnyk, Vladimir 1976

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AESTHETIC AND ENGINEERING ANALYSIS OF ALOUETTE RIVER CROSSING by VLADIMIR PASICNYK, P.Eng. For. Eng., Czech Technical U n i v e r s i t y i n Prague, Czechoslovakia, 1955 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF FORESTRY i n the Department of Forestry We accept t h i s thesis as conforming to the required standard. THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1976 @ V l a d i m i r Pasicnyk, 1976 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an advanced d e g r e e a t t he U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t 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 f o r r e f e r e n c e and s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t 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 u n d e r s t o o d t h a t c o p y i n g o r 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 g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . V l a d i m i r P a s i c n y k F a c u l t y o f F o r e s t r y The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r , B . C . ABSTRACT T h i s t h e s i s d e a l s w i t h b r i d g e d e s i g n as an i m p o r t a n t p a r t o f r o a d d e s i g n and l a y o u t . B r i d g e s f r e q u e n t l y d o m i n a t e r o a d s and r a i l w a y s , and a r e , i n many c a s e s , a p r o m i n e n t f e a t u r e o f t h e l a n d s c a p e . D i s c r i m i - n a t i n g s e l e c t i o n o f t h e t y p e o f b r i d g e and m a t e r i a l t o be u s e d , h a v i n g r e g a r d t o t e c h n i c a l and a e s t h e t i c r e q u i r e m e n t s , i s t h e r e f o r e e s s e n t i a l . Road c o n s t r u c t i o n and b r i d g e d e s i g n a r e b o t h a p p l i e d a r t s i n l a n d s c a p i n g , and s h o u l d be c o n s i d e r e d as s u c h t h r o u g h o u t t he p l a n n i n g s e q u e n c e . S i n c e t h e m a i n t h r u s t o f t h i s t h e s i s i s d i r e c t e d t o w a r d t h e a e s t h e t i c and e n g i n e e r i n g a s p e c t s , no a t t e m p t has b e e n made t o i n c l u d e o v e r a l l e c o n o m i c a n a l y s e s o r d e t a i l s o f c o n s t r u c t i o n ; h o w e v e r , t o i n d i c a t e t h e b a s i c n a t u r e o f t h e e n g i n e e r i n g p r i n c i p l e s and t o d e m o n s t r a t e a p p r o - p r i a t e d i m e n s i o n s o f b r i d g e componen t s , c a l c u l a t i o n s and s k e t c h e s o f a few b r i d g e s a r e i n c l u d e d . V a r i o u s t y p e s o f b r i d g e s a r e e v a l u a t e d and d i s c u s s e d i n t e rms o f t h e i r a c c o r d a n c e w i t h modern e n v i r o n m e n t a l r e q u i r e m e n t s . The d e s i g n o f t h e new b r i d g e a c r o s s t h e A l o u e t t e R i v e r a t t h e U . B . C . R e s e a r c h F o r e s t i s t a k e n as a p a r t i c u l a r ca se s t u d y , t h e a n a l y s e s o f t h i s c r o s s - i n g s h o w i n g t h a t t h o u g h t f u l s e l e c t i o n o f b o t h b r i d g e and l o c a t i o n c a n n o t o n l y enhance t h e l a n d s c a p e , b u t a l s o i m p r o v e r o u t e c o n d i t i o n s . E n g i n e e r s s h o u l d b l e n d t h e i r t a l e n t s w i t h n a t u r e s o as t o c r e a t e a h a r m o n i o u s l a n d s c a p e . i i TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS . i i i L I S T OF FIGURES v ACKNOWLEDGEMENT i x C h a p t e r I - INTRODUCTION 1 1 .1 M e t h o d o f S t u d y o f F o r e s t B r i d g e A c r o s s A l o u e t t e R i v e r 1 1 .2 I n t r o d u c t i o n t o A e s t h e t i c s . 3 1.3 E l e m e n t s o f A e s t h e t i c s 4 1 . 3 . 1 B a s i c C o n c e p t s 4 1 . 3 . 2 Dominance , E l e m e n t s 4 1 . 3 . 2 . 1 Form 5 1 . 3 . 2 . 2 L i n e . 5 1 . 3 . 2 . 3 C o l o u r . 5 1 . 3 . 2 . 4 T e x t u r e 5 1.3.3 Dominance P r i n c i p l e s 5 1 .3 . 4 V a r i a b l e F a c t o r s 6 1.4 S t r u c t u r a l A e s t h e t i c s . 7 C h a p t e r I I - ANALYSIS OF BRIDGE AESTHETICS . 11 2 . 1 Roadway and G u a r d r a i l 12 2 . 1 . 1 Roadway . . . 12 2 . 1 . 2 G u a r d r a i l 21 2 . 2 S u p p o r t i n g S t r u c t u r e 24 2 . 2 . 1 Beams 28 2 . 2 . 2 A r c h e s 30 2 . 2 . 3 S u s p e n s i o n S t r u c t u r e 34 2.3 P i e r s and Abu tmen t s 36 2 .4 B r i d g e Heads 39 C h a p t e r I I I - DIFFERENT TYPES OF BRIDGES I N MAIN LANDSCAPE FORMS 42 3 . 1 F l a t C o u n t r y 44 3 . 1 . 1 C o n c r e t e A r c h B r i d g e 44 3 . 1 . 2 H o w e - t r u s s B r i d g e 45 3 . 1 .3 S u s p e n s i o n B r i d g e 45 3 . 2 H i l l y T e r r a i n 4.5 3.3 M o u n t a i n o u s C o u n t r y 4t> 3 . 4 R i v e r C r o s s i n g 46 i i i Page Chapter IV - ANALYSIS OF ALOUETTE RIVER CROSSING 50 4.1 De s c r i p t i o n of the Landscape Area and Alouette River Crossing 50 4.2 Present S i t u a t i o n 51 4.3 Proposed Alignment of the Route 52 4.4 Engineering Calculations on Proposed Types of Bridges . . . . . . 53 4.5 M a t e r i a l 54 4.6 Aesthetic Analysis of Considered Types of Bridges. 55 4.6.1 Single Beam Bridge 55 4.6.2 Single Strutframe Bridge . . . 55 4.6.3 Double Strutframe Bridge 57 4.6.4 Three-hinged Arch Bridge 57 4.6.5 Cantilevered Beam Bridge 59 4.6.6 Suspension Bridge 59 Chapter V - SUMMARY AND CONCLUSIONS 64 BIBLIOGRAPHY 66 APPENDICES I - Present S i t u a t i o n Design S p e c i f i c a t i o n s V e r t i c a l & Hor i z o n t a l Alignment 68 II - Simple Beam Bridge 75 II I - Continuous Beam (Two Eaual Spans) Single Strutframe Bridge 87 IV - Continuous Beam - Three Spans Double Strutframe Bridge Three-hinged Arch Bridge 101 V - C a n t i l e v e r e d Beam Bridge 114 i v L I S T OF FIGURES F i g u r e Page 1. O l d b r i d g e i n F l o r e n c e , I t a l y 9 2. B r i d g e i n a n a t u r a l s e t t i n g - J a p a n e s e G a r d e n 9 3. Roadway-above 13 4. H a l f - s u n k roadway 13 5. R o a d w a y - b e l o w 13 6. S i d e v i e w o f t h e b r i d g e ( shape) 14 7. T h r e e d i m e n s i o n a l ( p e r s p e c t i v e ) v i e w o f t h e b r i d g e ( fo rm)14 8. F u l l c o n c r e t e a r c h and g u a r d r a i l 15 9. R a i l w a y b r i d g e w i t h e x t e n d e d p i e r s 15 10. G e n e r a l v i e w o f a b r i d g e w i t h h a l f - s u n k roadway 17 11. Uppe r and l o w e r v i e w o f a b r i d g e w i t h a h a l f - s u n k roadway 17 12. I n s i d e v i e w o f b r i d g e w i t h s i d e w a l k s w i t h i n t h e s t r u c t u r e 18 13. S i d e w a l k s o u t s i d e t h e m a i n s t r u c t u r e 18 14. Change o f t h e p o s i t i o n o f t h e roadway 20 15. A l t e r n a t i v e s o l u t i o n o f c h a n g i n g p o s i t i o n o f roadway . . 20 16. L i g h t l o o k i n g g u a r d r a i l 22 17. I n t e r f e r e n c e o f t h e roadway and t h e g u a r d r a i l by e x t e n d e d p i e r s 22 18. P r o p e r s o l u t i o n f o r t h e u n b r o k e n roadway and g u a r d r a i l . 23 19. L i o n s G a t e B r i d g e - p r o p e r b a l a n c e o f a s t r u c t u r e . . . 23 20. P r o p e r l o c a t i o n o f t h e c a b l e to t h e roadway and g u a r d r a i l w i t h s u s p e n s i o n b r i d g e 25 21. I m p r o p e r l o c a t i o n o f t h e c a b l e t o t h e roadway and g u a r d r a i l . 25 v Figure Page 22. Improper balance between beam and arch 27 23. Improper balance between beam and arch 27 24. D i f f e r e n t solutions of truss bridge arrangement . . . 29 25. A e s t h e t i c a l l y s u i t a b l e d i f f e r e n t shapes of the beams . 31 26. Fixed end arch bridge 33 27. Two-hinged arch bridge 33 28. Three-hinged arch bridge 33 29. E l l i p t i c f u l l arch 35 30. New type of suspension bridge 35 31. King truss 35 32. Queen truss 37 33. Reverse king truss 37 34. Trussed girder bridge 37 35. Bridge head at Lions Gate Bridge 40 36. S t r i k i n g suspension bridge s t r u c t u r e 41 37. P r o p o r t i o n a l i t y of Lions Gate Bridge 41 38. Neighbourhood of bridges - proper s o l u t i o n 43 39. Close and d i s t a n t object observance - non homogenous appearance 43 40. High arch bridge i n mountainous t e r r a i n 47 41. Beam bridge i n mountainous t e r r a i n 47 42. Tunneling of the stream 48 43. Tunneling of the stream 48 44. Simple beam bridge 56 45. Asymmetrical s i n g l e strutframe bridge 56 v i Figure Page 46. Symmetrical s i n g l e strutframe bridge . . . . 56 47. Symmetrical double strutframe bridge 58 48. Asymmetrical three-hinged arch bridge 58 49. Symmetrical three-hinged arch bridge . . . 58 50. Cantilevered beam bridge 60 51. Simple suspension bridge 60 52. Simple beam bridge . 61 53. Single strutframe bridge 61 54. Double strutframe bridge 62 55. Symmetrical three-hinged arch bridge 62 56. Asymmetrical three-hinged arch bridge 63 57. Cantilevered beam bridge 63 58. A e r i a l p i c t u r e of southern part of U.B.C. Research Forest with bridge l o c a t i o n 69 59. View of the present bridge from the south bank . . . . 70 60. Side view of the bridge and v a l l e y from the east . . . 70 61. D e t a i l of south abutment 71 62. Design v e h i c l e - 50 ton 5 axle truck 71 63. Plan of proposed alignment 73 64. P r o f i l e of proposed alignment 74 65. Arrangement of roadway with wheel guards and guard r a i l s 82 66. Two equal spans continuous beam moment influence l i n e s 90 67. Two equal spans continuous beam shear influence l i n e s 92 v i i Figure Page 68. Three span continuous beam moment influence l i n e s . . . 104 69. Three span continuous beam shear influence l i n e s . . . 106 70. Graphical s o l u t i o n of forces i n three-hinged arch . . I l l 71. Cantilevered beam bridge - p r o f i l e 130 v i i i ACKNOWLEDGEMENT I w i s h to e x p r e s s my s i n c e r e t h a n k s t o my a d v i s o r , P r o f e s s o r L . A d a m o v i c h , whose u n d e r s t a n d i n g g u i d a n c e a l l o w e d me t o f i n i s h t h i s t h e s i s . I a l s o w i s h to t h a n k my f o r m e r a d v i s o r , P r o f e s s o r A . S . M i c h e l l , o f t h e F a c u l t y o f F o r e s t r y , U n i v e r s i t y o f T o r o n t o , who k i n d l y h e l p e d me t o u n d e r s t a n d t h e b a s i c p r i n c i p l e s o f C a n a d i a n f o r e s t r y . i x 1 C h a p t e r I INTRODUCTION 1.1 M e t h o d o f s t udy o f t he f o r e s t b r i d g e a c r o s s A l o u e t t e R i v e r The c h r o n o l o g i c a l s e q u e n c e o f t h e s t u d y i s as f o l l o w s : (a) The c o l l e c t i o n o f i n f o r m a t i o n c o n t a i n i n g t h e p r e s e n t s i t u a t i o n a l r e q u i r e m e n t s and t h e c o n d i t i o n s g o v e r n i n g f u t u r e i m p r o v e m e n t ; (b) F i e l d w o r k - d e t a i l e d s t a d i a s u r v e y o f t h e p r e s e n t l o c a t i o n i n c l u d i n g e l e v a t i o n s o f t h e r o a d and b r i d g e , and p h o t o g r a p h i n g the s i t e i n r e l a t i o n t o s u r r o u n d i n g l a n d s c a p e ; (c ) O f f i c e w o r k on t h e d e t a i l e d p l a n o f t h e b r i d g e s i t e and a p p r o a c h e s ; (d) The d e t e r m i n a t i o n and p l o t t i n g o f t he s e l e c t e d b r i d g e s i t e and t h e l o c a t i o n o f t h e a p p r o a c h e s i n p l a n and p r o f i l e , w i t h h o r i z o n t a l and v e r t i c a l a l i g n m e n t ; (e) E v a l u a t i o n o f t h e l a n d s c a p e t y p e and e n v i r o n m e n t o f t h e b r i d g e s i t e ; ( f ) S e l e c t i o n o f d i f f e r e n t t y p e s o f b r i d g e s mos t s u i t a b l e t o t h e e n g i n e e r i n g r e q u i r e m e n t s and the e n v i r o n m e n t ; (g) S e l e c t i o n o f t y p e s o f m a t e r i a l mos t s u i t a b l e t o t he e n v i r o n m e n t and t o t h e b r i d g e t y p e ; (h) The l o c a t i n g o f bank abu tmen t s and i n t e r m e d i a t e s u p p o r t s a c c o r d i n g t o t h e c o n s i d e r e d m a t e r i a l , e n v i r o n m e n t a l r e q u i r e m e n t s , and o v e r a l l a p p e a r a n c e o f t h e b r i d g e ; 2 ( i ) E n g i n e e r i n g c a l c u l a t i o n s o f t h e d i m e n s i o n s o f t h e m a i n p a r t s o f t h e s e l e c t e d t y p e s o f b r i d g e s i n a c c o r d a n c e w i t h C S A - S 6 D e s i g n o f H i g h w a y Bridges"*"; ( j ) B i l l o f m a t e r i a l s f o r t he m a i n e l e m e n t s o f t h e s e l e c t e d t y p e s o f b r i d g e s ; (d) E v a l u a t i o n o f t h e a n a l y z e d t y p e s o f b r i d g e s f r o m t h e a e s t h e t i c p o i n t o f v i e w , g i v i n g c o n s i d e r a t i o n to e c o n o m i c s and the f i n a l r e c o m m e n d a t i o n o f t he most s u i t a b l e t y p e . C a n a d i a n S t a n d a r d s A s s o c i a t i o n , D e s i g n o f H i g h w a y B r i d g e s , CSA S t a n d a r d S 6 - 1 9 6 6 , May 1966 ( O t t a w a , C a n a d a : C a n a d i a n S t a n d a r d s A s s o c i a t i o n , 1966) . 3 1.2 I n t r o d u c t i o n to A e s t h e t i c s B a s i c a e s t h e t i c f e e l i n g i s n a t u r a l t o e v e r y o n e who o b s e r v e s an o b j e c t o r l a n d s c a p e . K n o w l e d g e and e d u c a t i o n , h o w e v e r , e l e v a t e t h i s n a t u r a l a e s t h e t i c f e e l i n g t h r o u g h c o m p r e h e n s i o n ( o f t h e a e s t h e t i c s ) 2 3 and e x p e r i e n c e e x t e n d s t h i s s t i l l f u r t h e r . Newby s u m m a r i z e d M u n r o ' s e x p l a n a t i o n o f a e s t h e t i c s v e r y c l e a r l y b y s a y i n g : " I f we e x p r e s s v i s u a l p e r c e p t i o n o f a l a n d s c a p e as an a e s t h e t i c e x p e r i e n c e , i t c o u l d t a k e t h i s g e n e r a l e q u a t i o n f o r m s u g g e s t e d by Thomas Munro ( 1 1 ) : AE = PO + CP + E C . The a e s t h e t i c e x p e r i e n c e (AE) t h u s i s t h e sum o f r e l a t i o n s h i p s b e t w e e n t h e p e r c e i v e d o b j e c t o r l a n d s c a p e ( P O ) , t h e c h a r a c t e r i s t i c s o f t h e p e r c e i v e r ( C P ) , and t h e e n v i r o n m e n t a l c o n d i t i o n s o r c i r c u m s t a n c e s (EC) a t t h e t i m e o f e x p o s u r e . The p e r c e i v e d o b j e c t o r l a n d s c a p e i n c l u d e s e x i s t i n g , s u g g e s t e d and a n t i c i p a t e d q u a l i t i e s , c u l t u r a l and h i s t o r i c a l m e a n i n g s , and f o r m a l a r r a n g e m e n t s i n s p a t i a l , t e m p o r a l , c a u s a l , and o t h e r modes o f o r g a n i z a t i o n . The c h a r a c t e r - i s t i c s o f t h e p e r c e i v e r i n v o l v e s t a b l e , p e r m a n e n t , o r s l o w l y c h a n g i n g t r a i t s s u c h as s e x , p h y s i q u e , i n t e l l i g e n c e , p e r s o n a l i t y , s t a g e o f m a t u r a t i o n , s p e c i a l a p t i t u d e s , f a m i l i a l b a c k g r o u n d , and e d u c a t i o n ; a l s o i n v o l v e d a r e t r a n s i t o r y , r a p i d l y c h a n g i n g t r a i t s s u c h as mood, i n t e r e s t , e x p o s u r e to s o c i a l t r e n d s o r f a d s , and t h e a c t i v i t y o f t h e moment. F i n a l l y t h e e n v i r o n m e n t a l c o n d i t i o n s o r c i r c u m s t a n c e s s u r r o u n d i n g t h e i n t e r a c t i o n i n c l u d e s u c h t h i n g s as p h y s i c a l l o c a t i o n , p r e s e n c e o f o t h e r p e o p l e , o t h e r p e r c e p t u a l s t i m u l i , and t h e p h y s i c a l and c u l t u r a l e n v i r o n m e n t . " F . L . Newby, M a n - N a t u r e - B e a u t y : A r e s e a r c h d i l e m m a . P a p e r . V o l . V I , S e c t i o n 2 6 , X I V I U F R O - K o n g r e s s , M u n c h e n , Germany, 1 9 6 7 . p . 4 5 2 . 3 T . M u n r o , Toward s c i e n c e i n a e s t h e t i c s . (New Y o r k , N . Y . : The L i b e r a l A r t P r e s s , 1 9 5 6 ) . p . 2 7 . 4 1.3 E l e m e n t s o f A e s t h e t i c s B a s i c e l e m e n t s o f a n a l y s i s have b e e n s e t i n o r d e r t o f a c i l i - t a t e e v a l u a t i o n o f a e s t h e t i c s and as a r e s u l t , i m p r o v e l a n d s c a p e 4 management . They have b e e n g r o u p e d i n t o : 1.3.1 B a s i c C o n c e p t s 1.3.2 Dominance E l e m e n t s 1.3.3 Dominance P r i n c i p l e s 1.3.4 V a r i a b l e F a c t o r s 1.3.1 B a s i c C o n c e p t s B a s i c c o n c e p t s d e a l w i t h c h a r a c t e r i s t i c l a n d s c a p e , d i v i d e d f o r s i m p l i f i c a t i o n i n t o s u b g r o u p s o f l a n d s c a p e f o r m s , a c c o r d i n g to t h e g o v e r n i n g d o m i n a n t e l e m e n t s . B a s i c c o n c e p t s a l s o i n c l u d e v a r i e t y , w h i c h d e a l s w i t h o b j e c t - r i c h l a n d s c a p e s and s e r v e s as a s i g n i f i c a n t g u i d e l i n e i n d e t e r m i n i n g how much v a r i e t y i s d e s i r a b l e i n l a n d s c a p e . D e v i a t i o n s f r o m c h a r a c t e r - i s t i c s l a n d s c a p e , w h i c h a r e a l s o i n c l u d e d i n b a s i c c o n c e p t s , a r e c a u s e d b y t h e p r o v i s i o n o f n e c e s s a r y r e s o u r c e s f o r a n a t i o n ' s economy. 1.3.2 Dominance E l e m e n t s Dominance e l e m e n t s i n c l u d e f o r m , l i n e , c o l o u r and t e x t u r e . A l t h o u g h a l l o f them a r e u s u a l l y p r e s e n t , e a c h one e x e r t s a d i f f e r i n g d e g r e e o f v i s u a l power o r d o m i n a n c y . U . S . D e p a r t m e n t o f A g r i c u l t u r e , N a t i o n a l F o r e s t L a n d s c a p e M a n a g e - m e n t , F e b . 1 9 7 3 , V o l . I ( W a s h i n g t o n , D . C : Government P r i n t i n g O f f i c e , 1973) . p . 2 - 1 3 . 5 1 . 3 . 2 . 1 Form The mass o f an o b j e c t , o r o f a c o m b i n a t i o n o f o b j e c t s , t ' . iat a p p e a r s u n i f i e d i s d e f i n e d as " f o r m " . I n two d i m e n s i o n a l p i c t u r e s i t i s c a l l e d " s h a p e " b u t s i n c e mos t l a n d s c a p e o b j e c t s a r e t h r e e d i m e n s i o n a l , t h e t e r m " f o r m " i s more o f t e n u s e d . 1 . 3 . 2 . 2 L i n e S i n c e a l i n e i s a p o i n t t h a t h a s b e e n e x t e n d e d , i t c a n be a n y t h i n g t h a t i s a r r a n g e d i n a row o r a s e q u e n c e . A l i n e c a n be c o n s i d e r e d s e p a r a t e l y o r i t c a n make up t h e s i l h o u e t t e o f a f o r m . I t c a n a l s o be t h e i n t e r s e c t i o n o f two p l a n e s . A l l t h e s e may be f o u n d i n s h o r e l i n e s , t i m b e r l i n e s , a v a l a n c h e p a t h s , v e g e t a t i v e b o u n d a r i e s , e t c . 1 . 3 . 2 . 3 C o l o u r E v e n when t h e o b j e c t s h a v e i d e n t i c a l f o r m , l i n e and t e x t u r e , c o l o u r e n a b l e s us t o d i f f e r e n t i a t e b e t w e e n them. T h i s c o l o u r dominance o f t e n depends on t h e p o s i t i o n o f t h e o b s e r v e r . D u s t and m o i s t u r e c a u s e d i s t a n t c o l o u r s t o become muted b y a b l u i s h h a z e , w h i l e f o r e g r o u n d c o l o u r s r e m a i n s t r o n g and d o m i n a n t . 1 . 3 . 2 . 4 T e x t u r e D i s t a n c e v a r i e s t h e d o m i n a n c y o f t e x t u r e . ( F o r e x a m p l e , l e a f p a t t e r n s a r e d o m i n a n t when v i e w i n g a t r e e f rom a d i s t a n c e o f a few f e e t , h o w e v e r , m a j o r b r a n c h e s become d o m i n a n t a t a few h u n d r e d f e e t , w h i l e e n t i r e g r o u p s o f t r e e s a r e t h e d o m i n a n t t e x t u r e a t a d i s t a n c e o f a few m i l e s . ) 1 . 3 . 3 Dominance P r i n c i p l e s The v i s u a l dominancy o f f o r m , l i n e , c o l o u r and t e x t u r e a r e 6 a f f e c t e d by s i x b a s i c p r i n c i p l e s , w h i c h a r e : c o n t r a s t , s e q u e n c e , a x i s , c o n v e r g e n c e , c o - d o m i n a n c e and enf ramement . G r e a t c o n t r a s t s a r e i m m e d i a t e l y a p p a r e n t t o a l l o b s e r v e r s , w h i l e c o n t r a s t s w i t h l i t t l e o r no v i s u a l e f f e c t , s i m p l y c a n n o t be s e e n . A t t i m e s , c r e a t i n g s h a r p c o n t r a s t s i n t he n a t u r a l e n v i r o n m e n t c a n be b e n e f i c i a l , b u t t h e n t h e o b j e c t i n q u e s t i o n must be so w e l l i n t r o d u c e d t h a t i t c a n s t a n d up t o t h e c l o s e s c r u t i n y w h i c h i t s p r o m i n e n c e w i l l demand. The q u e s t i o n o f c o n t r a s t i s p r o b a b l y t h e mos t s i g n i f i c a n t i n b r i d g e d e s i g n , and b l e n d i n g s h o u l d t a k e p r e c e d e n c e o v e r c o n t r a s t i n c a s e s w h e r e o n l y a m e d i o c r e c o n t r a s t c a n be a c h i e v e d o r where c o n t r a s t i s u n d e s i r a b l e . 1 . 3 . 4 V a r i a b l e F a c t o r s Dominance e l e m e n t s a r e a l s o a f f e c t e d by v a r i a b l e f a c t o r s w h i c h c a n be c o n s i d e r e d as more o r l e s s s u b j e c t i v e . T h e y i n c l u d e : m o t i o n , l i g h t , a t m o s p h e r i c c o n d i t i o n s , s e a s o n , d i s t a n c e , o b s e r v e r ' s p o s i t i o n , s c a l e and t i m e . They h e l p t o i d e n t i f y t h e mos t c r i t i c a l l o c a t i o n o r t i m e a t w h i c h t o j u d g e t h e p o t e n t i a l v i s u a l i m p a c t , u n d e r t h e mos t s e v e r e and s e n s i t i v e c o n d i t i o n s p o s s i b l e . 7 1.4 S t r u c t u r a l A e s t h e t i c s B r i d g e d e s i g n i s c l o s e l y a l l i e d to a r c h i t e c t u r e and s h o u l d , t h e r e f o r e , be c o n s i d e r e d an a p p l i e d a r t . A n a d e q u a t e t y p e o f d e s i g n s h o u l d be s e l e c t e d f o r e a c h b r i d g e , no m a t t e r w h a t p u r p o s e i t i s to s e r v e . Tempora ry b r i d g e s , e x p l i c i t l y d e s i g n e d t o s e r v e f o r a s h o r t t i m e , s h o u l d be c o n s i d e r e d e x c e p t i o n s . H o w e v e r , e v e n t h i s m i g h t b a q u e s t i o n a b l e ; t e m p o r a r y b r i d g e s may s e r v e f o r l o n g p e r i o d s o f t i m e e v e n a f t e r t h e i r p r i m a r y f u n c t i o n i s o v e r , u s u a l l y f o r r e c r e a t i o n a l p u r p o s e s l i k e h i k i n g , h u n t i n g , e t c . L e C o r b u s i e r , a r c h i t e c t and p a i n t e r , i n h i s b o o k " T o w a r d s a New A r c h i t e c t u r e " ^ , d e f i n e s e n g i n e e r i n g a e s t h e t i c s and b e a u t y by s a y i n g t h a t an e n g i n e e r a p p l i e s e c o n o m i c l a w s , and c a l c u l a t i o n s t o a c h i e v e and c r e a t e ha rmony , when he w o r k s i n a c c o r d a n c e w i t h t h e s e l a w s . C a l c u l a t i o n s , w h i c h come f rom n a t u r a l l a w s , p r o v i d e t h e t o o l s w i t h w h i c h t h e e n g i n e e r c r e a t e s t h e r e s u l t i n g a r c h i t e c t u r e and i n t u r n , communica t e s w i t h t h e o b s e r v e r t h r o u g h h a r m o n y . He s e p a r a t e s c o n s t r u c t i o n f r o m a r t i s t i c w o r k by s a y i n g : "We u s e s t o n e , w o o d , c o n c r e t e , we b u i l d h o u s e s and p a l a c e s , t h a t a l l i s a q u e s t i o n o f c o n s t r u c t i o n . We e m p h a s i z e t h e w o r k . T h i s a l l h a s a b i g i n f l u e n c e on m e , . I f e e l happy and ( I ) s a y : I t i s b e a u t i f u l . H e r e we h a v e a c o n s t r u c t i o n a r t . " To s u m m a r i z e L e C o r b u s i e r ' s e x p r e s s i o n s , we c a n s a y t h a t t h e b e a u t y o f an e n g i n e e r i n g s t r u c t u r e l i e s i n i t s ha rmony , i t s b a l a n c e . 5 L e C o r b u s i e r , V e r s Une A r c h i t e c t u r e ( "Towards a New A r c h i t e c t u r e " ) , ( P a r i s : V i n c e n t , F r e a l & C i e . , 1 9 5 8 ) . p . 8 0 . 8 The b a l a n c e t h e n has to be c o n s i d e r e d w i t h i n t h e s t r u c t u r e i t s e l f , and w i t h t h e s u r r o u n d i n g l a n d s c a p e . I t s h o u l d be p o i n t e d o u t t h a t c r i t i c i s m o f e a c h a r t , e v e n a p p l i e d a r t , i s v e r y s u b j e c t i v e . I t i s d i f f i c u l t t o s a t i s f y e v e r y b o d y . T h e r e a r e , h o w e v e r , g e n e r a l l y a c c e p t e d b a s i c p r i n c i p l e s , w h i c h i f f o l l o w e d , c a n p r o v i d e v i s u a l a p p r e c i a t i o n . I t seems t h a t s e l e c t i n g an a c c e p t a b l e a r c h i t e c t u r a l t y p e o f b r i d g e i n c i t i e s i s s i m p l e r t h a n i n t h e c o u n t r y ( F i g u r e s 1 and 2 ) , t h e m a i n r e a s o n b e i n g t h a t t h e t y p e o f b r i d g e i n c i t i e s i s a c t u a l l y d i c t a t e d by t h e s u r r o u n d i n g a r c h i t e c t u r e - o r i n t e n d e d a r c h i t e c t u r e - w h i ] t h e s o l u t i o n f o r r u r a l l o c a t i o n s i s u s u a l l y more c o m p l e x . A s k e t c h s t u d y , o r p l o t t i n g t h e d e s i g n e d b r i d g e o n t o p h o t o g r a p h s , i m m e d i a t e l y shows any d i s c o r d w i t h t h e e n v i r o n m e n t . S e l e c t i o n o f a p r o p e r b r i d g e t y p e o u t s i d e the c i t i e s r e q u i r e s more c o n s i d e r a t i o n , d e p e n d i n g more on t h e t y p e o f r o a d o r h i g h w a y and. t h e g e n e r a l l a n d s c a p e . (a) I n mos t c a s e s , s i n c e b r i d g e s a r e t h e most e x p e n s i v e p a r t o f t h e r o a d , t h e b r i d g e s i t e i s n a t u r a l l y p r e v a l e n t o v e r t h e r o a d l o c a t i o n . (b) The f u n c t i o n o f t h e b r i d g e and t h e t y p e o f t r a n s p o r t a t i o n i t has to s e r v e , d i c t a t e i t s t e c h n i c a l r e q u i r e m e n t s - s i z e and d i m e n s i o n s . (c ) R e c e n t l y , t h e i d e a o f m u l t i p u r p o s e r o a d s has b e e n e x t e n s i v e l y s t r e s s e d so t h e s c e n i c v a l u e s and t h e a n c i l l a r y f e a t u r e s ; i . e . s i d e w a l k s , p a r k i n g a r e a s and so o n , h a v e t o b e c o n s i d e r e d a l s o . (d) The b r i d g e s t r u c t u r e , m a t e r i a l , p r o p o r t i o n s , e t c . , mus t f o l l o w some b a s i c p r i n c i p l e s o f a e s t h e t i c d e s i g n i n o r d e r t o p l e a s e n o t o n l y t h o s e who u s e t h e b r i d g e b u t a l s o t h o s e who l o o k a t i t . F i g u r e 2 - B r i d g e i n a n a t u r a l s e t t i n g . - J a p a n e s e G a r d e n . 10 A v e r y u n i q u e and c o m p l e x a n a l y s i s o f b r i d g e a e s t h e t i c s has 6 b e e n done by P a c h o l i k . A l t h o u g h h i s a n a l y s i s d e a l s m o s t l y w i t h b r i d g e s i n E u r o p e a n c i t i e s , some comments abou t t h e o u t - o f - c i t y and A m e r i c a n b r i d g e s a r e i n c l u d e d . The p r i n c i p l e s o f some o f h i s i d e a s a r e d i s c u s s e d i n t h i s p a p e r u n d e r a n a l y s i s o f b r i d g e a e s t h e t i c s , and i t s p r a c t i c a l a p p l i c a b i l i t y i s u s e d i n t h e A l o u e t t e R i v e r C r o s s i n g s t u d y . L . P a c h o l i k , E s t e t i k a M o s t n i c h S t a v e b ( " A e s t h e t i c s o f B r i d g e S t r u c t u r e s " ) ( P r a g u e : U s t a v p r o Ucebne Pomucky P r u m y s l o v y c h a O d b o r n y c h S k o l v P r a z e , 1 9 4 6 ) . p . 26 - 8 4 . 11 C h a p t e r I I A N A L Y S I S OF BRIDGE AESTHETICS A e s t h e t i c s d e a l s w i t h h a r m o n y , and harmony d e a l s w i t h b a l a n c e . I n g e n e r a l , l a r g e b r i d g e s h a v e b e e n u s e d i n a n a l y z i n g s t r u c t u r a l a e s t h e t i c s , s i n c e t h e s e examples and a rgumen t s a r e more r e a d i l y u n d e r - s t o o d . H o w e v e r , t h e same p r i n c i p l e s a p p l y t o s m a l l b r i d g e s o n m u l t i - p u r p o s e r o a d s , whe re v e r y few l a r g e spans a r e e x p e c t e d . O b v i o u s l y , t h e e f f e c t o f o b s e r v a t i o n w i l l depend on o b s e r v i n g d i s t a n c e . E a c h b r i d g e has f o u r e l e m e n t s w h i c h h a v e t o be d e s i g n e d i n a c e r t a i n s e q u e n c e o f impor tance '* ' . 2.1 Roadway and g u a r d r a i l s 2.2 S u p p o r t i n g s t r u c t u r e 2.3 P i e r s and abu tmen t s 2.4 B r i d g e heads E a c h h i g h e r e l e m e n t i s d o m i n a n t t o t h e o t h e r s w h i c h a r e b e l o w . C h a n g i n g t h e s e q u e n c e o f i m p o r t a n c e , i . e . i f a h i g h e r e l e m e n t i s s u p p r e s s e d by a l e s s e r o n e , t h i s c a u s e s t h e n a t u r a l b a l a n c e o f t h e s t r u c t u r e t o be a e s t h e t i c a l l y d e s t r o y e d and t h e b e a u t y t o be l o s t . T h i s d i v i s i o n i s l o g i c a l , s i n c e i t i s b a s e d o n f u n c t i o n a l s e q u e n c e , i . e . roadway i s mos t i m p o r t a n t b e c a u s e i t has t h e m a i n ^ L . P a c h o l i k , E s t e t i k a M o s t n i c h S t a v e b ( " A e s t h e t i c s o f B r i d g e S t r u c t u r e s " ) ( P r a g u e : U s t a v p r o Ucebne Pomucky P r u m y s l o v y c h a O d b o r n y c h S k o l v P r a z e , 1 9 4 6 ) . p . 6 5 . 12 f u n c t i o n , w h i l e t h e s u p p o r t i n g s t r u c t u r e h o l d s s e c o n d p l a c e b e c a u s e i t a l l o w s the roadway t o be c a r r i e d o v e r t h e o b s t r u c t i o n and so o n . I n C a n a d a , b r i d g e s a r e n o t u s u a l l y d i v i d e d i n t o g r o u p s a c c o r d i n g t o t h e p o s i t i o n o f t he roadway and s u p p o r t i n g s t r u c t u r e . S i n c e t h e e v a l u a t i o n has b e e n made f o r t h a t p o s i t i o n i n g , F i g u r e s 3, A and 5 c l a r i f y t he n o m e n c l a t u r e u sed i n the t e x t o f t h i s p a p e r . 2.1 Roadway and g u a r d r a i l 2.1.1 Roadway The p u r p o s e o f t h e b r i d g e i s t o t r a n s f e r t h e r o u t e and t h e t r a f f i c s a f e l y o v e r an o b s t r u c t i o n ( r i v e r , deep v a l l e y , a n o t h e r r o a d ) . I t i s d i f f i c u l t t o e x p r e s s t h e roadway i t s e l f a r t i s t i c a l l y . H o w e v e r , i t has t o be e m p h a s i z e d as much as p o s s i b l e by a c o n t i n u o u s l i n e and a p r o p e r l y s e l e c t e d g u a r d r a i l . The e m p h a s i s on the roadway a p p e a r a n c e i s e x t r e m e l y i m p o r t a n t b e c a u s e o f i t s m a i n f u n c t i o n . The l a c k o f c o n t i n u i t y c r e a t e s an u n b a l a n c e d - l o o k i n g s t r u c t u r e . C o n t i n u i t y o f roadway a p p l i e s m a i n l y t o t h e s i d e v i e w ( F i g u r e 6) and t o t h e t h r e e d i m e n s i o n a l v i e w ( F i g u r e 7 ) . I n t h e p e r s p e c t i v e v i e w , e s p e c i a l l y , t h e c o n t i n u i t y w i t h t h e r o a d l i n e o r h i g h w a y i s d i r e c t l y i n v o l v e d . Somet imes e m p h a s i s o f t h e r o a d i s n e g l e c t e d , e s p e c i a l l y i n t h e c a s e o f c o n c r e t e beam o r a r c h b r i d g e s , s t e e l t r u s s e s o r some wooden s t r u c t u r e s . A common f a i l i n g i s u s u a l l y t h e l a c k o f d e f i n i t i o n o f t h e s t r u c t u r a l p a r t s , r e s u l t i n g i n a u n i f o r m i t y f rom t h e l o w e r edge o f t h e s u p p o r t i n g s t r u c t u r e up t o t h e u p p e r edge o f t h e g u a r d r a i l s ( F i g u r e 8 ) . A n o t h e r common p i t f a l l , i s v i s u a l l y b r e a k i n g the roadway and an o t h e r w i s e w e l l - d e s i g n e d g u a r d r a i l by e x t e n d i n g t h e p i e r s up t o t h e t o p o f t h e F i g u r e 3 - R o a d w a y - a b o v e . . F i g u r e 4 - H a l f - s u n k roadway > F i g u r e 5 - R o n d w a y - b e l o w . F i g u r e 6 - S i d e v i e w o f t h e b r i d g e ( s h a p e ) . F i g u r e 7 - T h r o e d i m e n s i o n a l ( p e r s p e c t i v e ) v i e w o f t h e b r i d g e ( f o r m ) . I 15 16 g u a r d r a i l o r h i g h e r ( F i g u r e 9 ) . T h i s s e r v e s m a i n l y t o a n c h o r t h e g u a r d r a i l i n t h e p i e r s b u t s t a t i c a l l y t h i s i s n o t n e c e s s a r y . O t h e r t y p e s o f v i s u a l l y s u p p r e s s e d r o a d w a y s o c c u r when t h e s u p p o r t i n g s t r u c t u r e i n t e r s e c t s t h e r o a d w a y . T h i s t y p e o f d e t r a c t i o n c a n be f o u n d , o f c o u r s e , w i t h a l l t y p e s o f h a l f s u n k roadway b r i d g e s and c a n be c l e a r l y d e f i n e d b y w a t c h i n g t h e u p p e r and l o w e r o u t l i n e ( c o n t o u r s ) o f t h e b r i d g e . The i m p r e s s i o n t h e n o b t a i n e d i s o f two s e p a r a t e s t r u c t u r e s ( F i g u r e s 10 and 1 1 ) . As f a r as t h e o t h e r two t y p e s o f roadway a r e c o n c e r n e d ( r o a d w a y - a b o v e and r o a d w a y - b e l o w ) , t h e r e a r e b a s i c a l l y no p r o b l e m s w i t h roadway a e s t h e t i c s . S e l e c t i o n o f t h e p r e f e r a b l e s u p p o r t i n g s t r u c t u r e , t h e r e f o r e , depends a l m o s t e n t i r e l y o n t h e l a n d s c a p e ( s e e l a t e r ) . T h e r e i s one more e f f e c t w h i c h s h o u l d be m e n t i o n e d h e r e and t h a t i s t h e e f f e c t o f g u a r d r a i l s . S i n c e t h e g u a r d r a i l i s an e f f i c i e n t t o o l f o r u n d e r l i n i n g t h e f u n c t i o n a l ' i m p o r t a n c e o f t h e r o a d w a y , i t c a n be u s e d more e f f e c t i v e l y o n r o a d w a y - a b o v e b r i d g e s t h a n o n r o a d w a y - b e l o w b r i d g e s . The i n s i d e v i e w o f t h e b r i d g e has n o t b e e n c o n s i d e r e d v e r y o f t e n and y e t i t h a s b e e n f o u n d t h a t some t y p e s o f r o a d w a y - b e l o w b r i d g e s , e s p e c i a l l y s t e e l c l o s e d f rame s t r u c t u r e s , h a v e a d e p r e s s i v e i n f l u e n c e on d r i v i n g o r w a l k i n g p e r s o n s ( F i g u r e 1 2 ) . P s y c h o l o g i c a l l y , i t i s q u i t e n a t u r a l f o r p e o p l e t o p r e f e r an u n o b s t r u c t e d v i e w and an open a i r f e e l i n g t h a n t o w a l k o r d r i v e i n an i r o n b o x . The l a t t e r f e e l i n g i s s i m i l a r t o one w h i c h p e o p l e h a v e w h i l e d r i v i n g i n a t u n n e l . I t s h o u l d be k e p t i n m i n d t h a t t h e p s y c h o l o g i c a l e f f e c t i s s l i g h t l y d i f f e r e n t w i t h r e i n f o r c e d c o n c r e t e b r i d g e s s i n c e t h e r e i s a 1 17 U p p e r c o n t o u r Lower c o n t o u r F i g u r e 11 - Upper and l o w e r v i e w o f a b r i d g e w i t h a h a l f - s u n k r o a d w a y . F i g u r e 13 - S i d e w a l k s o u t s i d e t h e m a i n s t r u c t u r e . 19 d i f f e r e n t a r r a n g e m e n t o f d i a g o n a l s and w i n d b r a c i n g . A s u b s t i t u t e a r r a n g e m e n t c a n be found f o r s t e e l o r wood c l o s e d frame s t r u c t u r e by l o c a t i n g t h e s i d e w a l k s o u t s i d e t h e m a i n s u p p o r t i n g s t r u c t u r e ( F i g u r e 1 3 ) . T h i s i s a l s o s a f e r f o r t h e , p e d e s t r i a n . The p r o f i l e o f t h e roadway s h o u l d a l s o be c o n s i d e r e d a l o n g w i t h t h e i n s i d e v i e w . P r e f e r a b l y , t h e p r o f i l e s h o u l d be s t r a i g h t ; e i t h e r h o r i z o n t a l o r s l i g h t l y s l o p e d to one end'. S l i g h t s l o p i n g to b o t h ends o f t h e b r i d g e i s a c c e p t a b l e , b u t s t e e p s l o p i n g s h o u l d be a v o i d e d , a s t h e r e i s l i m i t e d v i s i b i l i t y f r o m one end o f t h e b r i d g e t o t h e o t h e r and a s u d d e n a p p e a r a n c e o f o n - c o m i n g t r a f f i c c a n be u n p l e a s a n t . L a s t , b u t n o t l e a s t i n t h e i n s i d e v i e w a n a l y s i s , i s t h e w i d t h o f t he r o a d w a y . The w i d e r t h e roadway t h e b e t t e r . The w i d t h o f t h e r o a d , o f c o u r s e , i s l a r g e l y d e p e n d e n t upon t h e number o f l a n e s l e a d i n g f r o m t h e r o a d o r h i g h w a y . L o n g and v e r y e x p e n s i v e s t r u c t u r e s a r e somet imes n a r r o w e r , s i n c e t h e maximum c a p a c i t y f o r a g i v e n speed on t h e b r i d g e i s p r e c a l c u l a t e d f o r u n b r o k e n t r a f f i c ( L i o n s G a t e B r i d g e , V a n c o u v e r , B . C . , F i g u r e 1 9 ) . T h e s e t y p e s o f s t r u c t u r e may a p p e a r t o be o u t o f p r o p o r t i o n ( i n w i d t h , h e i g h t and l e n g t h ) , and a l s o i n o v e r a l l a p p e a r a n c e . H o w e v e r , i t w o u l d be an e x p e n s i v e p r o p o s i t i o n t o keep p r o p o r t i o n a l i t y f o r s u c h s t r u c t u r e s . P a r t i c u l a r l y i n roadway e m p h a s i s , w h e r e t h e q u e s t i o n o f p r o p o r t i o n s a r i s e s , t h e s u s p e n s i o n b r i d g e seems t o be a c o n v e n i e n t s t r u c t u r e ( F i g u r e 1 9 ) . Somet imes a change f rom t h e r o a d w a y - a b o v e t o t h e r o a d w a y - b e l o w a r r a n g e m e n t ( F i g u r e 1 4 , 15) and b a c k a g a i n i s n e c e s s a r y b e c a u s e o f t he i n c r e m e n t i n o v e r h e a d c l e a r a n c e . S u c h a change c a n r e a d i l y F i g u r e 15 - A l t e r n a t i v e s o l u t i o n o f c h a n g i n g p o s i t i o n o f r o a d w a y . 21 a f f e c t t h e a e s t h e t i c a p p e a r a n c e and t h e r e a r e v e r y l i m i t e d means o f s o l v i n g t h i s p r o b l e m f r o m t h e a e s t h e t i c p o i n t o f v i e w . One o f t h e few p o s s i b i l i t i e s i s t o s e t one o r more l o n g and d o m i n a n t spans a c r o s s t h e r i v e r w i t h t h e r o a d w a y - b e l o w a r r a n g e m e n t , w h i l e m a i n t a i n i n g s h o r t s p a n s o n b a n k s w i t h t h e r o a d w a y - a b o v e . S i n c e s h o r t s p a n s g i v e t h e i m p r e s s i o n o f e x t e n d e d a b u t m e n t s , t h e f u n c t i o n a l a p p e a r a n c e o f t h e b r i d g e i s i n harmony w i t h t h e a p p r o a c h e s ( F i g u r e s 1 4 , 1 5 ) . T h i s s o l u t i o n m i g h t seem a b i t c l u m s y b u t i t f u l l y c o r r e s p o n d s w i t h t h e t h e o r y o f u n b r o k e n roadway l i n e . Of c o u r s e , some f l e x i b i l i t y i n t h i s s o l u t i o n i s t o be e x p e c t e d , s i n c e d i f f e r e n t c i r c u m s t a n c e s ( e . g . l a n d s c a p e ) m i g h t b r i n g o u t d i f f e r e n t i m p r e s s i o n s a b o u t t h e same t y p e o f cons t r u e t i o n . 2 . 1 . 2 G u a r d r a i l A s m e n t i o n e d b e f o r e , t h e g u a r d r a i l i s an i m p o r t a n t c o n s t r u c t i v e and a e s t h e t i c a c c e s s o r y o f t h e roadway b e c a u s e i t h e l p s t o e m p h a s i z e t h e f u n c t i o n a l a p p e a r a n c e o f t h e r o a d w a y , e s p e c i a l l y w i t h t h e r o a d w a y - above b r i d g e s . S i n c e t h e f u n c t i o n o f t h e g u a r d r a i l i s a l s o t o d i r e c t t r a f f i c v i s u a l l y , t h e c o n s t r u c t i o n s h o u l d be l i g h t i n c o m p a r i s o n t o t h e s u p p o r t i n g s t r u c t u r e and t h e r o a d w a y . T h e r e a r e many ways o f u s i n g g u a r d r a i l s p r o p e r l y . The m o s t e f f i c i e n t i s t h e u n b r o k e n h a n d r a i l l i n e ( o f t he g u a r d r a i l ) , p a r a l l e l t o t h e r o a d w a y . F i g u r e s 9 and 17 do n o t f o l l o w t h i s r u l e and d e m o n s t r a t e t h e e f f e c t o f a b r o k e n g u a r d r a i l ( w h i c h s h o u l d be a v o i d e d ) . A f u l l c o n c r e t e g u a r d r a i l n e v e r l o o k s l i g h t ( F i g u r e 8) a n d , t h e r e f o r e , s h o u l d be a r t i c u l a t e d i n some o t h e r way ( F i g u r e s 16 and 1 8 ) . The u s e o f d i f f e r e n t m a t e r i a l a n d / o r c o l o u r s i s a l s o v e r y e f f e c t i v e . F i g u r e 17 - I n t e r f e r e n c e o f t he roadway and t h e g u a r d r a i l by e x t e n d e d p i e r s . 23 24 The c o n s t r u c t i o n m a t e r i a l does n o t need to be o f t h e same n a t u r e , b u t d i f f e r e n t t y p e s o f m a t e r i a l , i f u s e d , must be i n h a r m o n y . S t o n e and w o o d , o r c o n c r e t e and s t e e l , a r e known t o be good c o m b i n a t i o n s , w h e r e a s , w o o d - s t e e l o r s t o n e - s t e e l a r e l e s s p r e f e r a b l e . A w o o d - c o n c r e t e c o m b i n a t i o n i s p r o b a b l y t h e w o r s t k i n d . S i n c e t h e g u a r d r a i l i s j u d g e d n o t o n l y f o r o u t s i d e a p p e a r a n c e b u t a l s o f r o m i n s i d e t h e b r i d g e , i t has t o c r e a t e a f e e l i n g o f s a f e t y f o r p e d e s t r i a n s and d r i v e r s . F o r v e r y h i g h b r i d g e s , t h e h e a v i e r t y p e o f g u a r d r a i l i s recommended. S h o r t p o s t s do n o t a c t i n t h e same way as t he e x t e n d e d s u p p o r t on F i g u r e 1 7 , b e c a u s e t h e y a r e u n i f o r m l y d i v i d e d , r e g a r d l e s s o f s u p p o r t s . F u r t h e r m o r e , t h i s o u t s i d e v i e w a p p e a r a n c e i s n o t a s d e t r a c t i n g as t h a t o f a n e x t e n d e d s u p p o r t . The same c r i t e r i a a p p l y t o t h e g u a r d r a i l o n t h e s u s p e n s i o n b r i d g e , b u t t h e g u a r d r a i l s h o u l d n o t be i n t e r s e c t e d by s u p p o r t i n g c a b l e s , o t h e r w i s e t h e c o n t i n u i t y i s d i s r u p t e d . The d i f f e r e n t e f f e c t s a r e shown i n F i g u r e s 20 and 2 1 . I n summary, t h e b e s t a e s t h e t i c r e s u l t s f o r t h e roadway and t h e g u a r d r a i l a r e g e n e r a l l y o b t a i n e d w i t h t h e s u s p e n s i o n ( F i g u r e 19) and t h e r o a d w a y - a b o v e b r i d g e s ( F i g u r e 1 8 ) , s i n c e t h e y a l l o w c l e a r l i n e s w h i c h b e s t e x p r e s s t h e n a t u r a l b e a u t y o f an u n b r o k e n r o a d w a y . 2 . 2 S u p p o r t i n g S t r u c t u r e The s u p p o r t i n g s t r u c t u r e i s t h e n e x t most \ s i g n i f i c a n t e l e m e n t w h i c h d e t e r m i n e s t h e b e a u t y o f a b r i d g e . The s u p p o r t i n g s t r u c t u r e h a s t o e x p r e s s t h e s t r e n g t h , w h i c h the eyes o f o n l o o k e r s s u b c o n s c i o u s l y e x p e c t , i . e . s u p p o r t i n g e l e m e n t s n o t o n l y have t o be s t r o n g enough 25 F i g u r e 21 - I m p r o p e r l o c a t i o n o f t h e c a b l e t o t h e roadway and g u a r d r a i l . 26 a c c o r d i n g t o s t a t i c and d y n a m i c c a l c u l a t i o n s , b u t t h e y a l s o h a v e t o l o o k s t r o n g . T h i s r e q u i r e m e n t i s n o t a l w a y s f u l f i l l e d , e s p e c i a l l y when two s u p p o r t i n g e l e m e n t s (beam and a r c h ) s h a r e t h e s t r e n g t h . A p r o p e r r a t i o b e t w e e n t h e s e two e l e m e n t s i s t h e mos t i m p o r t a n t f a c t o r i n t h e a e s t h e t i c s o f b r i d g e s ( F i g u r e s 22 and 23) . T h e r e a r e t h r e e b a s i c t y p e s o f s u p p o r t i n g s t r u c t u r e w h i c h a r e a e s t h e t i c a l l y s u i t a b l e and a l l o f them h a v e t h o u s a n d s o f y e a r s o f h i s t o r y b e h i n d them. They a r e : 2 . 2 . 1 Beams 2 . 2 . 2 A r c h e s 2 . 2 . 3 S u s p e n s i o n s t r u c t u r e A l l o f t h e s e h a v e t o have c l e a r c o n t o u r s . A s m e n t i o n e d b e f o r e , t h e roadway and t h e s u p p o r t i n g s t r u c t u r e s h o u l d n o t i n t e r s e c t , o t h e r w i s e t h e harmony o f b o t h i s t a k e n away and t h e c l e a r n e s s o f t h e c o n t o u r s i s s p o i l e d . C o n t o u r s make t h e b e a u t y o f b r i d g e s , and no o t h e r c i v i l e n g i n e e r i n g s t r u c t u r e s ' c o n t o u r s a r e as i m p o r t a n t as t h o s e o f b r i d g e s . The b r i d g e i s i m m e d i a t e l y i m p r e s s i v e i f t h e c o n t o u r s a r e c o r r e c t and e x p r e s s i v e . The b r i d g e i s t h e n p e r c e i v e d and a p p r e c i a t e d . O t h e r w i s e i t r e m a i n s u n a t t r a c t i v e and even o f f e n d i n g . The b r i d g e h a s two m a i n c o n t o u r s : u p p e r and l o w e r . One i s p e r f o r m e d by t h e r o a d w a y , t h e o t h e r by t h e s u p p o r t i n g s t r u c t u r e w h i c h some t imes i n c l u d e s t h e p r o f i l e o f t h e p i e r s . The i m p o r t a n c e o f t h e r o a d - way has b e e n d e a l t w i t h e a r l i e r . I t w o u l d be a m i s t a k e to d e s i g n a t h i n l o o k i n g roadway w i t h s t r o n g ( t h i c k ) l o o k i n g s u p p o r t i n g s t r u c t u r e and v i c e v e r s a ( F i g u r e s 22 and 2 3 ) . By r e f e r r i n g t o and u t i l i z i n g t h e F i g u r e 22 - I m p r o p e r b a l a n c e b e t w e e n beam and a r c h . F i g u r e 23 - I m p r o p e r b a l a n c e b e t w e e n beam and a r c h . 28 t h r e e b a s i c t y p e s o f s u p p o r t i n g s t r u c t u r e s m e n t i o n e d a b o v e , i n c o r r e c t l i n e s c a n more r e a d i l y be e l i m i n a t e d f r o m b r i d g e d e s i g n . Beams, a r c h e s , and s u s p e n s i o n s y s t e m s h a v e n a t u r a l p r e c e d e n t s i n t he p a s t , w h e r e b y a f a l l e n t r e e , o v e r a r i v e r , s e r v e d as a beam; two t r e e s b e n t t o f o r m an a r c h and l i a n a s fo rmed a s u s p e n s i o n b r i d g e . A n a l o g i e s c a n be f o u n d b e t w e e n t h e a r c h i t e c t u r e o f b r i d g e s and b u i l d i n g s . The i n d u s t r i a l r e v o l u t i o n , w h i c h was r e f l e c t e d i n t h e a r c h i t e c t u r e o f t h e s e c o n d h a l f o f t h e l a s t c e n t u r y as a new a r c h i t e c t u r a l t r e n d - " s e c e s s i o n " - b r o u g h t o u t u n n a t u r a l and s o m e t i m e s u n n e c e s s a r y l i n e s . Up t o t h a t t i m e , we c a n f o l l o w n a t u r a l l i n e s i n s t r u c t u r e s . A f t e r t h i s " s e c e s s i o n " was o v e r , one n o t i c e d a s l o w comeback i n a r c h i t e c t u r e t h r o u g h economy on t h e one hand and n a t u r a l a e s t h e t i c f e e l i n g o n t h e o t h e r . 2 . 2 . 1 Beams S t r a i g h t c o n t o u r s a r e p r e f e r a b l e i n t h e v a r i o u s t y p e s o f beams w h e t h e r t h e y be s i m p l e beams o r s t r a i g h t t r u s s e s o f l o n g s p a n b r i d g e s ( F i g u r e 24 ( b ) ) . D i f f e r e n t h e i g h t s o f t h e beams ( F i g u r e 25 ( b ) ) w h i c h may b e u s e d o n m u l t i p l e s p a n b r i d g e s do n o t i n t e r f e r e w i t h t h i s p r i n c i p l e . On t h e c o n t r a r y , beams g r a d e d i n h e i g h t , a c c o r d i n g t o s p a n l e n g t h , w i t h h a u n c h e s ( b a t t e r s ) a r e more e m p h a t i c t h a n t h e same h e i g h t o f beam i n e a c h s p a n . A c o n t i n u o u s beam i s p r e f e r a b l e t o a s i m p l e beam i n e a c h s p a n . Upper s t r a p s , w i t h d i s c o n n e c t e d t o p s , g i v e t h e i m p r e s s i o n o f an u n f i n i s h e d s t r u c t u r e ( F i g u r e 24 ( a ) ) . I n a r o a d w a y - a b o v e t r u s s beam, t h e ends t e r m i n a t e i n abu tmen t s w i t h a n a t u r a l e f f e c t . H o w e v e r , i n a r o a d w a y - b e l o w t r u s s beam, i f t h e 29 (a) D i s c o n n e c t e d u p p e r s t r a p s . (b) N a t u r a l a p p e a r a n c e o f r o a d w a y - a b o v e t r u s s . ( c ) B o r d e r p i e r s w i t h r o a d w a y - b e l o w . F i g u r e 24 - D i f f e r e n t s o l u t i o n s o f t r u s s b r i d g e a r r a n g e m e n t . 30 t r u s s has a v e r t i c a l member, i t l o o k s h a r d and f o r c e f u l . B o r d e r p i e r s o r p a r t i a l l y o b l i q u e ends o f t h e d i a g o n a l i m p r o v e t h e l o o k o f t h i s t y p e o f c o n s t r u c t i o n ( F i g u r e 25 ( a ) ) . A e s t h e t i c a l l y s u i t a b l e shapes o f beams a r e shown on p i c t u r e s 25 ( a ) , (b) and ( c ) . Somet imes beams a r e d e s i g n e d a c c o r d i n g t o t h e r e l a t i v e maximum moment; i . e . a p p l y i n g a c o n s t a n t s t r e s s a c r o s s t h e l e n g t h o f t h e e n t i r e beam. The l a r g e s t d e p t h o f t h e beam o c c u r s i n t h e c e n t e r . T h i s e f f e c t i s n o t a e s t h e t i c a l l y p l e a s i n g . S i n c e one e x p e c t s v i s u a l l y t o s e e s t r e n g t h a t t h e s u p p o r t s , s u c h a beam g i v e s t h e f e e l i n g t h a t i t w i l l f a i l i n s h e a r a t t h e s u p p o r t . 2 . 2 . 2 A r c h e s The a r c h b e l o n g s to a h i g h e r , a e s t h e t i c a l l y more v a l u a b l e c a t e g o r y t h a n t h e beam. The a r c h , s e r v i n g as a s u p p o r t i n t h e r o a d w a y - above b r i d g e s , c r e a t e s a mos t n a t u r a l a p p e a r a n c e i n t h e w h o l e s t r u c t u r e . A s m e n t i o n e d b e f o r e , t h e p r o p e r b a l a n c e b e t w e e n t h e a r c h and beam t h i c k - n e s s h a s to be c o n s i d e r e d . T h i s a p p l i e s m a i n l y to a s o l i d t y p e o f a r c h (wood and c o n c r e t e ) w h i l e s t e e l t r u s s a r c h e s seem t o be l e s s s e n s i t i v e s i n c e t h e y a r e n o t as o b t r u s i v e . A r c h e s a r e u s u a l l y c o n s t r u c t e d a c c o r d i n g t o e q u i l i b r i u m p o l y - gons o r moment l i n e s , w h i c h v a r y w i t h d i f f e r e n t t y p e s o f a r c h e s . A e s t h e t i c a l l y , t h e mos t p l e a s i n g i s t h e f i x e d end p a r a b o l i c a r c h w i t h a t h i n c r o w n and c o n s i d e r a b l y t h i c k e r b u t t s ( F i g u r e 2 6 ) . I t g i v e s t h e f e e l i n g o f a s a f e s t r u c t u r e , b u t as a s t r u c t u r a l t y p e i t i s s t a t i c a l l y m u l t i p l y - i n d e t e r m i n a t e and r e q u i r e s c a r e f u l c a l c u l a t i o n s s i n c e o t h e r i n f l u e n c e s s u c h as s h r i n k a g e and t e m p e r a t u r e changes h a v e to be c o n s i d e r e d . 1 31 32 The t w o - h i n g e d a r c h has the o p p o s i t e a p p e a r a n c e ( F i g u r e 2 7 ) . I t i s t h i c k e r a t t h e c r o w n t h a n a t t h e b u t t s and does n o t g i v e t h e same i m p r e s s i o n o f s t a b i l i t y as t h e f i x e d end a r c h . The d e s i g n i s s i m p l e r s i n c e i t i s o n l y a s i m p l y - i n d e t e r m i n a t e s t r u c t u r e ; a n d , i f i t i s c a r e f u l l y d e s i g n e d , i t c a n a p p e a r smooth l o o k i n g and a e s t h e t i c a l l y p l e a s i n g . The t h r e e - h i n g e d a r c h i n a l o n g s p a n i s p r o b a b l y t h e mos t d i f f i c u l t t o a c c e p t f r o m t h e a e s t h e t i c p o i n t o f v i e w and i s now r a r e l y u sed f o r c o n c r e t e ( F i g u r e 2 8 ) . I t i s , h o w e v e r , t h e s i m p l e s t t o d e s i g n s t r u c t u r a l l y s i n c e i t i s a s t a t i c a l l y d e t e r m i n e d s t r u c t u r e , and f o r s h o r t spans v i s u a l l y p l e a s i n g c o n t o u r s c a n be o b t a i n e d . The same p r i n c i p l e s c a n be a p p l i e d f o r r o a d w a y - b e l o w b r i d g e s as f o r r o a d w a y - a b o v e . The mos t i m p o r t a n t i s t h e p r o p e r b a l a n c e b e t w e e n t h e roadway and t h e a r c h t h i c k n e s s . I n t h e r o a d w a y - a b o v e a r r a n g e m e n t s a t h i c k roadway ( w i t h beam) and a t h i n a r c h c a n c r e a t e t h e i m p r e s s i o n t h a t t h e beam i s c a r r y i n g t h e w h o l e l o a d and t h a t t h e r e i s no need f o r t h e a r c h ( F i g u r e 2 3 ) . I f t h e t h i c k n e s s e s a r e i n t e r c h a n g e d , i t t h e n c r e a t e s t h e i m p r e s s i o n t h a t t h e a r c h has b e e n b u i l t as a monument and t h e roadway has b e e n f o r g o t t e n ( F i g u r e 2 2 ) . S i m i l a r v i s u a l e f f e c t s c a n be c r e a t e d w i t h i m p r o p e r r o a d w a y - b e l o w a r r a n g e m e n t s . The shape o f t h e a r c h i s n o t as i m p o r t a n t as t h e r e l a t i v e t h i c k n e s s . I f the a r c h i s t o o t h i c k , i t c a n g i v e t h e i m p r e s s i o n t h a t i t i s a c t u a l l y t h e r o a d w a y , and t h a t t h e roadway i s o n l y a c h o r d h o l d i n g t h e a r c h t o g e t h e r . E q u a l t h i c k n e s s o f a r c h and roadway s h o u l d be a v o i d e d s i n c e t h e s u p p o r t i n g s t r u c t u r e a p p e a r s u n d e r m i n e d , w h i l e t h e roadway w i t h t h e beam a p p e a r s more o b v i o u s , a l l t h i s c r e a t i n g a c o n s e q u e n t F i g u r e 26 - F i x e d end a r c h b r i d g e . F i g u r e 28 - T h r e e - h i n g e d a r c h b r i d g e . 34 l a c k o f b a l a n c e . The t o t a l i m p r e s s i o n o f s u c h a b r i d g e i s t h a t o f a heavy s t r u c t u r e . The b e s t p r o p o r t i o n w o u l d seem t o be a s l i g h t l y t h i c k e r a r c h t h a n r o a d w a y . The v e r t i c a l c o n n e c t o r s s h o u l d be p r o p o r t i o n a t e so as n o t t o d e t r a c t f r o m t h e i m p r e s s i o n o f smooth l i n e s . P a r a b o l i c c u r v e s i n g e n e r a l l o o k b e t t e r t h a n s i m p l e c u r v e s , e s p e c i a l l y when t h e r a t i o b e t w e e n t h e h e i g h t o f t h e a r c h and t h e s p a n i s s m a l l . When t h e r a t i o i s h i g h , t h e d i f f e r e n c e i s n o t n o t i c e a b l e . F l a t a r c h e s a r e u s u a l l y more a d m i r e d t h a n h i g h a r c h e s , b e c a u s e to t h e d i s c r i m i - n a t i n g eye t h e y show t h e a b i l i t y and s k i l l o f t h e d e s i g n e r . Common r a t i o s o f t h e h e i g h t and t h e s q u a r e o f t h e l e n g t h o f t h e c h o r d a r e b e t w e e n 1 /250 and 1 / 5 0 0 . The f l a t t e s t known a r c h , i n Rome, has a r a t i o o f 1 / 1 0 0 0 . Some o l d e r t y p e s o f b r i d g e s w e r e d e s i g n e d as f u l l a r c h w i t h roadway ( F i g u r e 2 9 ) . E l l i p t i c a r c h e s w e r e some t imes u s e d f o r s t a t i c a l r e a s o n s b u t t hey h a v e an a e s t h e t i c d i s a d v a n t a g e b e c a u s e t h e y make t h e p i e r s and t h e roadway t h i c k e r . 2 . 2 . 3 S u s p e n s i o n S t r u c t u r e A s u s p e n s i o n b r i d g e ( F i g u r e 20) p r o v i d e s t h e i m p r e s s i o n o f a c o n t i n u o u s roadway c o u p l e d w i t h t h e b e a u t y o f t h e t h i n n a t u r a l c u r v e s o f t h e c a b l e . The v e r t i c a l c o n n e c t o r s a r e t h i n and do n o t i n t e r f e r e w i t h e i t h e r e l e m e n t . A n i m p o r t a n t c o n s i d e r a t i o n i s t h e p r o p e r d i s t a n c e b e t w e e n t h e c a b l e and t h e r o a d w a y . As d i s c u s s e d e a r l i e r , t h e g u a r d r a i l s h o u l d n o t be c r o s s e d by t h e c a b l e ( F i g u r e 2 1 ) . On t h e o t h e r h a n d , t o o l a r g e a d i s t a n c e b e t w e e n t h e c a b l e and t h e roadway i s n o t a e s t h e t i c a l l y s u i t a b l e b e c a u s e i t l o s e s p r o p o r t i o n and the n a t u r a l a p p e a r a n c e o f t h e c a b l e c u r v e . 1 35 F i g u r e 31 - K i n g t r u s s . 36 A new type of r e l a t i v e l y short span suspension construction has been developed r e c e n t l y . Instead of a continuous arch, the cables are anchored i n the beam (Figure 30). B a s i c a l l y , i t i s a very d e l i c a t e looking s t r u c t u r e and can be used with great t e c h n i c a l and ae s t h e t i c e f f e c t . I t i s also r e l a t i v e l y inexpensive and simple to construct. Other types of bridges such as king and queen trusses (Figures 31 and 32), even i f economical, do not generally correspond to the aesthetic p r i n c i p l e s which are covered i n th i s paper. They are basic t y p i c a l l y - f u n c t i o n a l engineering s t r u c t u r e s , simple to design and to construct. They have been often used e s p e c i a l l y i n the past but they always take away from the harmony of the landscape i n some way. Comments about the reversed s t e e l trusses can be compared to e a r l i e r comments about the beam which i s designed according to the moment l i n e . These structures have an unnatural appearance and give the f e e l i n g that they could break close to the support. Inverse strutframe structures (Figures 33 and 34) do not have the same negative e f f e c t as those which are described above i f cables are used f o r tensioned parts, but even they cannot be considered as f u l l y a e s t h e t i c a l l y s u i t a b l e structures since they do not follow the described aesthetic p r i n c i p l e s of supporting elements. 2.3 Pier s and Abutments C h i e f l y because of i t s function, a p i e r or abutment i s an independent element which acts as a complex u n i t . If a support i s designed as a s i n g l e column or w a l l , there i s a lack of complexity which gives the f e e l i n g that more of the same elements are required since i t " F i g u r e 34 - T r u s s e d g i r d e r b r i d g e . 38 s h o u l d a l s o a c t as an enf ramement . T h e r e f o r e , p i e r s a r e b u i l t i n r o w s , w h e t h e r as i n f i l l a t t h e ends o f a r c h e s o r t o t r a n s f e r t h e l o a d f r o m t h e s u p p o r t i n g s t r u c t u r e t o t h e f o o t i n g . A n i m p o r t a n t q u e s t i o n a r i s e s r e g a r d i n g s e l e c t i o n o f m a t e r i a l . W h i l e t h e s u p e r s t r u c t u r e c a n be o f v a r i o u s m a t e r i a l s , c o n c r e t e o r s t o n e a r e p r e f e r a b l e f o r t h e s u p p o r t s s i n c e i t i s i m p o r t a n t t h a t t h e y r e s i s t t h e i n f l u e n c e o f w a t e r . I n some t y p e s o f c o n s t r u c t i o n , e x t e n s i o n s o f t h e p i e r s c a n be o f wood o r s t e e l , e s p e c i a l l y i n deep v a l l e y s w h e r e h i g h p i e r s a r e n e c e s s a r y . I t h a s b e e n m e n t i o n e d p r e v i o u s l y t h a t t h e p i e r s h o u l d n o t d i s t u r b t h e f l u e n c y o f t h e r o a d w a y . The o n l y a c c e p t a b l e e x t e n s i o n o f t h e abu tmen t s c a n be a t t h e ends o f t h e b r i d g e , t o e m p h a s i z e t h e b r i d g e e n t r a n c e and m o n u m e n t a l i t y . S o l i d l o n g p i e r s s h o u l d be b u i l t s l o p e d o r i n s t e p s , b e c a u s e a s t r a i g h t v e r t i c l e p r i s m a p p e a r s t o w i d e n a t t h e t o p and g i v e t h e f e e l i n g o f u n c e r t a i n t y and i n s t a b i l i t y . F rom the a e s t h e t i c p o i n t , t h e y h a v e t o be d e s i g n e d c a r e f u l l y a c c o r d i n g t o t h e s e l e c t e d b r i d g e t y p e , h e i g h t o f t h e f i l l t h a t t h e y a r e t o s u p p o r t , and t h e t y p e o f b a n k s . Somet imes t h e y have t o be m a s s i v e and a l s o s h o u l d g i v e a m a s s i v e i m p r e s s i o n t o keep t h e p r o p e r b a l a n c e b e t w e e n t h e t y p e o f t h e b r i d g e and h e i g h t o f a b u t m e n t . The u s e o f n a t u r a l o u t c r o p s f o r h e a v y abu tmen t s g i v e s the same e f f e c t , however i t i n t e r f e r e s l e s s w i t h t h e e n v i r o n m e n t t h a n w i t h p u r e c o n c r e t e f a c i n g . Somet imes i t i s b e t t e r to u s e d i v i d e d bank abu tmen t s ( F i g u r e 6 and 7) w h i c h make t h e c o n s t r u c t i o n l i g h t e r and a i r y - l o o k i n g and w h i c h c a n be v e r y a c c e p t a b l e s i n c e a i r and l i g h t c a n a l s o be c o n s i d e r e d as c o n s t r u c t i o n m a t e r i a l . 39 T h i s a p p l i e s e s p e c i a l l y when d i v i d e d bank a b u t m e n t s a r e u s e d t o e l i m i n a t e l o n g and h i g h f i l l i n f l a t v a l l e y s . 2 . 4 B r i d g e Heads A p p r o a c h e s s h o u l d a l w a y s be marked i n some a p p r o p r i a t e manner i n o r d e r t o w a r n t h e d r i v e r o f t h e o n c o m i n g b r i d g e . T h e r e a r e d i f f e r e n t means o f a c c o m p l i s h i n g t h i s , d e p e n d i n g upon t h e roadway a r r a n g e m e n t . The r o a d w a y - b e l o w b r i d g e c o n s t r u c t i o n , w h i c h i s above g r o u n d l e v e l , i s s t r i k i n g i n i t s e l f and o b v i o u s t o t h e a p p r o a c h i n g d r i v e r so t h a t no a d d i t i o n a l e l e m e n t i s n e c e s s a r y , w h i l e a p r o p e r means o f a n n o u n c i n g t h e b r i d g e i s needed w i t h t h e r o a d w a y - a b o v e b r i d g e s . B r i d g e heads on t h e p i l e p i e r s , p o s t s w i t h come r e p r e s e n t a t i o n a l s t a t u s , and s i m i l a r means c a n be u s e d ( F i g u r e s 24 ( c ) , 35 and 3 6 ) . M o n u m e n t a l i t y , i f r e q u i r e d , c a n a l s o be o b t a i n e d by w i d e n i n g t h e a p p r o a c h e s w i t h t h e u s e o f l a n d - s c a p i n g . F u n c t i o n a l b r o w - l o g o r s i m i l a r t y p e s o f a p p r o a c h e s , w h i c h d i r e c t t r a f f i c o n t o t h e r o a d w a y , a r e somet imes u s e d on f o r e s t b r i d g e s i n B r i t i s h C o l u m b i a . S u c h a p p r o a c h e s do n o t i n t e r f e r e a e s t h e t i c a l l y , s i n c e no a c t u a l m o n u m e n t a l i t y i n h i g h v e g e t a t i o n ( f o r e s t ) c o v e r t y p e i s needed ( F i g u r e s 17 and 1 8 ) . T h e r e f o r e t h e s e a p p r o a c h e s c a n be u s e d f o r m u l t i - p u r p o s e b r i d g e s . F i g u r e 35 - B r i d g e head a t L i o n s G a t e B r i d F i g u r e 37 - P r o p o r t i o n a l i t y o f L i o n s G a t e B r i d g e . 42 C h a p t e r I I I DIFFERENT TYPES OF BRIDGES I N MAIN LANDSCAPE FORMS A b r i d g e i s a b u i l d i n g e l e m e n t w h i c h , i n i t s n a t u r a l s u r r o u n d i n g s , may i m p r o v e o r mar t h e l a n d s c a p e . I t c a n be s t a t e d b o t h f r o m f o r m e r l y m e n t i o n e d a e s t h e t i c p r i n c i p l e s and f r o m the e x p e r i e n c e s 1 2 3 4 o f v a r i o u s a u t h o r s ( A d a m o v i c h , Newton , L o r e n z and P a c h o l i k ) t h a t , i n g e n e r a l , t h e s e l e c t i o n o f a b r i d g e t y p e — i t s s h a p e , p r o p o r t i o n s , and m a t e r i a l — d e p e n d s d i r e c t l y on t h e t y p e o f t e r r a i n ( f l a t , h i l l y , m o u n t a i n - o u s ) , g r o u n d c o v e r ( r o c k s , s a n d , l o w v e g e t a t i o n , f o r e s t ) , t y p e o f t r a n s - p o r t a t i o n ( p r o p e r b a l a n c e w i t h c o n n e c t i n g r o a d on e i t h e r s i d e ) , r e l a t i o n - s h i p t o n e i g h b o u r i n g b r i d g e s ( F i g u r e s 38 and 39) and so o n . The r o a d l o c a t i o n i s i n f l u e n c e d by p o s s i b l e r i v e r c r o s s i n g s and v i c e v e r s a . The f a r d i s t a n t v i e w o f t h e b r i d g e s h o u l d n o t be n e g l e c t e d , s i n c e i t o f f e r s a r e f r e s h i n g v i s u a l moment t o l o n g d i s t a n c e t r a v e l l e r s . x L . A d a m o v i c h , F o r e s t T r a n s p o r t a t i o n . C o u r s e a t t h e F a c u l t y o f F o r e s t r y , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B . C . 1972 - 1 9 7 3 . 2 N . T . N e w t o n , D e s i g n on t h e L a n d ( C a m b r i d g e , M a s s . : H a r v a r d U n i v e r s i t y - P r e s s , 1 9 7 3 ) . P- 2 - 1 7 . 3 E . H . H . L o r e n z , T r a s s i e r u n g und G e s t a l t u n g v o n S t r a s s e n u r v j A u t o Bahnen ( ' ' L a y o u t and D e s i g n o f S t r e e t s and H i g h w a y s " ) (Wiesbaden und B e r l i n B a u m v e r l a g , 1 9 7 1 ) . p . 23 - 5 2 . 4 L . P a c h o l i k , E s t e t i k a M o s t n i c h S t a v e b ( " A e s t h e t i c s o f B r i d g e S t r u c t u r e s " ) ( P r a g u e : U s t a v p r o Ucebne Pomucky P r u m y s l o v y c h a Odbornyc.h S k o l v P r a z e , 1 9 4 6 ) . p . 13 - 3 4 . F i g u r e 38 - N e i g h b o u r h o o d o f b r i d g e s - p r o p e r s o l u t i o n . F i g u r e 39 - C l o s e and d i s t a n t o b j e c t o b s e r v a n c e - non homogenous a p p e a r a n c e . 44 I n o r d e r to s a t i s f y a l l t h e r e q u i r e m e n t s , many a l t e r n a t i v e s have t o be c o n s i d e r e d . The b e s t g r o u n d s f o r j u d g i n g the mos t a p p r o p r i a t e b r i d g e t y p e come f rom g r o u n d p h o t o g r a m m e t r y , p l o t t i n g t h e d i f f e r e n t 5 6 t y p e s w i t h p h o t o g r a p h i c p i c t u r e s t a k e n f rom d i f f e r e n t p o i n t s o r a n g l e s ' Somet imes even a s k e t c h on t h e p h o t o g r a p h i c p i c t u r e i s s u f f i c i e n t as shown o n F i g u r e s 54 t o 5 9 . 3 . 1 F l a t C o u n t r y I t i s g e n e r a l l y a c c e p t e d t h a t f l a t c o u n t r y r e q u i r e s f l a t t y p e b r i d g e s (beam o r f l a t a r c h w i t h r o a d w a y - a b o v e ( F i g u r e 3 ) ) , w h i l e h i g h a r c h b r i d g e s a d a p t t h e m s e l v e s b e t t e r t o m o u n t a i n o u s c o u n t r y . T hese p r i n c i p l e s , h o w e v e r , h a v e v a r i a t i o n s and t h e mos t s i g n i f i c a n t one a r i s e s f r o m t h e need o r d e s i r e t o change a m o n o t o n o u s , f l a t c o u n t r y s i d e b y b u i l d i n g some d o m i n a n t e l e m e n t i n o r d e r t o i m p r o v e t h e l a n d s c a p e a p p e a r a n c e . I n s u c h c a s e s , s e v e r a l t y p e s o f b r i d g e s may be c o n s i d e r e d : 3 . 1 . 1 C o n c r e t e A r c h B r i d g e A c o n c r e t e a r c h b r i d g e , w i t h a r o a d w a y - b e l o w ( F i g u r e 3) w o u l d be v e r y e f f e c t i v e , e s p e c i a l l y i n l o w v e g e t a t i o n g r o u n d c o v e r . I n t h i s i n s t a n c e , one must keep i n m i n d t h e f a c t t h a t a s e r i e s o f a r c h e s i s n o t a e s t h e t i c a l l y p l e a s i n g . E . H . H . L o r e n z , T r a s s i e r u n g und G e s t a l t u n g v o n S t r a s s e n und A u t o Bahnen ( " L a y o u t and D e s i g n o f S t r e e t s and H i g h w a y s " ) ( W i e s b a d e n und B e r l i n B a u m v e r l a g , 1 9 7 1 ) . p . 72 - 7 5 . ^ L . P a c h o l i k , E s t e t i k a M o s t n i c h S t a v e b ( " A e s t h e t i c s o f B r i d g e S t r u c t u r e s " ) ( P r a g u e : U s t a v p r o Ucebne Pomucky P r u m y s l o v y c h a O d b o r n y c h S k o l v P r a z e , 1 9 4 6 ) . p . 13 - 3 4 . 45 3 . 1 . 2 H o w e - t r u s s B r i d g e A s t r a i g h t s t e e l t r u s s o r wooden ( H o w e - t r u s s ) b r i d g e , w i t h i t s monumenta l l o o k i n g end p i l l a r s , has the d i s a d v a n t a g e o f l o o k i n g s u i t a b l e f rom t h e s i d e v i e w o n l y i f t h e r i v e r o r t h e s k y i s i n t he b a c k g r o u n d , o t h e r w i s e t h e y a c t as d i s t u r b i n g e l e m e n t s . 3 . 1 . 3 S u s p e n s i o n B r i d g e A s u s p e n s i o n b r i d g e , w i t h c o n c r e t e s u p p o r t s ( w h i c h i n them- s e l v e s l o o k v e r y i m p r e s s i v e ) , o f f e r s a p l e a s i n g c o m b i n a t i o n o f c o n c r e t e and s t e e l . T h i s p l e a s i n g c o m b i n a t i o n w i t h s u s p e n s i o n b r i d g e s i s q u i t e r e c e n t and i t s ou tcome i s v e r y e f f i c i e n t and e f f e c t i v e . I t was f i r s t i n t r o d u c e d i n F r a n c e a f t e r t h e S e c o n d W o r l d W a r , a p p a r e n t l y f o l l o w i n g m i d d l e E u r o p e a n p a t t e r n s ( c h a i n b r i d g e s w i t h s t o n e t o w e r s , e . g . B u d a p e s t , H u n g a r y ) i n o r d e r t o cope w i t h t he s h o r t a g e o f s t e e l . The same b a l a n c e d e f f e c t may be o b t a i n e d by u s i n g s t e e l s u p p o r t s ( F i g u r e 3 7 ) . 3 . 2 H i l l y T e r r a i n H i l l y and r o l l i n g t e r r a i n w i t h i t s c h a n g i n g g r o u n d c o v e r seems t o be t h e l e a s t demanding when i t comes to c h o i c e o f b r i d g e t y p e . T h i s t y p e o f c o u n t r y s i d e i s u s u a l l y v e r y c o l o u r f u l and a l m o s t any t y p e o f b r i d g e s t r u c t u r e f i t s w e l l i f l o c a l c o n d i t i o n s a r e c o n s i d e r e d e x c e p t t h e s u s p e n s i o n b r i d g e w h i c h i s d o m i n a t i n g t y p e a n d , t h e r e f o r e , s h o u l d n o t be u s e d b e t w e e n two v a l l e y s , w h e r e the d o m i n a t i n g e l e m e n t s become s u p p r e s s e d and an e n v i r o n m e n t a l u n b a l a n c e r e s u l t s . W i t h some e x c e p t i o n s , b r i d g e s s h o u l d be b u i l t s t r a i g h t , b e c a u s e t h e s i d e f o r c e s o f v e h i c l e s i n c u r v e s r e q u i r e a d d i t i o n a l l a t e r a l b r a c i n g . S i t u a t i o n s , whe re two segment b r i d g e s d i v i d e d by a s h o r t 46 s t r a i g h t road, are required should be avoided and the whole route should be r e v i s e d . Such an arrangement i s not only expensive, but also a e s t h e t i c a l l y unpleasing. To improve the d i s t a n t view of the bridge and to make i t more impressive, the curves on both sides of the bridge should be so located that t r a v e l l e r s , en route, w i l l be able to admire the beauty of the bridge construction and i t s environmental e f f e c t . Sometimes symmetry i s considered very important and then an odd number of spans i s preferred. This i s more important with arch bridges and roadway-above (Figure 3) than with any other type of bridges. Where other types are concerned, supplementary arrangements can eliminate t h i s requirement. However, symmetry of the long divided bank abutments i s always necessary i n order to keep proper balance. 3.3 Mountainous Country Mountainous country, i n general, does not adapt i t s e l f to beam type bridges. These bridges (beam type) cut off the view of the v a l l e y s and look too f o r c e f u l while the arch bridges are not as f o r c e f u l and appear to be i n harmony with the landscape (Figure 40). However, even beam bridges may be used i n mountainous areas, when properly located and c a r e f u l l y designed, e i t h e r as contrasting v i s u a l elements or where the p o s i t i o n of the bridge i s low i n r e l a t i o n to the background (Figure 41). 3.4 River Crossing Tunneling or choking the flow, as shown i n Figures 42 and 43, i s b a s i c a l l y environmental i n t e r f e r e n c e , and should be avoided. If F i g u r e 40 - H i g h a r c h b r i d g e i n m o u n t a i n o u s t e r r a i n . F i g u r e 41 - Beam b r i d g e i n m o u n t a i n o u s t e r r a i n . F i g u r e 43 - T u n n e l i n g o f t h e s t r e a m . 49 t h e c a n t i l e v e r beam i s u s e d , t h e n t h e b e n d i n g moment v a l u e s a r e l o w e r and i t c o u l d be u sed f o r l o n g e r spans i n g e n e r a l . T h e n , t h e r e i s no i n t e r f e r e n c e i n t h e f l o w o f t h e r i v e r . A c o m p a r i s o n b e t w e e n t h e s i m p l e beam and c a n t i l e v e r e d beam e f f e c t c a n b e s e e n i n t h e c a s e s t u d y o f t h e A l o u e t t e R i v e r , w h i c h f o l l o w s i n t h e n e x t c h a p t e r . E v e n i f t h e A l o u e t t e R i v e r i s n o t c h o k e d by t h e i n t r o d u c t i o n o f a h i g h b a n k s u p p o r t , t h e a e s t h e t i c v a l u e t o t h e e n v i r o n m e n t i s h i g h e r when a c a n t i l e v e r e d beam' t y p e o f b r i d g e i s u s e d s i n c e i t opens up t h e v i e w w h i l e d i m i n i s h i n g t h e f i l l . A p a r t f r o m the A l o u e t t e R i v e r c a s e , t h e t u n n e l i n g e f f e c t c a n be e l i m i n a t e d b y d e s i g n i n g the t y p e o f b r i d g e t h a t u s e s i n d i v i d u a l ( F i g u r e 15) i n t e r m e d i a t e s u p p o r t s , r a t h e r t h a n h e a v y b a n k s u p p o r t s . T u n n e l i n g s h o u l d be a v o i d e d n o t o n l y b e c a u s e o f i t s a d v e r s e e f f e c t o n t h e l a n d s c a p e b u t a l s o f o r i t s d e t r i m e n t a l e f f e c t on f i s h l i f e . The u s e o f a c a n t i - l e v e r e d beam o r h i g h f i l l may be a q u e s t i o n o f e c o n o m i c s ( e i t h e r f i l l o r b r i d g e s t r u c t u r e c o s t s ) b u t , as m e n t i o n e d b e f o r e , t h e s i d e e f f e c t s s h o u l d n e v e r be o v e r l o o k e d . I n summary, i t may be s t a t e d t h a t any b a s i c t y p e o f b r i d g e s t r u c t u r e c a n be s e l e c t e d f o r any p a r t i c u l a r c o u n t r y s i d e . H o w e v e r , p r o p o r t i o n a l i t y and b a l a n c e , w i t h t h e i m m e d i a t e s u r r o u n d i n g s and t h e b a c k g r o u n d , has t o b e c o n s i d e r e d i n o r d e r to f u l f i l l t h e r e q u i r e m e n t s o f e n v i r o n m e n t a l a e s t h e t i c s . 50 C h a p t e r I V ANALYSIS OF ALOUETTE RIVER CROSSING The g e n e r a l p r i n c i p l e s d i s c u s s e d i n t h e c h a p t e r s o n a e s t h e t i c s a r e a p p l i e d i n d e s i g n c o m p a r i s o n s o f t h e new b r i d g e a c r o s s t h e A l o u e t t e R i v e r . F o r t h i s p a r t i c u l a r c a s e , s e v e r a l t y p e s h a v e b e e n s e l e c t e d i n o r d e r t o show t h e s u i t a b i l i t y o f e a c h . I n d i v i d u a l t y p e s a r e d r awn t o s c a l e (1 i n c h = 30 f e e t ) , f o r p u r p o s e s o f v i s u a l c o m p a r i s o n and t o a i d i n s e l e c t i n g t h e mos t s u i t a b l e o n e . B a s i c a l l y , two b r i d g e l e n g t h s w e r e c o n s i d e r e d . M o s t o f t h e t y p e s c o n s i d e r e d w e r e 80 f e e t l o n g , b e t w e e n two h i g h s u p p o r t s , b u t two t y p e s ( c a n t i l e v e r e d and s u s p e n s i o n ) w e r e c o n s i d e r e d f o r 160 f e e t t o t a l l e n g t h . The d i s a d v a n t a g e s o f t h e d i f f e r e n t h e i g h t o f s u p p o r t s on e a c h bank c a n be s e e n on t h e d r a w i n g s a l o n g w i t h a s u p p l e m e n t a r y s o l u t i o n f o r e a c h c a s e . 4 . 1 D e s c r i p t i o n o f t h e L a n d s c a p e A r e a and A l o u e t t e R i v e r C r o s s i n g The a r e a o f t h e U . B . C . R e s e a r c h F o r e s t i s b a s i c a l l y h i l l y , c o v e r e d by a m i x e d f o r e s t . The f a s t f l o w i n g A l o u e t t e R i v e r , w h i c h c r o s s e s t h i s a r e a , f o l l o w s a p a t h o f c o n t i n u o u s r a p i d s , embanked by a r o c k y c a n y o n . A s f o r t he l a n d s c a p i n g o f a p a r t i c u l a r a r e a , marked i n A p p e n d i x I , t h e m o u n t a i n o u s t y p e has to be c o n s i d e r e d , s i n c e t h e m a i n v i e w o f t h e b r i d g e f rom t h e n o r t h e r n p a r t o f t h e a p p r o a c h r o a d has a r u g g e d , i r r e g u l a r t o p o g r a p h y i n the b a c k g r o u n d . The m o u n t a i n o u s l a n d s c a p e i s 51 u n d e r l i n e d by the a p p e a r a n c e o f t h e d o m i n a t i n g Mount B l a n s h a r d i n t h e f a r d i s t a n c e t o t h e n o r t h o f t h e b r i d g e . 4 . 2 P r e s e n t S i t u a t i o n The A l o u e t t e R i v e r fo rms a n a t u r a l b o r d e r b e t w e e n t h e e a s t e r n a r e a ( s e e A p p e n d i x I ) and the m a i n w e s t e r n p a r t o f t h e U . B . C . R e s e a r c h F o r e s t . U n t i l now t h e e a s t e r n a r e a has s e e n a l i m i t e d amount o f l o g g i n g w h i l e many p l o t s s e r v e r e s e a r c h p u r p o s e s . H o w e v e r , i n t h e n e a r f u t u r e an i n c r e a s e i n l o g g i n g i s e x p e c t e d . The e x i s t i n g a p p r o a c h l e a d s a l m o s t t o t h e g e o g r a p h i c a l c e n t e r o f t h e e a s t e r n a r e a and t h e p r e s e n t b r i d g e a c r o s s t h e A l o u e t t e R i v e r i s e c o n o m i c a l l y l o c a t e d a t t h e s h o r t e s t r i v e r c r o s s i n g . The l o c a t i o n o f t h e b r i d g e i s marked on t h e a e r i a l p h o t o g r a p h i n A p p e n d i x I . B e c a u s e t h e c r i b abu tmen t s and some o f t he s t r i n g e r s h a v e r o t t e d , t h e D i r e c t o r o f t h e F o r e s t has d e c i d e d t o h a v e a new b r i d g e b u i l t i n t h e same p l a c e . The p r e s e n t l a y o u t o f t he a p p r o a c h r o a d i s s u b s t a n d a r d s i n c e t h e new h a u l i n g t r u c k s , as shown i n F i g u r e 6 4 , r e q u i r e a b i g g e r r a d i u s c u r v e t h a n t h e o l d e r t y p e s . I n a d d i t i o n , t h e 18% s l o p e o f t h e r o a d s e c t i o n s o u t h o f t h e r i v e r does n o t meet p r o p e r s a f e t y r e q u i r e m e n t s , r o a d s t a b i l i t y and v e h i c l e m e c h a n i c s . As no f i n a l d e c i s i o n abou t a new b r i d g e has y e t b e e n made, t h i s p a p e r i n t r o d u c e s some i d e a s f o r i t s p o s s i b l e d e s i g n and m a t e r i a l s ; t h e s e , s u p p l e m e n t e d by c a l c u l a t i o n s and a e s t h e t i c a n a l y s i s , may p r o v e t o be u s e f u l i n t h i s o r o t h e r s i m i l a r c a s e s . 52 I n t h e a n a l y s i s , v i s u a l q u a l i t y h a s b e e n c o n s i d e r e d as an i m p o r t a n t a d d i t i o n a l i n t a n g i b l e v a l u e , s i n c e t h e a r e a i s f r e q u e n t e d b y v i s i t o r s f rom a l l p a r t s o f t h e w o r l d . 4 . 3 P r o p o s e d A l i g n m e n t o f t h e R o u t e The b a s i c d a t a f o r t h e b r i d g e d e s i g n and r o a d a l i g n m e n t w e r e o b t a i n e d b y t e r r a i n r e c o n n a i s s a n c e and s t a d i a s u r v e y . To i m p r o v e the p r e s e n t s i t u a t i o n , t h e h o r i z o n t a l and v e r i c a l a l i g n m e n t o f t h e r o a d has b e e n r e d e s i g n e d as shown o n t h e p l a n and p r o f i l e i n A p p e n d i x I . A minimum r a d i u s o f 100 f e e t has b e e n c o n s i d e r e d f o r t he h o r i z o n t a l c u r v e , w i t h s p i r a l t r a n s i t i o n c u r v e s o f 50 f o o t l e n g t h s on t h e s o u t h s i d e o f t h e r i v e r . On t h e n o r t h s i d e , a s p i r a l c u r v e has b e e n d e s i g n e d . To a v o i d s i d e f o r c e s o n t h e b r i d g e , a s t r a i g h t s e c t i o n , t h e l e n g t h o f one t r u c k (50 f e e t ) , as shown i n A p p e n d i x I , has b e e n a l l o w e d a t e a c h end o f t h e b r i d g e . The new a l i g n m e n t a l l o w s a maximum 25 m . p . h . s p e e d o f t r u c k s i n t h a t s e c t i o n w i t h a 6% s u p e r e l e v a t i o n i n t h e c u r v e . A t b o t h s i d e s o f t h e r i v e r , t h e r o a d g r a d e has b e e n p a r t l y m a i n t a i n e d i n o r d e r t o a v o i d e x c e s s i v e c o s t s f o r e a r t h w o r k . To o b t a i n a smooth p r o f i l e , t h e r u n n i n g s u r f a c e o f t he b r i d g e h a s b e e n d e s i g n e d w i t h a 3% s l o p e , and p a r a b o l i c t r a n s i t i o n c u r v e s w e r e i n t r o d u c e d i n t h e s l o p e c h a n g e s . The m a i n b e n e f i t o b t a i n e d f r o m s u c h an a l i g n m e n t i s t he e l i m i n a t i o n o f t h e 18% g r a d e b e t w e e n s t a t i o n s 5 + 5 0 and 7 + 0 0 ( A p p e n d i x I ) . A n a l t e r n a t e s o l u t i o n i n v o l v i n g a s h o r t e r t r a n s i t i o n c u r v e was c o n s i d e r e d w i t h t h e p o s s i b i l i t y o f p r o v i d i n g a d d i t i o n a l s h o r t s p a n s a t b o t h ends o f t he b r i d g e and t h e e l i m i n a t i o n o f h e a v y abu tmen t s and 53 e x t r e m e f i l l b e h i n d them. I n t h i s c a s e , t h e abu tmen t s c o u l d be much s m a l l e r and the a e s t h e t i c s o f t h e beam b r i d g e w o u l d i m p r o v e . 4.4 E n g i n e e r i n g C a l c u l a t i o n s on P r o p o s e d Types o f B r i d g e s D i f f e r e n t t y p e s o f g l u l a m i n a t e d b r i d g e s have b e e n s e l e c t e d f o r d e s i g n c o m p a r i s o n . S i n c e t h e d i s t a n c e b e t w e e n t h e m a i n abu tmen t s i s 80 f e e t , t h e b r i d g e i s o n the e c o n o m i c b o r d e r l i n e o f t h e s i m p l e beam and o t h e r b r i d g e types"*". I n a d d i t i o n two t y p e s o f b r i d g e s w i t h o v e r a l l l e n g t h o f 160 f e e t h a v e b e e n a n a l y z e d . The c a l c u l a t i o n s p r e s e n t e d i n t h e a p p e n d i c e s a r e l i m i t e d t o t h e m a i n b r i d g e e l e m e n t s . T h e s e c a l c u l a t i o n s show o n l y t h e d i m e n s i o n s f o r p u r p o s e s o f t h e a e s t h e t i c c o m p a r i s o n o f s t r u c t u r a l b a l a n c e , o v e r a l l a p p e a r a n c e and f o r p r e l i m i n a r y c o s t e s t i m a t e . The c a l c u l a t i o n f o r e a c h t y p e o f b r i d g e i s l i s t e d i n t h e a p p e n d i c e s as f o l l o w s : (a) s i m p l e beam (b) s t r u t f r a m e ( two e q u a l s p a n c o n t i n u o u s beam) ( c ) d o u b l e s t r u t f r a m e ( t h r e e s p a n c o n t i n u o u s beam) (d) t h r e e - h i n g e d a r c h w i t h t h r e e s p a n c o n t i n u o u s beam) (e) c a n t i l e v e r e d beam S u s p e n s i o n b r i d g e has n o t b e e n c o n s i d e r e d f o r c o m p a r a t i v e d e s i g n b e c a u s e o f i t s a e s t h e t i c i m p r o p r i e t y i n t h e g i v e n l a n d s c a p e . R e s u l t s w e r e o b t a i n e d by a n a l y t i c a l c a l c u l a t i o n s and b y t h e u s e o f g r a p h s ( e . g . i n f l u e n c e l i n e s ) . "*" I . B a r b e r , F o r e s t T r a n s p o r t a t i o n . C o u r s e a t t h e F a c u l t y o f F o r e s t r y , U n i v e r s i t y o f T o r o n t o . 1969 - 1 9 7 0 . 54 I n t h e f i n a l c h a p t e r , t h e s e l e c t i o n o f t h e t y p e o f b r i d g e most s u i t e d i s made by b a l a n c i n g t h e t e c h n i c a l , a e s t h e t i c and e c o n o m i c r e q u i r e m e n t s . 4 . 5 M a t e r i a l To f i n d ou t w h e t h e r t h e m a t e r i a l f o r t h e b r i d g e mee ts t h e t e c h n i c a l , a e s t h e t i c and e c o n o m i c r e q u i r e m e n t s i n a c c e p t a b l e b a l a n c e , i t has t o be c h o s e n s i m u l t a n e o u s l y w i t h t h e fo rm o f t h e b r i d g e . G l u l a m i n a t e d t i m b e r m a t e r i a l f o r t h e b r i d g e has b e e n c h o s e n m a i n l y b e c a u s e o f i t s t e c h n i c a l a d v a n t a g e s , n a t u r a l b e a u t y and r e a s o n a b l e c o s t s i n B . C . As opposed t o l o g s t r i n g e r s , w h i c h a r e w i d e l y u s e d o n s h o r t s p a n b r i d g e s i n B . C . , g l u l a m i n a t e d beams c a n be o b t a i n e d i n a w i d e r a n g e o f l e n g t h s and c r o s s - s e c t i o n d i m e n s i o n s . The g r e a t e r s t r e n g t h a f f o r d e d by t h e s e l e c t e d m a t e r i a l a l l o w s more l o a d p e r s m a l l e r d i m e n s i o n . The r e q u i r e d s p a n , w h i c h c a n n o t be o b t a i n e d by u s e o f l o g s t r i n g e r s , i s a v a i l a b l e t h r o u g h t h e u s e o f g l u l a m i n a t e d beam so t h a t t h e r e - c h a n n e l i n g o f t h e r i v e r o f t e n s e e n b e n e a t h l o g g i n g b r i d g e s c a n be a v o i d e d . H i g h e r d u r a b i l i t y may be o b t a i n e d by u s i n g t r e a t e d m a t e r i a l f o r l a m i n a t e s . T r e a t m e n t o f t h i s m a t e r i a l i s more e f f i c i e n t and t h e r e f o r e more r e s i s t a n t t o r o t t h a n p r e s s u r e t r e a t e d l o g s o r sawn t i m b e r m a t e r i a l . Due t o t h e shape o f t h e beams f m a n i p u l a t i o n o f g l u l a m i n a t e d m a t e r i a l d u r i n g t h e c o n s t r u c t i o n i s s i m p l e r and f a s t e r t h a n t h a t o f l o g s t r i n g e r s . The e c o n o m i c a d v a n t a g e o f c h o o s i n g g l u l a m i n a t e d m a t e r i a l c a n be s e e n a l s o i n u s i n g h i g h e r s t r e n g t h l umbe r ( e . g . D o u g l a s F i r ) f o r 55 the more exposed laminates of the beam, while le s s exposed laminates can be made of lower strength lumber (e.g. Pine). Thus the chosen material for the case i n question has s a t i s f a c t o r i l y f u l f i l l e d a l l the above requirements. Concrete abutments f or the bridge would be based on the s o l i d rocky foundation (basis) on either side of the r i v e r . To avoid unpleasant wood-concrete combination, rock r i p - r a p of abutments would be used. 4.6 Aesthetic Analysis of Considered Types of Bridges 4.6.1 Simple Beam Bridge The simple beam bridge (Figures 44 and 52) i s balanced, according to s t r u c t u r a l a e s t h e t i c s . Engineering c a l c u l a t i o n s are shown i n Appendix I I . I t does not look a e s t h e t i c a l l y s u i t a b l e , however, for t h i s designed crossing, since i t i s not i n harmony with the rocky v a l l e y i n the background. I t cuts the view of the v a l l e y and i s not as impressive an engineering s t r u c t u r e because of the high f i l l on the banks. Since the new bridge i s designed on a higher l e v e l than the old one, the negative impression would be amplified. 4.6.2 Single Strutframe Bridge The s i n g l e strutframe bridge (Figure 45) has been designed using two s i n g l e spans. The continuous beam i s supported by two s t r u t s , each at a d i f f e r e n t angle with the roadway. Engineering c a l c u l a t i o n s are shown i n Appendix I I I . This type i s a e s t h e t i c a l l y balanced because the supporting elements are almost of the same depth as the beams but the asymmetry of the s t r u t s i s a e s t h e t i c a l l y unacceptable. Setting the basis of the s t r u t s at the same distance from the roadway (Figure 46 and 53), making i t symmetrical, greatly improves the appearance of this type 56 Figure 44 - Simple beam bridge. Figure 45 - Asymmetrical s i n g l e strutframe bridge. Figure 46 - Symmetrical s i n g l e strutframe bridge. 57 o f b r i d g e . I t a l s o f i t s i n b e t t e r w i t h t h e s u r r o u n d i n g s b e c a u s e i t s o f t e n s the s t r a i g h t l i n e s o f t he s i m p l e beam. 4 . 6 . 3 D o u b l e S t r u t f r a m e B r i d g e The d o u b l e s t r u t f r a m e b r i d g e ( F i g u r e s 47 and 54) i s d e s i g n e d as a t h r e e - s p a n c o n t i n u o u s beam. E x t e r n a l spans have e q u a l l e n g t h and i n n e r s p a n l e n g t h i s = 0 . 7 5 as recommended i n v a r i o u s t e x t b o o k s 2 3 on s t a t i c s ' . The d o u b l e s t r u t f r a m e b r i d g e was c a l c u l a t e d m a i n l y t o p r o v i d e a c o m p a r i s o n i n e l e m e n t s , and to show t h e d i f f e r e n c e i n a p p e a r a n c e b e t w e e n i t and t h e s i n g l e s t r u t f r a m e ( A p p e n d i x I V ) . The d o u b l e s t r u t t y p e l o o k s more b a l a n c e d and l i g h t e r i n a p p e a r a n c e . The o v e r a l l c o n c e p t i s more p l e a s i n g t h a n t h e s i n g l e s t r u t b e c a u s e t h e s t e e p e r and s h o r t e r s t r u t s s o f t e n t h e r i g i d i t y o f t h e beam, a t t h e same t i m e p r o d u c i n g a l o g i c a l a r r a n g e m e n t , s t r u c t u r a l l y . 4 . 6 . 4 T h r e e - h i n g e d A r c h B r i d g e The t h r e e - h i n g e d a r c h b r i d g e ( F i g u r e s 49 and 55) w i t h a c o n t i n u o u s beam i s u sed i n t h e same manner as t h e d o u b l e s t r u t f r a m e b r i d g e . The a p p e a r a n c e o f t h i s t y p e o f b r i d g e i s o n l y s l i g h t l y a f f e c t e d by t h e d i f f e r e n t l e v e l o f a r c h b a s e s ( F i g u r e s 48 and 5 6 ) . The smooth l i n e s have t h e same e f f e c t as w i t h t h e t w o - h i n g e d a r c h . I t seems t h a t d i v i d i n g b o t h s u p p o r t i n g e l e m e n t s ( a r c h and beam) has a good e f f e c t on e m p h a s i z i n g t h e d i f f e r e n t f u n c t i o n o f b o t h o f them. F o r a e s t h e t i c r e a s o n s , t h e d e p t h o f b o t h p a r t s o f t h e a r c h i s n o t s e t a c c o r d i n g t o t h e moment d i a g r a m , as i s 2 L . A d a m o v i c h , E r d e s z e t i H i d e p t e s , ( " L e c t u r e s o n F o r e s t B r i d g e s " ) ( S o p r o n , H u n g a r y : U n i v e r s i t y o f S o p r o n , 1 9 4 9 ) . p . 4 4 . ( M i m e o g r a p h e d . ) 3 Z . B a z a n t , F . K l o k n e r , and J . K o l a r , S t a t i k a S t a v e b n i c h K o n s t r u k t , ( " S t a t i c s o f C i v i l E n g i n e e r i n g S t r u c t u r e s " ) ( P r a g u e : C e s k a M a t i c e T e c h n i c k a , 1 9 3 0 ) . 58 F i g u r e 49 - S y m m e t r i c a l t h r e e - h i n g e d a r c h b r i d g e . 59 c u s t o m a r y . Maximum d e p t h i s m a i n t a i n e d t h r o u g h o u t t he t o p o f t h e a r c h . The r a t i o be tween b o t h s u p p o r t i n g e l e m e n t s c o r r e s p o n d s w i t h t h e p r i n c i p l e s . o f s t r u c t u r a l a e s t h e t i c s . 4 . 6 . 5 C a n t i l e v e r e d Beam B r i d g e The c a n t i l e v e r e d beam b r i d g e ( F i g u r e 50) has f u n d a m e n t a l l y t h e same e f f e c t i n c u t t i n g t h e v i e w o f t h e v a l l e y as t h e s i n g l e beam b r i d g e . H o w e v e r , t h e e l i m i n a t i o n o f t he h i g h abu tmen t s and h e a v y f i l l s r e s u l t s i n a much g r e a t e r v i e w i n g a r e a as w e l l as p r o j e c t i n g a s e n s e o f " l i g h t n e s s " i n t he e n g i n e e r i n g d e s i g n ( A p p e n d i x V ) . From a s t r u c t u r a l l y a e s t h e t i c p o i n t o f v i e w , t h i s d e s i g n , w i t h i t s s l e n d e r l o o k i n g p i e r s , i s p e r f e c t l y b a l a n c e d . W i t h i t s l i g h t c o n t r a s t i n g e f f e c t , t h i s t y p e o f t h e b r i d g e seems t o f i t t h i s a r e a t h e b e s t . 4 . 6 . 6 S u s p e n s i o n B r i d g e The s u s p e n s i o n b r i d g e ( F i g u r e 51) does n o t f i t t h i s a r e a a e s t h e t i - c a l l y b e c a u s e i t i s too d o m i n a n t a s t r u c t u r e , as m e n t i o n e d i n t h e c h a p t e r o n a e s t h e t i c s - T h i s becomes v e r y a p p a r e n t when t r a v e l l i n g d o w n h i l l on t h e a p p r o a c h r o a d , w h e r e t h e d o m i n a t i n g e f f e c t , w h i c h t h i s t y p e o f s t r u c t u r e n o r m a l l y c r e a t e s i n o t h e r l a n d s c a p e s , i s l o s t . T h i s t y p e a l s o w o u l d n o t be e c o n o m i c a l l y j u s t i f i e d f o r t h i s c a s e s t u d y . O t h e r w i s e t h i s t y p e o f b r i d g e i s p r o p e r l y b a l a n c e d , e s p e c i a l l y i f t h e c a b l e s a r e a n c h o r e d above t h e g u a r d r a i l as shown on the a l t e r n a t i v e d rawn i n f u l l l i n e ( F i g u r e 5 3 ) . 3 F i g u r e 51 - S i m p l e s u s p e n s i o n b r i d g e . F i g u r e 53 - S i n g l e s t r u t f r a m e b r i d g e . F i g u r e 54 - D o u b l e s t r u t f r a m e b r i d g e . F i g u r e 55 - S y m m e t r i c a l t h r e e - h i n g e d a r c h b r i d g e . F i g u r e 57 - C a n t i l e v e r e d beam b r i d g e . 64 C h a p t e r V SUMMARY AND CONCLUSION Upon c o m p l e t i o n o f t h e A l o u e t t e R i v e r C r o s s i n g s t u d y , f r o m t h e a e s t h e t i c p o i n t o f v i e w two t y p e s o f b r i d g e s c a n be c o n s i d e r e d a p p r o p r i a t e f o r t h i s p a r t i c u l a r c a s e , n a m e l y , t h e a r c h b r i d g e and t h e c a n t i l e v e r e d beam b r i d g e . The a r c h b r i d g e w i t h r o a d w a y - a b o v e l o o k s v e r y n e a t and b l e n d s i n a p p e a r a n c e w i t h t h i s m o u n t a i n o u s a r e a . I t i s s t r u c t u r a l l y b a l a n c e d and t h e a r c h s e a t i n g p a r t l y e l i m i n a t e s t h e n e g a t i v e e f f e c t o f h i g h abu tmen t s as t h e y a p p e a r i n b r i d g e s w i t h s i m p l e beam. N a t u r a l r o c k r i p - r a p f i t s i n t o t h e r o c k y s u r r o u n d i n g s and e l i m i n a t e s t h e u n n a t u r a l l o o k o f p u r e c o n c r e t e f a c i n g . On t h e o t h e r h a n d , c a n t i l e v e r e d beam b r i d g e has a s l i g h t l y c o n t r a s t i n g e f f e c t w h i c h does n o t i n t e r f e r e w i t h t h e m o u n t a i n o u s t y p e o f l a n d s c a p e i n t h e way t h e s i m p l e beam b r i d g e t y p e w o u l d , b u t s i n c e i t i s s t r u c t u r a l l y p e r f e c t l y b a l a n c e d , i t u n d e r l i n e s t h e b e a u t y o f t h e e n g i n e e r - i n g s t r u c t u r e and i s , t h e r e f o r e , mos t f a v o u r a b l e . From t h e t e c h n i c a l p o i n t o f v i e w c a n t i l e v e r e d beam b r i d g e w o u l d be l e a s t demand ing b e c a u s e o f t h e s m a l l a b u t m e n t s and t h e minimum f i l l . C o n s t r u c t i o n w o u l d be f a s t e r and s i m p l e r t h a n w i t h t he o t h e r t y p e s c o n s i d e r e d . 65 E c o n o m i c a l l y , t he c a n t i l e v e r e d beam b r i d g e i s mos t f e a s i b l e b e c a u s e o f the b i g s a v i n g on c o n c r e t e abu tmen t s and e a r t h f i l l m a t e r i a l . A s p e r p r e l i m i n a r y e s t i m a t e s i n a p p e n d i c e s , c o s t s o f i n d i v i d u a l t y p e s a r e as f o l l o w s : S i m p l e beam b r i d g e ( A p p e n d i x I I ) $ 1 0 8 , 2 6 2 S t r u t f r a m e b r i d g e ( A p p e n d i x I I I ) $ 1 3 0 , 7 1 1 D o u b l e s t r u t f r a m e b r i d g e ( A p p e n d i x I V ) $ 1 2 7 , 1 7 4 A r c h beam b r i d g e ( A p p e n d i x I V ) $ 1 1 4 , 5 9 2 C a n t i l e v e r e d beam b r i d g e ( A p p e n d i x V) $ 1 0 1 , 5 5 7 I n summary, t h e c a n t i l e v e r e d beam b r i d g e a p p e a r s t o be t h e mos t s u p e r i o r f r o m e a c h p o i n t o f v i e w and t h e r e f o r e w o u l d , u n d o u b t e d l y , be recommended f o r t h e A l o u e t t e R i v e r C r o s s i n g . 66 BIBLIOGFAPHY A d a m o v i c h , L . G e o m e t r i c d e s i g n s t a n d a r d s o f f o r e s t r o a d s : A n a e s t h e t i c v i e w . 8 t h C a n a d i a n R o a d s i d e C o n f e r e n c e P a p e r s . U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B . C . 1 9 7 1 . . F o r e s t T r a n s p o r t a t i o n . C o u r s e a t t h e F a c u l t y o f F o r e s t r y , U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r , B . C . 1 9 7 2 - 7 3 . . E r d e s z e t i H i d e p t e s . Mimeographed l e c t u r e s on f o r e s t b r i d g e s . S o p r o n , H u n g a r y . 1 9 4 9 . B a r b e r , J . F o r e s t T r a n s p o r t a t i o n . C o u r s e a t t h e F a c u l t y o f F o r e s t r y , U n i v e r s i t y o f T o r o n t o , O n t a r i o . 1 9 6 9 - 7 0 . B a z a n t , Z . , K l o k n e r , F . and K o l a r , J . S t a t i k a S t a v e b n i c h K o n s t r u k c t , T e c h n i c k y P r u v o d c e N o . 4 , C e s k a M a t i c e T e c h n i c k a , P r a h a , C z e c h o s l o v a k i a . 1 9 3 1 . B e c h y n e , S . and K o l a r , J . M o s t n i S t a v i t e l s t v i , T e c h n i c k y P r u v o d c e N o . X I C e s k a M a t i c e T e c h n i c k a , P r a h a , C z e c h o s l o v a k i a . 1 9 3 0 . E i c h n e r , H . The m e a n i n g o f ' g o o d ' i n a e s t h e t i c j u d g e m e n t . B r i t i s h J o u r n a l o f A e s t h e t i c s . V o l . 3_(4) . 1 9 6 3 . H e p b u r n , R . W . A e s t h e t i c a p p r e c i a t i o n o f n a t u r e . B r i t i s h J o u r n a l o f A e s t h e t i c s . V o l . 3 . (3) . 1 9 6 3 . L e C o r b u s i e r . V e r s une A r c h i t e c t u r e . ( "Towards a New A r c h i t e c t u r e " ) . V i n c e n t , F r e a l & C i e . , P a r i s . 1 9 5 8 . L o r e n z , E . H . H . T r a s s i e r u n g und G e s t a l t u n g v o n S t r a s s e n und A u t o B a h n e n . B a u m v e r l a g . W i e s b a d e n und B e r l i n . 1 9 7 1 . M e r g e r , J . P r o j e k t o v a n i M e s t s k y c h K o m u n i k a c i . S t a t n i N a k l a d e t e l s t v i . T e c h n i c k e L i t e r a t u r y , P r a h a , C z e c h o s l o v a k i a . 1 9 5 6 . M e y e r , F . R o u t e s u r v e y i n g and d e s i g n . F o u r t h e d i t i o n . I n t e r n a t i o n a l T e x t b o o k Company, S c r a n t o n , P e n n s y l v a n i a . 1 9 7 1 . M i c h a l o s , J . and W i l s o n , E . N . S t r u c t u r a l m e c h a n i c s and a n a l y s i s . The M a c M i l l a n Company, C o l l i e r - M a c M i l l a n Canada L t d . , T o r o n t o , O n t a r i o . 1 9 6 9 . M u n r o , T . Toward s c i e n c e i n a e s t h e t i c s . The L i b e r a l A r t P r e s s , New Y o r k . 1 9 5 6 . New Y o r k , N . Y . A m e r i c a n I n s t i t u t e o f S t e e l C o n s t r u c t i o n . S t e e l C o n s t r u c t i o n . F i f t h e d i t i o n . 1 9 5 1 . 67 Newby, F . L . M a n - N a t u r e - B e a u t y : A r e s e a r c h d i l e m m a . X I V . I U F R O - K o n g r e s s , M u n c h e n , Germany , p a p e r s . V o l . V I , S e c t i o n 2 6 . 1 9 6 7 . N e w t o n , N . T . D e s i g n on t h e l a n d . The B e l k n a p P r e s s o f H a r v a r d U n i v e r s i t y P r e s s , C a m b r i d g e , M a s s a c h u s e t t s . 1 9 7 3 . O t t a w a , C a n a d a . C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n . T i m b e r C o n s t r u c t i o n . 1 9 6 3 . O t t a w a , C a n a d a . D e s i g n o f h i g h w a y b r i d g e s . CSA S t a n d a r d s S6 - 1 9 6 6 . O t t a w a , C a n a d a . L a m i n a t e d T i m b e r I n s t i t u t e o f C a n a d a . T i m b e r D e s i g n M a n u a l . 1 9 7 2 . P a c h o l i k , L . E s t e t i k a M o s t n i c h S t a v e b ( " A e s t h e t i c s o f B r i d g e S t r u c t u r e s " ) . U s t a v P r o Ucebne Pomucky P r u m y s l o v y c h a O d b o r n y c h S k o l v P r a z e . P r a g u e . 1 9 4 6 . R o n a i , F . M e c h a n i k a I ( S t a t i k a ) . E r d e s z e t i es F a i p a r i E g y e t e i n F a i p a r i M e r n o k i K a r . 1 9 6 6 . S c o f i e l d , W . F . and O ' B r i e n , W . H . M o d e r n t i m b e r e n g i n e e r i n g . F i f t h e d i t i o n . S o u t h e r n P i n e A s s o c i a t i o n , New O r l e a n s , L o u i s i a n a . 1 9 6 3 . S i m o n d s , J . O . L a n d s c a p e a r c h i t e c t u r e , t h e s h a p i n g o f m a n ' s n a t u r a l e n v i r o n m e n t . M c G r a w - H i l l Book Company I n c . , New Y o r k . 1 9 6 1 . U . S . A . N a t i o n a l Lumber M a n u f a c t u r e r s A s s o c i a t i o n . P r e p a r e d b y T i m b e r E n g i n e e r i n g Company. T i m b e r d e s i g n and c o n s t r u c t i o n h a n d b o o k . F . W . Dodge C o r p o r a t i o n , New Y o r k . 1 9 5 6 . V a n c o u v e r , C a n a d a . The F o r e s t C l u b , U n i v e r s i t y o f B r i t i s h C o l u m b i a . F o r e s t r y Handbook f o r B r i t i s h C o l u m b i a . T h i r d e d i t i o n . 1 9 7 1 . W a s h i n g t o n , D . C , U . S . A . T i m b e r C o n s t r u c t i o n M a n u a l . P r e p a r e d by A m e r i c a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n . J o h n W i l e y and S o n s , I n c . , New Y o r k . 1 9 6 6 . W a s h i n g t o n , D . C , U . S . A . U . S . D e p t . o f A g r i c u l t u r e , F e b . 1 9 7 3 . N a t i o n a l F o r e s t L a n d s c a p e Management . V o l . I . U . S . Government P f i n t i n p r i f f i c e , W a s h i n g t o n , D . C . 1 9 7 3 . APPENDIX I P r e s e n t S i t u a t i o n D e s i g n S p e c i f i c a t i o n s V e r t i c a l & H o r i z o n t a l A l i g n m e n t F i g u r e 58 - A e r i a l p i c t u r e o f s o u t h e r n p a r t o f U . B . C . R e s e a r c h F o r e s t w i t h b r i d g e l o c a t i o n . - S c a l e 1" = 1 ,090 f e e t . 70 F i g u r e 60 - S i d e v i e w o f t h e b r i d g e and v a l l e y f rom the e a s t . F i g u r e 62 - D e s i g n v e h i c l e - 50 t o n 5 a x l e t r u c k . 72 DESIGN S P E C I F I C A T I O N S One l a n e b r i d g e w i t h w h e e l g u a r d s and g u a r d r a i l s . T o t a l l e n g t h : (a) 1 s p a n - 80 f t . (b) 3 spans - 40 - 80 - 40 f t . T o t a l w i d t h : 16 f t . C l e a r w i d t h : 14 f t . D e s i g n v e h i c l e : 50 t o n 5 a x l e o n - h i g h w a y truck"*" ( F i g u r e 62) M a t e r i a l : R u n n i n g d e c k 3 " u n t r e a t e d p i n e 4" t r e a t e d D . f i r T i e s 8" x 6" ( o n edge) - 1 2 " c c . t r e a t e d D . f i r S t r i n g e r s : G l u l a m i n a t e d D . f i r 2 A l l o w a b l e s t r e s s e s o f t h e d e s i g n m a t e r i a l D o u g l a s F i r - wet s e r v i c e c o n d i t i o n s B e n d i n g 1 ,900 p s i L o n g i t u d i n a l s h e a r 145 p s i C o m p r e s s i o n p a r a l l e l t o g r a i n 1 ,200 p s i C o m p r e s s i o n combined w i t h b e n d i n g 1 ,400 p s i C o m p r e s s i o n p e r p e n d i c u l a r t o g r a i n 305 p s i M o d u l u s o f e l a s t i c i t y 1 , 6 9 0 , 0 0 0 p s i C o s t e s t i m a t e s a r e b a s e d on a v e r a g e c o n s t r u c t i o n and m a t e r i a l c o s t s r e c o r d e d i n T a k l a L o g g i n g Company L t d . , P r i n c e G e o r g e , B . C . "*" F o r e s t r y Handbook f o r B r i t i s h C o l u m b i a , The F o r e s t C l u b , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1971 ( V a n c o u v e r , C a n a d a ) . p . 6 7 6 . 2 T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 3 . ^} H- CO l-t o O J 1 -d c - i— 1 z> (-• 3 O r. c* ' — 0 •3 o r. o =- Q- Ci CJ f-; Zl ro 3 r r i; o CO 74 F i g u r e , r.4 - P r o f i l e of proponed a l i g n m e n t . APPENDIX I I S i m p l e Beam B r i 76 SIMPLE BEAM BRIDGE STRINGERS: Dead l o a d c a l c u l a t i o n : R u n n i n g p l a n k s t r e a t e d 3 " x 1 4 ' (48 l b s . / c u . f t . ) 168 l b s . / I n . f t . u n t r e a t e d 4" x 1 4 ' (58 l b s . / c u . f t . ) 270 l b s . / I n . f t . T i e s 6" x 8" x 1 6 ' (58 l b s . / c u . f t . ) 309 l b s . / I n . f t . S t r i n g e r - i n t e r i o r 212 l b s . / l n . f t . - e x t e r i o r 160 l b s . / l n . f t . D i a p h r a g m s 8 3 / 4 " x 6 3 " (130 l b s . / c u . f t . ) 5 (3) 4 , 0 g 0 1 4 Q = 98 l b s . / l n . f t . W h e e l g u a r d s and g u a r d r a i l s (one s i d e ) 82 l b s . / l n . f t . T o t a l : I n t e r i o r s t r i n g e r (56 + 90 + 103 + 2 1 2 + 3 3 ) 494 l b s . / l n . f t . E x t e r i o r s t r i n g e r (28 + 45 + 52 + 160 + 17 + 82) 384 l b s . / l n . f t . L i v e l o a d c a l c u l a t i o n : 50 t o n s = 100 k i p s = R M = ^ ! - P T e max L L L L P e - P T e T x = — - r r L L 2R / n 20 x 20 + 20 x 16 - 4 x 25 - 20 x 10 . . , x = 40 z z-rz = 4 0 - 2 . 1 2 x 100 x = 3 7 . 9 f t . 2 M = 1 Q ° il7'9) 300 = 1 ,795 - 300 = 1 ,495 f t . kiDS max 80 ' 1 77 I n t e r i o r s t r i n g e r : D i s t r i b u t i o n f a c t o r 1 -| = = 1.0 Unbalanced load f a c t o r .65 M = 0.65 (1,495) = 971.8 f t . kips = .494 ( 8 0 ) 2 . TJL 8 395.2 f t . kips M , = 1,367.0 f t . kips T o t a l 3 3 S - 1 - 3 6 ^ U 1 2 - ° n 0 ) ° 8>634 i n / req 1,900 holes for rods 750 in. = 9,384 i n . " T o t a l From TDM t a b l e s 2 : 14 1/4" x 63"; S = 9,426.4 in.' Check f o r shear s t r e s s e s : L/4 = 20 f t . 3d = 15.75 f t . — > governs £4.2S' I iff.o' \->.c\, ie.*' M -1 >5-7S' I -A I •y- V max '_ 10(24.25) + 25(40.25 + 44.25) + 20(60.25 + 64.25) = g k 80 V_ = 0.65 (60.56) = = 39.36 kips Li JJ VDL = -* 9 A 2 ( 8 0 ) p. 29. = 19.76 kips V T o t a l = 5 9 " 1 2 k i P S f =  1,5 lll'l2^ = 98.8 p s i < 125 p s i • O.K. v by / . o For i n t e r i o r s t r i n g e r s use 14 1/4" x 63" x 82' Design of highway bridges: CSA Standards S6, 1966 (Ottawa, Canada) 2 Timber Design Manual: Laminated Timber I n s t i t u t e of Canada, 1972 (Ottawa, Canada), p. 25. C h e c k f o r b e a r i n g : P o s i t i o n o f l o a d - / 4o' '. /ff' \<*-, \*\ 72, J. R = 1 0 ( 4 0 ) + 2 5 ( 5 6 +60) + 2 0 ( 7 6 + 80) L L 80 I n t e r i o r s t r i n g e r : R = 0 . 6 5 ( 8 0 , 2 5 0 ) R , WL ^ 494 (80) "DL ^ o t a l A = 71'3H2 = 236 in. 2 b = 1 2 . 2 5 i n . ; a = 1 9 . 2 5 i n . b e a r i n g p l a t e s 12 1 /4" x 2 0 " o r c a p s 1 2 " x 2 0 " x 1 6 ' = 8 0 . 2 5 k i p s = 52 , 162 l b s . = 1 9 , 7 6 0 l b s . = 7 1 , 9 2 2 l b s . E x t e r i o r s t r i n g e r : E c c e n t r i c i t y 2 f t . A" p. "A" 1 by e c c e n t r i c r i v e t : 2 ( 7 . 5 ) A 2 ( 7 . 5 ) 2 + 2 ( 2 . 5 ) 2 ( 0 . 2 5 + 0 .12)W = 0 .37 W 79 M = 1 , 4 9 5 ( . 3 7 ) = 5 5 3 . 2 f t . k i p s i-iLi • 3 8 4 ( 8 0 ) 2 " D L = 8 " 3 0 7 ' 2 f t - k l p s M = 8 6 0 . 4 f t . k i p s T o t a l _ 8 6 0 . 4 ( 1 2 , 0 0 0 ) _ 3 S r e q 1 ,900 i n * S = 700 i n . 3 h o l e s 3 S = 6 , 1 3 4 i n . T o t a l From TDM t a b l e s 3 : 10 3 / 4 " x 6 3 " ; S = 7 1 1 1 . 1 i n . 3 > O . K . Check f o r s h e a r s t r e s s e s : V T T = 0 . 3 7 V = 0 . 3 7 ( 6 0 . 5 6 ) = 2 2 . 4 0 k i p s L L max • 3 8 4 ( 8 0 ) = 1 5 . 3 6 k i p s DL 2 3 7 . 7 6 k i p s f 1 - 5 ( 3 7 , 7 6 0 ) D / . < 1 0 c . . . _ v r = — _ ; _ \ = 84 p sx < 125 p s i >O.K. v o / /. J F o r e x t e r i o r s t r i n g e r s u s e 10 3 / 4 " x 6 3 " x 8 2 ' C h e c k f o r b e a r i n g : R j ^ = 0 . 3 7 ( 8 0 . 2 5 ) = 2 9 , 6 9 2 l b s . = 15__360 l b s . K r o t a l 4 5 > 0 5 2 l b s - A - ^ 2 1 2 " 1 4 7 . 7 i n . 2 r e q 305 b = 1 0 . 7 5 i n . ; a = 1 3 . 7 4 i n . b e a r i n g p l a t e s 10 3 / 4 " x 1 4 " o r caps 1 2 " x 20" x 1 8 ' — > 0 . K . 3 T i m b e r D e s i g n M a n u a l : L a m i n a t e d T i m b e r I n s t i t u t e o f C a n a d a , 1972 ( O t t a w a , C a n a d a ) , p . 24 . 80 C h e c k f o r d e f l e c t i o n : (From TDM t a b l e s ) 3 4 A 5PL ., • 5wL ., A = n384 E I A n384 E I A DL K, - 1 . 6 * ( 3 - 4 ( f ) 2 ) ; K A T =1.0 Li Li I j, Ot-34 , , 18 / 0 , , 1 8 . 2. \ " L 6 80 ( 3 ~ 4 ( 8 0 } > K A 2 = 1- 6 it 3- 4 (I ) 2> *A " f <3 " 4(I)2> 3 K A = 1.6 25 (3 - A ( | § ) 2 ) 4 80 % 5 = 1 - 6 i < 3 - 4 ( f ) 2 ) = 1 .007 = 1 .549 = 1 .594 = 1 .304 = 1 .144 , 5 ( 1 0 , 0 0 0 ) ( 8 0 x 12) 1 < 0 0 7 = Q o e . n < A l 4 x 3 8 4 ( 1 . 6 9 ) 1 0 6 ( 2 9 6 , 9 3 1 ) A 2 + 3 = 5 ( 2 5 , 0 0 0 ) (80 x 12) 3 ^ _ ^ ^ 4 x 3 8 4 ( 1 . 6 9 ) 10 ( 2 9 6 , 9 3 1 ) 5 ( 2 0 , 0 0 0 ) (80 x 1 2 ) 3 ^ = Q , 2 8 l n < 4 x 3 8 4 ( 1 . 6 9 ) 1 0 ° ( 2 9 6 , 9 3 1 ) LL 0 . 7 9 i n . 4 T i m b e r D e s i g n M a n u a l : L a m i n a t e d T i m b e r I n s t i t u t e o f C a n a d a , 197 2 ( O t t a w a , C a n a d a ) , p . 127 - 1 2 8 . I 81 . = 0 . 7 9 0 i n . L L , 5 ( 7 3 . 2 ) ( 8 0 x 12) 4 1 . 0 o 0 . 0 , 8 0 6 i n , 4 x 3 8 4 ( 1 . 6 9 ) 1 0 ( 2 9 6 , 9 3 1 ) A T o t a l = 1.596 i n . < 1.6—> O . K . L 80 x 12 . , . = 1.6 x n . " A L L 600 600 RUNNING P L A N K S : 2 l a y e r s 3 " u n t r e a t e d p i n e 4 " t r e a t e d D . f i r W h e e l l o a d ( c o n s i d e r i n g u n b a l a n c e d l o a d ) = 0 . 6 5 ( 2 5 ) = 1 6 . 2 5 k i p s D i s t r i b u t i o n f a c t o r 5 y ^ r = ~ r = 0 . 2 2 2 4 . 5 4 . 5 A c t i n g l o a d 0 . 2 2 2 ( 1 6 . 2 5 ) = 3 . 6 0 8 k i p s M = 3 . 6 0 8 ( 1 . 2 5 ) = 4 . 5 1 f t . k i p s max r - j , \ s - A ^ I l ^ o o i , 4 1. 6 2 l n . 3 ' i r e q 1 ,300 T i e s 6" x 8" on e d g e , 1 2 " c c . C h e c k f o r s h e a r s t r e s s e s : y _ 1 0 P ( L - x ) ( x / d ) 2 = 1 0 ( 3 . 6 0 8 ) ( 5 - 2 . 5 ) ( 2 . 5 / . 6 6 ) 2 = ± ? 2 2 ^ 9 L ( 2 + ( x / d ) 2 ) 9 ( 5 . 0 ) ( 2 + ( 2 . 5 / . 6 6 ) 2 ) A = 1 , 5 * 1 , 7 2 2 = 2 0 . 7 i n . 2 < 48 i n . 2 >0.K. r e q 125 C h e c k f o r b e a r i n g : f c =  3 » 6 ° 8 _ 5 0 p s i < 280 p s i > 0 . K . 1 6 x 12 1 v D e s i g n o f h i g h w a y b r i d g e s : CSA S t a n d a r d s S 6 , 1966 ( O t t a w a , C a n a d a ) . p . 2 9 . 82 /G-0" 2' 3- k F i g u r e 65 - A r r a n g e m e n t o f roadway w i t h w h e e l g u a r d s and g u a r d r a i l s 83 ABUTMENTS: N o r t h Abu tmen t -X- 0 K 11 \ > 6 S o i l b a c k f i l l P a c k c o u r s e s and - 135 l b s . / - - . u . f t . G = 3 2 ° 3 0 ' A d d i t i o n a l p r e s s u r e f r o m t r u c k c a l c u l a t e d f o r s u b s t i t u t i o n h e i g h t o f s o i l P = 2 x 2 5 k + 20 x 2 0 k = max = 9 0 , 0 0 0 l b s . f o r 4 a x l e s P 9 0 , 0 0 0 , 0 1 V = = — ' _ = 621 c u . f t . s w . n 135 s o i l w = 7 7 ^ = 1 .69 f t . s 400 T o t a l " h " f o r a c t i n g s o i l i s 1 8 . 6 8 f t . R e s u l t a n t o f e a r t h p r e s s u r e i s c o n s i d e r e d h o r i z o n t a l as t h e a n g l e o f o v e r f i l l i s t o o s m a l l t o be c o n s i d e r e d . F r i c t i o n b e t w e e n s o i l and c o n c r e t e w a l l was c o n s i d e r e d z e r o c o n s i d e r i n g we t s o i l c o n d i t i o n s . E a r t h p r e s s u r e c a l c u l a t i o n : T, r , i w h 2 . r c o s 6 P = R = k — ; k = cos 6 / 2 2 - v cos - c o s c o s j 2 2 +* cos - co s CO s 6 = 1 .00 ; c o s 6 = 0 . 8 4 3 4 ; k = 1 x . 4 6 3 1 .537 = 0 . 3 0 2 R = 0 . 3 0 2 1 3 5 x 1 8 - 6 R = 7 , 1 0 0 l b s / I n . f t . o f abu tmen t Moment f r o m p r e s s u r e o f s o i l : 1 8 . 6 8 M = 7 , 1 0 0 •• s -> 4 4 , 1 0 0 l b . f t . Moments a c t i n g a g a i n s t s o i l p r e s s u r e a r o u n d p o i n t A . 8 4 W e i g h t o f c o m p o n e n t s : w.^ = 4 . 5 x 1 0 . 7 5 x 0 . 1 5 = 7 . 2 6 k i p s w 2 = 3 x 6 . 2 5 x 0 . 1 5 = 2 . 8 1 k i p s w 3 = - | x 4 . 5 x 1 0 . 7 5 x 0 . 1 5 = 3 . 6 3 k i p s 7 0 , 2 4 0 , , 0 , . w, = —t-,— = 4 . 3 9 k i p s 4 16 W T o t a l " 1 8 ' 0 9 k l p S M = 7 . 2 6 x 6 . 7 5 = 4 9 . 0 0 f t . k i p s M 2 = 2 . 8 1 x 7 . 5 = 2 1 . 0 8 f t . k i p s M 3 = 3 . 6 3 x 3 . 0 = 1 0 . 8 9 f t . k i p s = 4 . 4 x 5 . 2 5 = 2 3 . 1 f t . k i p s M ., = 1 0 4 . 0 7 f t . k i p s T o t a l L o c a t i o n o f r e s u l t a n t i n f o o t i n g b o t t o m - d i s t a n c e f r o m A " T o t a l " M s " W T o t a l ( x ) 1 0 4 . 0 7 - 4 4 . 1 = 1 6 . 8 ( x ) x " l f t o f " 3 ' 3 2 f t ' T h e r e f o r e r e s u l t a n t l i e s w i t h i n m i d d l e 1/3 — > - 0 . K . 85 South Abutment • 7S z.o' I e.s\ I4.s- Same conditions as f o r North Abutment. A d d i t i o n a l pressure from tr':ck = 2 f t . T o t a l h = 26 f t . Earth pressure: 2 P = 0.302 x 1 3 3 2 X 2 6 = 13.7 kips M . = 13.7 x ^ ~ = 119.2 f t . kips s o i l 3 Weight components: w.. = 4.5 x 17.75 x 0.15 = 11.98 kips w 2 = 3.0 x 6.25 x 0.15 = 2.81 kips w, = 8.5 x 17.75 70,240 16 1^ = 11.98 x 10.75 M 2 = 2.81 x 11.5 M 3 = 11.32 x 5.66 M. = 4.39 x 9.25 4 " T o t a l " s o i l 266.22 - 1.1.9.2 x = 30.5 W T o t a l = 128.78 f t . kips = 32.34 f t . kips = 64.05 f t . kips = 40.61 f t . kips = 266.22 f t . kips = 119.2 f t . kips = 4.82 ft.> 4.33 f t . x 0.15 = 11.32 kips - 4.39 kips = 30.5 kips O . K . 86 B I L L OF MAIN MATERIAL AND PRELIMINARY COST ESTIMATE R u n n i n g d e c k ( u n t r e a t e d ) 3" x 1 4 ' x 8 2 ' = 3 , 4 4 4 fbm @ $230/Mfbm = $ 792 ( t r e a t e d ) 4" x 1 6 ' x 8 2 ' = 4 , 5 9 2 fbm C? $340/Mfbm = $ 1 ,561 T i e s 82 ( 8 " x 6" x 1 6 ' ) = 5 , 2 4 8 fbm @ $380/Mfbm = $ 1 ,994 G u a r d r a i l ( u n t r e a t e d ) 2 x 10 ( 8 " x 8" x 5 ' ) = 1 ,440 fbm @ $260/Mfbm = $ 659 2 ( 8 2 ' x 6" x 8") 656 fbm 2 ( 8 2 ' x 4 " x 8") 437 fbm T o t a l = 2 , 5 3 3 fbm W h e e l g u a r d ( t r e a t e d ) 2 ( 8 2 ' x 10" x 12") = 1 ,640 fbm @ $380/Mfbm = $ 623 T o t a l =• $ 5 ,629 S t r i n g e r s : I n t e r i o r 2 (14 1 /4" x 6 3 " x 8 2 ' ) = 1 ,023 c u . f t . E x t e r i o r 2 (10 3 / 4 " x 6 3 " x 8 2 ' ) 772 c u . f t . D i a p h r a g m s 15 (6 3 / 4 " x 6 0 " x 5 ' ) 210 c u . f t . T o t a l 2 , 0 0 5 c u . f t . @ $ 27 $ 5 4 , 1 3 5 C o n c r e t e A b u t m e n t s N o r t h A b u t m e n t : — ( 4 . 5 x 1 0 . 7 5 ) + (3 x 6 . 2 5 ) + ( 4 - 5 I 1 0 ' 7 5 ) 16 = 5 5 . 1 c u . y d . S o u t h A b u t m e n t : ( 4 . 5 x 1 7 . 7 5 ) + (3 x 6 . 2 5 ) 1 1 7 ' 7 5 ) 16 = 103 . 2 c u . y d T o t a l = 158 .3 c u . y d @ $250 = $ 3 9 , 5 7 5 T o t a l f i l l 2 , 7 4 1 C C Y 1 = 4 , 0 5 6 L C Y 2 @ $ 2 . 2 0 $ 8 . 9 2 3 T o t a l f o r s i m p l e beam b r i d g e = $ 1 0 8 , 2 6 2 CCY - Compacted c u b i c y a r d s LCY - L o o s e c u b i c y a r d s APPENDIX I I I C o n t i n u o u s Beam (Two E q u a l S S i n g l e S t r u t f r a m e B r i d g e > 88 CONTINUOUS BEAM TWO EQUAL S P A N S : C o n d i t i o n s a r c t h e same as f o r s i n g l e beam c a l c u l a t i o n s . S o l v e f o r d e s i g n t r u c k 50 t o n . F i n d M ( n e g a t i v e a n d / o r p o s i t i v e ) a c c o r d i n g t o ° max t h e t h e o r e m o f t h r e e moments u s i n g i n f l u e n c e l i n e s . M = ( P . y . + P 9 y 9 P J , ) L max 1 1 11 n l A AT" 8 A S u p e r p o s i t i o n o f t h e t r u c k ( p o s i t i o n i n w h i c h t h e maximum moment o c c u r s ) h a s b e e n f o u n d by t r i a l and e r r o r . V a l u e s u s e d f o r i n f l u e n c e l i n e s ( F i g u r e s 66 and 67) w e r e c a l c u l a t e d by A d a m o v i c h 1 . N e g a t i v e moment i s a l w a y s g o v e r n i n g when t h e same h e i g h t o f t h e beam i s d e s i g n e d . F o r c h a n g i n g h e i g h t a l s o p o s i t i v e moment ( b e t w e e n s u p p o r t s ) has t o b e f o u n d . A T h r e e moment e q u a t i o n . 2? ^ L, y % "V M A L x + 2 M R ( L x + L 2 ) + M c L 2 = 1/4 ( ^ + « 2 L ^ ) - P , a 1 "1* P 2 b 2 ( L 2 2 - c / ) 1 T A d a m o v i c h K r d o s z o t i U 1 d £ i i t £ 5 . . ( " L e c t u r e s on F o r e s t B r i d g e s " ) > 89 S i n c e L.. = L _ and w, = w„ and M , = 0, M = 0. 1 2 1 2 A c Dead l o a d moment. M = - 1/8 w L 2 max L i v e l o a d moment. M P a P c max 4L - E [ — ( L " a ) ] - E[— ( L - c ) ] S u p e r p o s i t i o n o f t h e d e s i g n v e h i c l e ( A p p e n d i x I ) . 7> T> t 4' /' x X /£•' • i0.s'\ ./. / . P l = P 2 = 2 0 k i p s P 3 = P 4 = 25 k i p s = 10 k i p s M ( l i v e ) - - [ ( 0 . 0 8 4 + 0 . 0 6 6 ) 20 + ( 0 . 0 8 0 + 0 . 0 9 2 ) 25 + in s x 0 . 0 6 3 x 10] 40 = - 3 2 9 . 2 f t . k i p s re 66 - Two e q u a l s p a n s c o n t i n u o u s beam moment I n f l u e n c e l i n e s . ( V a l u e s p l o t t e d on doc l i e s o f e a c h s p a n ) . 91 D i s t r i b u t i o n o f t h e l o a d b e t w e e n i n t e r i o r and e x t e r i o r s t r i n g e r s i s t h e same as c a l c u l a t e d f o r s i m p l e beam b r i d g e ( A p p e n d i x I I ) . I n t e r i o r s t r i n g e r : M . _ = - . 6 5 M = - . 65 ( 3 2 9 . 2 ) = - 2 1 3 . 9 8 f t . k i p s L L max Dead l o a d . Deck and t i e s 249 p . l . f . o r l b s . / c u . f t . S t r i n g e r s 84 p . l . f . o r l b s . / c u . f t . D i a p h r a g m s 16 p . l . f . o r l b s . / c u . f t . T o t a l 349 p . l . f . o r l b s . / c u . f t . M _ L = - 1/8 wL = - 1/8 ( . 3 4 9 ) ( 4 0 ) = - 7 2 . 8 0 f t . k i p s M T o t a l = - 2 8 6 . 7 8 f t . k i p s 3 i n . S - 2 8 6 . 7 6 ( 1 2 , 0 0 0 ) _ r e q 1 ,900 10 3 / 4 " x 3 3 " ; S = 1 , 9 5 1 . 1 i n . 3 ; A «= 3 5 4 . 8 i n . 2 C h e c k f o r s h e a r s t r e s s e s : Dead l o a d . 2 U s i n g t a b u l a t e d c o e f f i c i e n t s f rom TC . V = . 219 wL = .219 ( . 3 4 9 ) 80 = 6 . 1 1 k i p s = . 3 1 5 wL = . 3 1 5 ( . 3 4 9 ) 80 = 8 .79 k i p s D L i v e l o a d . 3 U s i n g s h e a r i n f l u e n c e l i n e s c a l c u l a t e d by A d a m o v i c h ( F i g u r e 66) 2 T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 1 5 . 3 L . A d a m o v i c h , E r d e s z e t i H i d e p t e s , ( " L e c t u r e s on F o r e s t B r i d g e s " ) ( S o p r o n , H u n g a r y : U n i v e r s i t y o f S o p r o n . 1 9 4 9 ) . p . 4 4 . ( M i m e o g r a p h e d . )  93 Superposition of design v e h i c l e has been considered separately for outer and intermediate supports. •4o' ~7k /- V A = (1.00 + .88) 20 + (.42 + .31) 25 = 55.85 kips A -7~ £ 4 ' I '<S~' y . /<r' — y V B = (.79 + .87) 20 + (.99 + .95) 25 + (.56) 10 = 87.30 kips Shear for i n t e r i o r s t r i n g e r . V = .65 x 87.30 = 56.745 kips Governing shear occurs at R ^ . V D L = 8.790 kips V L L = 56.745 kips V T o t a l " 6 5 ' 5 3 3 k i p S f v . 1 . 5 V 1.5(65.535) m§x = — 3 5 Z - 8 = 2 7 7 P s i > 1 4 5 P s i n x A 0 •N.G. As per the c a l c u l a t i o n , shear forces are governing f a c t o r over the moment with continuous beam, w h i l s t with the simple beam the s i t u a t i o n i s opposite. Try: 14 1/4" x 49 1/2"; A = 705.4 i n . 2 ; w = 162 p . l . f . V D L = .315 (432) 80 = 10,886 l b s - V j = (as per above) = 56,745 l b s . V T o t a l » 67,631 lbs 94 f = 1 , 5 ^ 7 ; 6 3 1 ) = 1 4 3 . 8 p s i < 145 p s i - + 0 . K . .r / u 5 .4 F o r i n t e r i o r s t r i n g e r s u s e 14 1 /4" x 49 1 /2" x 8 2 ' . E x t e r i o r s t r i n g e r : Dead l o a d . Deck and t i e s 125 p . l . f . ( as c a l c u l a t e d f o r s i m p l e beam b r i d g e , A p p e n d i x I I ) S t r i n g e r s 102 p . l . f . D i a p h r a g m s 8 p . l . f . H a n d r a i l and w h e e l g u a r d 82 p . l . f . 317 p . l . g . M _ L = 1/8 ( . 3 1 7 ) ( 4 0 ) 2 = 6 3 . 4 f t . k i p s M . T = .37 (M ) = .37 ( 3 2 9 . 2 ) = 1 2 1 . 8 f t . k i p s X L max — " T o t a l " 1 8 5 ' 2 f t - k ± p S s , 1 8 5 ; 2 ^ ° ° Q > - 1 ,169 i n . 3 r e q 1 ,900 F o r e q u a l h e i g h t o f s t r i n g e r s c h o o s e : 8 3 / 4 " x 49 1 / 2 " ; S = 3 , 5 7 3 . 3 i n . 3 ; A = 4 3 3 . 1 i n . 2 C h e c k f o r s h e a r a t r e a c t i o n B : V _ T = . 3 1 5 (317) 80 = 7 , 9 8 8 l b s . JjJ_i V T T = .37 (V ) = 0 .37 ( 8 7 , 3 0 0 ) = 3 2 , 3 0 1 l b s . L L max 1 V _ . - = 4 0 , 2 8 9 l b s . i o t a l f 1 . 5 ( 4 0 , 2 8 9 ) . , n . _ . n v = ^ ]_— = ' 5 p s i < 145 p s i — > 0 , K . R e a c t i o n s : 4 Dead l o a d - u s i n g t a b u l a t e d c o e f f i c i e n t s f r o m TC . 4 T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 1 5 . 9.5 R. = .219 wL A R_ = . 6 2 5 wL L i v e l o a d - s i n c e s h e a r s t r e s s e s c a u s e d by m o v i n g l o a d a r e a p p r o x i m a t e e q u a l r e a c t i o n s , v a l u e s o f V a t A = R , and V a t B = L max A max J3 ( g o v e r n s ) . R_ - I n t e r i o r s t r i n g e r : = «65 ( v m a x ) = 5 6 . 7 4 k i p s R _ L = . 6 2 5 ( . 4 3 2 ) ( 8 0 ) = 2 1 . 6 0 k i p s Vtal - 7 8 . 3 4 k i p s E x t e r i o r s t r i n g e r : TLr = .37 (V ) = 3 2 . 3 0 k i p s L L max R _ L = . 6 2 5 ( . 3 1 7 ) ( 8 0 ) = 1 5 . 8 5 k i p s " T o t a l = A 8 ' 1 5 k i p S Check f o r b e a r i n g : I n t e r i o r s t r i n g e r : A = 78lH° «= 257 i n . 2 = 14 1 /4" x 18" r e q 305 E x t e r i o r s t r i n g e r : A =  h8'll° = 158 i n . 2 = 8 3 / 4 " x 1 8 . 1 " — ^ g o v e r n s r e q 305 C r o s s - e l e m e n t i n t h e m i d d l e s p a n w i l l be g l u l a m beam 10 3 / 4 " x 19 1 / 2 " w i t h e l e m e n t s p o s i t i o n e d h o r i z o n t a l l y . S t r u t s : S o l v e d as l o n g s i m p l e c o l u m n s 5 . L o a d i n g on s t r u t s c o n s i d e r e d e q u a l l y d i s t r i b u t e d i n r e g a r d w i t h p r e v i o u s l y c a l c u l a t e d e c c e n t r i c i t y . 5 T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 1 7 . 4"' / 3, 0 A ^ 5 ' G r a p h i c a l s o l u t i o n : < » - <? . « / - 2 L . = / ( 3 8 ) + ( 1 0 . 1 2 ) - 3 9 . 3 2 f t . L„ = / ( 3 8 ) 2 f ( 1 7 . 1 2 ) = 4 1 . 6 8 f t . — ^ g o v e r n s J2 I n t e r i o r s t r i n g e r : S l e n d e r n e s s r a t i o : L„ 4 1 . 6 8 x 12 . , _ 0 = —ib~?7b~~ = 4 6 ' 5 3 a K = . 6 4 1 / E / F c = . 6 4 1 / 1 , 6 9 0 , O O P " - 2 2 . 2 7 < 1 ,400 f - - 2 7 4 (M90,ooo) _ n 3 > 9 p s i ( j ) 2 ( 4 6 . 5 3 ) 2 P ' 7 3 , 2 0 0 . . . . 2 A = = o n n = 342 i n . r e q 2 1 3 . 9 2 1 3 . 9 I 97 To obtain slendcrness r a t i o K > 50 glulaminated member of d . =10 3/4" has to be used, mm Use: 10 3/4" x 33" x 40' and 42' w = 83.8 p . l . f . ; S = 1,951.1 i n . 3 ; A = 354.8 i n . 3 > 342 i n . 2 — > O.K. Dead load reactions : R = R = .219 wL' = .219 (1.44) (80) = 25.2 kips = 1.59 k i p s / l n . f t . C A Rg = .625 wL = .625 (1.44) (80) = 72.0 kips = 4.50 k i p s / l n . f t . From g r a p h i c a l s o l u t i o n : RpOl) = 98.8 kips = 6.18 k i p s / l n . f t . R ] )(V) = 25.6 kips = 1.60 k i p s / l n . f t . R^H) = 98.8 kips = 6.18 k i p s / l n . f t . RJJ(V) = 45.5 kips = 2.84 k i p s / l n . f t . T i m b e r C o n s t r u e f i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 1 5 . 98 ' North Abutment 0 \ 0 - V 4 7.S- / M = 44.1 f t . (as c a l c u l a t e d i n s o i l Appendix II) Weight of components: w = 3.0(17.0)(0.15) = 7.65 k i p s / l n . f t , w 2 = 1.5(12.0)(0.15) = 2.70 k i p s / l n . f t . w 3 = 1.5(3.0)(0.15) = .68 k i p s / l n . f t . W 4 = RA w 5 - ^ ( H ) w, T o t a l = 1.59 k i p s / l n . f t . = 6.18 k i p s / l n . f t . = 1.60 k i p s / l n . f t , = 20.06 k i p s / l n . f t . ^ = 7.65(6.0) = 45.90 f t . kips M 2 = 2.7(3.75) = 10.12 f t . kips M 3 = .68(1.5) = 1.02 f t . kips M. = 1.59(4.0) = 6.36 f t . kips 4 M 5 = 6.18(1.5) = 9.27 f t . kips M £ = 1.6(1.5) 6 o t a l *w -M 2.40 f t . kips 75.08 f t . kips 75.08 - 20.06 = 55.02 f t . kips o t a l s o i l - 5 ~ ^ 7 = 2.74 ft.> 2.5 f t . > O.K 20.06 1 99 S o u t h A b u t m e n t AS- «4 4 u), /4.s - \ - — v -X- M . , » 1 1 9 . 2 f t . k i p s s o i l W e i g h t o f c o m p o n e n t s : = 1 0 . 0 ( 2 4 . 0 ) ( . 1 5 ) = 3 6 . 0 0 k i p s / l n . f t . w 2 = 1 . 5 ( 1 7 . 0 ) ( . 1 5 ) = 3 . 8 2 k i p s / l n . f t . M3 = 3 . 0 ( 1 . 5 ) ( . 1 5 ) = 0 . 6 8 k i p s / l n . f t . w . = R 4 c w, T o t a l 1 .59 k i p s / l n . f t . 6 . 1 8 k i p s / l n . f t . 2 . 8 4 k i p s / I n . f t . 5 1 . 1 1 k i p s / l n . f t . = 3 6 . 0 ( 9 . 5 ) = 3 4 2 . 0 f t . k i p s M 2 = 3 . 8 2 ( 3 . 7 5 ) = 1 4 . 3 2 f t . k i p s M 3 = . 6 8 ( 1 . 5 ) 1 .02 f t . k i p s M 4 = 1 . 5 9 ( 4 . 0 ) = 6 . 3 6 f t . k i p s M 5 = 6 . 1 8 ( 1 . 5 ) 9 . 2 7 f t . k i p s M , = 2 . 8 4 ( 1 . 5 ) = 4 . 2 6 f t . k i p s o "T o t a l T o t a l s o i l = 3 7 7 . 2 3 f t . k i p s = 3 7 7 . 2 3 - 1 1 9 . 2 = 2 5 8 . 0 3 f t . k i p s 2 5 8 . 0 3 5 1 . 1 1 = 5 . 0 5 f t . > 4 . 8 3 f t . >0.K. 100 B I L L OF MAIN MATERIAL AND PRELIMINARY COST ESTIMATE R u n n i n g d e c k , t i e s , w h e e l g u a r d and g u a r d r a i l = $ 5 , 6 2 9 S t r i n g e r s : I n t e r i o r 2 (14 1 /4" x 49 1 / 2 " x 8 2 ' ) = 803 c u . f t . E x t e r i o r 2 (8 3 / 4 " x 49 1 /2" x 8 2 ' ) = 493 c u . f t . D i a p h r a g m s 15 (6 3 / 4 " x 4 5 " x 5 ' ) = 158 c u . f t . S t r u t s 4 (10 3 / 4 " x 3 3 " x 4 2 ' ) = 413 c u . f t . 4 (10 3 / 4 " x 3 3 " x 40*) = 394 c u . f t . D i a p h r a g m s 18 (6 3 / 4 " x 3 0 " x 5 ' ) = 127 c u . f t . C r o s s e l e m e n t 8 3 / 4 " x 3 0 " x 1 6 ' = 29 c u . f t . T o t a l 2 ,417 c u . f t . @ $27 = $ 6 5 , 2 5 9 A b u t m e n t s N o r t h A b u t m e n t : ( [3 x 17] + [ 1 . 5 x 12] + [ 1 . 5 x 3 ] ) 16 = 4 3 . 6 c u . y d . S o u t h A b u t m e n t : ( [ 1 0 x 24] + [ 1 . 5 x 17] + [ 1 . 5 x 3 ] ) 16 = 1 6 0 . 0 c u . y d . T o t a l = 3 0 4 . 6 c u . y d . (? $250 = $ 5 0 , 9 0 0 T o t a l f i l l (From A p p e n d i x I I ) = $ 8 . 9 2 3 T o t a l f o r s t r u t f r a m e b r i d g e = $ 1 3 0 , 7 1 1 APPENDIX I V C o n t i n u o u s Beam - T h r e e Sp D o u b l e S t r u t f r a m e B r i d g e T h r e e - h i n g e d A r c h B r i d g e 102 CONTINUOUS BEAM THREE S P A N S : L l = L 3 ' L 2 = 0 , 7 5 L l ' Dead l o a d moment. ' M A L 1 + 2 M B ( L 1 + V + M C L 2 = 1 / 4 W ( L 1 3 + L 2 3 ) = 1 0 1 . 8 0 M_ + 2 1 . 8 0 M = 1 / 4 ( 7 5 0 ) ( 3 5 , 0 0 0 ) = _ 6 , 5 7 0 2 1 . 8 0 B 1 0 1 . 8 0 ~ 1 0 1 . 8 0 c M_ = 6 4 . 6 - 0 . 2 1 4 M c M _ L 2 + 2 M C ( L 2 + L 3 ) 4- = - 1 / 4 w ( L - 3 + L 3 3 ) 2 1 . 8 0 M„ + 1 0 1 . 8 M„ = - 6 , 5 7 0 6 , 5 7 0 2 1 . 8 C " 1 0 1 . 8 0 " 1 0 1 . 8 0 B M _ = - 6 4 . 6 - 0 . 2 1 4 M M B = - 6 4 . 6 - 0 . 2 1 4 ( 6 4 . 6 - 0 . 2 1 4 M^) M_ = - 6 4 . 6 - 1 3 . 8 + 0 . 0 4 5 8 M f i . 9 5 4 M B = - 7 8 . 4 f t . k i p s Mg = - 8 2 . 2 f t . k i p s M _ = - 6 4 . 6 - 0 . 2 1 4 x 8 2 . 2 = - 8 2 . 2 f t . k i p s 103 Live load M max According to influence lines (Figure 68). Superposition of the design vehicle. A ~ "A M max = - [(0.085 + 0.086) 25 + (0.063 + 0.067) x 20 - - 0.012 x 10)L 2 = [4.27 + 2.60 - 0.12] x 21.80 = -147.1 f t . kips Live M = -147.1 f t . kips max Dead M = -82.2 f t . kips max t a l = -229.3 f t . kips Interior stringer: M = .65 (229.3) = 149.04 f t . kips max r s = U 9 - ? 4 < " ' 0 0 ° > - 941 i n . 3 req 1,900 - 3 S, , approximately = 300 i n . holes 8 3/4" x 30"; w = 62.0 p . l . f . ; A = 262.5 i n . 2 ; S = 1,312.5 i n . 3 > 1,241 in. 3—»0.K. Exterior stringer: M = .37(229.3) = 84.84 f t . kips max s = 8 A - 8 4 ( q 2 ' ° 0 0 ) • 535 i n . 3 req 1,900 3 S approximately = 200 in. holes 5" x 30"; w = 35.4 p . l . f . ; A = 150.0 i n . 2 ; S = 750.0 > 735 in. -••O.K. F i g u r e 68 - T h r e e s p a n c o n t i n u o u s beam moment i n f l u e n c e l i n e s . ( V a l u e : ; p l o t t e d on d e c i l e s o f e a c h span ) . 105 S h e a r and r e a c t i o n s 1 , A A X . £ / . & ' • ' ^ A Z - So-o ' D = A = . 1 6 0 6 x w x L = 1 0 . 0 k i p s B , . = . 2 1 8 0 x w x L = 1 3 . 1 k i p s = . 183 x w x L = 1 1 . 0 k i p s <*A - • /• w = . 7 5 k i p s / f t . L = 80 f t . B ( L 2 ) R C = \ - \ L ± ) + B ( L 2 ) = 2 4 - 1 k i p S L i v e l o a d ( u s i n g i n f l u e n c e l i n e s , F i g u r e 6 9 ) . S u p e r p o s i t i o n o f t h e d e s i g n v e h i c l e . ^ A - / / _.. i A I * A -59/' I t ( 0 . 3 7 + . 55 ) 20 + ( . 9 8 + . 99 ) 25 + 0 . 1 4 x 10] = 79 k i p s max = V D L + V T T = 1 3 . 1 + 7 9 . 0 = 9 2 . 1 k i p s = 9 2 , 0 0 0 l b s . L L - 2 4 . 1 + 7 9 . 0 = 1 0 3 . 1 k i p s = 1 0 3 , 1 0 0 l b s . C h e c k f o r s h e a r s t r e s s e s . * I n t e r i o r s t r i n g e r : V = 0 . 6 5 V = 0 . 6 5 ( 9 2 , 0 0 0 ) = 5 9 . 8 k i p s max v t 1 . 5 ( 5 9 , 8 0 0 ) . ^ . . _ f = >o'o i = 402 p s i > 145 p s i — * N . G . v 2 2 3 . 1 S t e e l C o n s t r u c t i o n : A m e r i c a n I n s t i t u t e o f S t e e l C o n s t r u c t i o n , 1951 (New Y o r k , N . Y . , U . S . A . ) . p . 3 8 3 . 106 F i g u r e 69 - T h r e e s p a n c o n t i n u o u s beam s h e a r i n f l u e n c e l i n e s . ( V a l u e s p l o t t e d on d e c i l e s o f each span) . 107 • U s e : 14 1 / 4 " x 43 1 / 2 " ; w = 146 p . l . f . ; S = 4 , 4 9 4 . 1 i n . 3 ; A = 6 1 9 . 9 i n . f 1 . 5 ( 5 9 , 8 0 0 ) . . . , , . . . . _ „ v = — A = 1 4 4 . 7 p s i < 145 p s i —» O . K . E x t e r i o r s t r i n g e r : V = 0 . 3 7 V = . 3 7 ( 9 2 , 0 0 0 ) = 3 4 . 0 4 k i p s max f 1 . 5 ( 3 4 , 0 4 0 ) . • M r v = _27 5 — = 4 0 0 . 4 p s i > 145 p s i — > N . G . U s e : 8 3 / 4 " x 4 3 . 5 " ; w = 8 9 . 9 p . l . f . ; S = 2 , 7 5 9 . 5 i n . 3 ; A = 3 8 0 . 6 i n . 2 f 1 . 5 ( 3 4 , 0 4 0 ) . . . „ • n v v = oor, r— = 1 3 4 . 2 p s i < 145 p s i — > 0 . K . 3 o U . o 2 S t r u t s : s o l v e d as l o n g s i m p l e c o l u m n s . F o r c e s i n c o l u m n s c o n s i d e r e d e q u a l l y d i s t r i b u t e d as p e r c a l c u l a - t i o n o f e c c e n t r i c r i v e t i n A p p e n d i x I I . 7} = .'30./K 7^* < S ' o . / < r: C o m p r e s s i o n : C = . 3 7 ( 2 5 8 ) = 9 5 . 4 6 k i p s K"= . 6 4 1 /i_x - . 6 4 1 X'69 * ^ * f 4 = 2 2 . 2 7 / FC GC * 1 , 400 1 .0 S l e n d e r n e s s r a t i o : C r = ¥ = - 2 ^ ^ = 4 1 . 1 4 < 50 and > K t. a fc>. / _> T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 1 7 . 108 U s e s l e n d e r n e s s f a c t o r : _ 0 . 2 7 4 E _ 0 . 2 7 4 ( 1 . 6 9 x I Q 6 ) _ ( C C ) Z ( 4 1 . 1 4 ) ^ A = ^ = ^ = 3 4 8 . 9 i n . 2 r e q K^, 2 7 3 . 6 U s e : 8 3 / 4 " x 40 1 / 2 " ; w = 8 3 . 7 p . l . f . ; S = 2 , 3 9 2 . 0 i n . 3 ; A = 3 5 4 . 4 i n . 2 > 3 4 8 . 9 i n . 2 > 0 . K . H o r i z o n t a l s t r u t s : C = . 3 7 ( 2 3 5 ) = 8 6 . 9 5 k i p s C = L = 20(12) = 2 7 . 4 d 8 . 7 5 Use t h e same K = 2 7 3 . 6 . 8 6 , 9 5 0 , . _ _ . 2 A = 0-.o c = 3 1 7 . 8 i n . r e q 2 7 3 . 6 U s e : 8 3 / 4 " x 37 1 / 2 " ; w = 7 7 . 5 p . l . f . ; S = 2 , 0 5 0 . 8 i n . 3 ; A = 3 2 8 . 1 i n . 2 > 3 1 7 . 8 i n . 2 * 0 . K . Check f o r b e a r i n g : f ° l = 8 3 2 8 5 1 = 2 6 5 , 1 p s i < 3 0 5 p s i — * ° ' K " C r o s s - e l e m e n t s . 6 3 / 4 " x 4 5 " ; w = 7 1 . 7 p . l . f . ; S = 2 , 2 7 8 . 1 i n . 3 ; A = 3 0 3 . 8 i n . 109 B I L L OF MAIN MATERIAL AND PRELIMINARY COST ESTIMATE R u n n i n g d e c k , t i e s , w h e e l g u a r d and g u a r d r a i l (From A p p e n d i x I I ) = $ 5 , 6 2 9 I n t e r i o r 2 (14 1 /4" x 43 1 /2" x 8 2 ' ) 706 c u . f t . E x t e r i o r 2 (8 3 / 4 " x 43 1 /2" x 8 2 ' ) 433 c u . f t . D i a p h r a g m s 15 (6 3 / 4 " x 3 9 " x 5 ' ) 137 c u . f t . S l o p e d s t r u t s 8 (8 3 / 4 " x 40 1 / 2 " x 3 0 ' ) 590 c u . f t . D i a p h r a g m s 18 (6 3 / 4 " x 3 6 " x 5 ' ) 142 c u . f t . H o r i z o n t a l s t r u t s 4 (8 3 / 4 " x 37 1 / 2 " x 2 1 ' ) 191 c u . f t . D i a p h r a g m s 12 (6 3 / 4 " x 3 3 " x 5 ' ) 87 c u . f t . = 2 , 2 8 6 c u . f t . T o t a l @ $27 = $ 6 1 , 7 2 2 C o n c r e t e A b u t m e n t s (From A p p e n d i x I I I ) = $ 5 0 , 9 0 0 T o t a l f i l l (Fromp A p p e n d i x I I ) = $ 8 ,923 T o t a l f o r d o u b l e s t r u t f r a m e b r i d g e = $ 1 2 7 , 1 7 4 110 THREE-HINGED ARCH C a l c u l a t i o n o f r e a c t i o n s : ZMg = V D (76) - 3 8 . 1 ( 4 8 . 9 ) - 8 .9 ( 2 7 . 1 ) = 0 V D = 2 4 . 9 8 k i p s EM = 3 8 . 1 ( 2 7 . 1 ) + 8 .9 ( 4 8 . 9 ) - (76) D h, V„ = 1 9 . 3 1 k i p s h C £ M = - H„ ( 1 0 . 5 ) + (38) - 3 8 . 1 ( 1 0 . 8 ) = 0 D D = - 1 0 . 5 H D + 2 4 . 9 8 (38) - 4 1 1 . 4 8 = 0 H D = 5 1 . 2 2 k i p s H E = H D M g = V D (38) - 3 8 . 1 ( 1 0 . 8 ) = 2 4 . 9 8 (38) - 3 8 . 1 ( 1 0 . 8 ) = 5 3 7 . 7 6 f t . k i p s M H = T ^ - = 5 3 7 - 7 6 = 5 1 . 2 2 k i p s > O . K . h 1 0 . 5 M_ ( a t P ) = 2 4 . 9 8 ( 2 7 . 1 ) = 6 7 6 . 9 6 f t . k i p s h 1 = 6 7 6 - 9 6 ( 1 0 . 5 ) = 1 3 . 2 2 f t . 5 3 / . / D H = 6 7 6 - 9 6 = 5 1 . 2 2 k i p s — > O . K . n = h 1 - 9 . 6 = 1 3 . 2 2 - 9 . 6 = 3 . 6 2 f t . M = Hn = 5 1 . 2 2 ( 3 . 6 2 ) = 1 8 5 . 3 f t . k i p s = 2 , 2 2 3 , 6 0 0 l b . i n . max ) 111 F i g u r e 70 - G r a p h i c a l s o l u t i o n o f f o r c e s i n t h r e e - h i n g e d a r c h . 112 T h r u s t f rom g r a p h T = 5 4 . 8 k i p s Check f o r b e n d i n g moment and t h r u s t : max T + -4— z i b c 2 , 2 2 3 , 6 0 0 b x 2 54,800 bx -i r> r\ r-\ 1 1 ,900 " 1 ,200 b = 6 . 7 5 i n . S o l v e f o r " x " . 6 . 7 5 x 2 - 4 5 . 6 7 x - 7 , 0 2 2 = 0 x = - b t / b 2 - 4aC 112 2a / ( 4 5 . 6 7 ) 2 _ 4 5 . 6 7 ± / ( 4 5 . 6 7 ) + 4 ( 6 . 7 5 ) ( 7 , 0 2 2 ) _ . 2 ( 6 . 7 5 ) i n ' U s e : 6 3 / 4 " x 3 6 " 2 , 2 2 3 , 6 0 0 5 4 , 8 0 0 1 ,458 243 1 ,900 1 ,200 .803 + .188 = . 9 9 1 <1 — > 0 . K . Check f o r s h e a r : f = 1 - 5 ^ 8 ° ° > = 9 7 . 5 p s i < 145 p s i — O . K . v 243 P r o f i l e a t " D " : 6 3 / 4 " x 24" Check f o r t h r u s t ; f rom g r a p h T = 5 7 . 0 k i p s 5 ? _ i ? 0 0 = 352 p s i < 1 ,200 p s i > O . K . l o / P r o f i l e a t " B " : 6 3 / 4 " x 3 9 " Check f o r s h e a r ; f r o m g r a p h V = 2 5 . 0 k i p s , 1.5 ( 2 5 , 0 0 0 ) . . _ . f =  0 ) 0 o = 1 4 2 . 4 p s i < 145 p s i > O . K . v 2 6 3 . 3 v B I L L OF MAIN MATERIAL AND PRELIMINARY COST ESTIMATE R u n n i n g d e c k , t i e s , w h e e l g u a r d and g u a r d r a i l (From A p p e n d i x I I ) S t r i n g e r s & Diaph ragms (From d o u b l e s t r u t f r a m e b r i d g e ) = 1 ,276 c u . f t . A r c h beam A (6 3 / A " x [ - 4 * 3 9 x 77 ] ) = A55 c u . f t . D i a p h r a g m s 3 (6 3 / A " x 3A 1 / 2 " x 5 ' ) = 2A c u . f t . 6 (6 3 / A " x 27" x 5 ' ) = 38 c u . f t . 6 (6 3 / A " x 19 1 / 2 " x 5 ' ) = 27 c u . f t . T o t a l = 1 ,820 c u . f t . C o n c r e t e Abu tmen t s (From A p p e n d i x I I I ) T o t a l f i l l (From A p p e n d i x I I ) T o t a l f o r a r c h b r i d g e @ $27 APPENDIX V C a n t i l e v e r e d Beam B r i d g e 115 CANTILEVERED BEAM ~2T i iS" SO ' 4 Dead l o a d c a l c u l a t i o n a c c o r d i n g to TC t a b l e s . I n t e r i o r s t r i n g e r : DL - D e c k i n g and t i e s (as c a l c u l a t e d i n A p p . I I ) 249 S t r i n g e r s D i a p h r a g m s T o t a l E x t e r i o r s t r i n g e r : ' DL - D e c k i n g and t i e s S t r i n g e r s D i a p h r a g m s G u a r d r a i l and w h e e l g u a r d s T o t a l Dead l o a d moments . 160 34 p . l . f . p . l . f . 443 p . l . f , 125 110 17 82 p . l . f . p . l . f . p . l . f . p . l . f . 334 p . l . f . T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 110. 116 I n t e r i o r s t r i n g e r : W M , = s h 2 ( L 1 a L 2 + a 2 ) 2 = g ^ } 2 ( ( 4 0 ) 2 - 15(80) + ( 1 5 ) 2 ) 2 13.5 f t . k i p s M 2 = " 2 ( a L 2 - a ^ = " 0 5 ( 8 0 ) - ( 1 5 ) 2 ) = - 216.0 f t . k i p s W ( L 0 - 2 a ) 2 = nr 3" < 8 0 " 2 ( 1 5 ) ) 2 = 138.4 ft. k i p s 3 8 s 2 E x t e r i o r s t r i n g e r : M ,334 2 V 2 M l = 8 ( 4 0 ) 2 ( ( 4 0 ) " 1 5 ( 8 0 ) + ( 1 5 ) ) = 1 0 , 2 f t " M P S .334 ( 1 5(80) - (15) ) = -162.8 f t . k i p s M Q = ^ l 4 - (80 - 2 ( 1 5 ) ) 2 = 104.4 f t . k i p s L i v e l o a d moments . Suspended beam: I k k A/ 7Z- 100 *• I I X- d = 2J. f e e t (as c a l c u l a t e d i n A p p e n d i x I I ) x = 25 - 2.1 = 2 2 . 0 <=t. 2 100 M = 5n ~ 3 0 0 = 7 4 8 . 8 f t . k i p s max Portion of t o t a l load (as shown i n Appendix I I ) . I n t e r i o r s t r i n g e r : M = .65 M = . 6 5 ( 748 . 8 ) = 486.7 f t . kips LL max M_L = (for W = 398 p . l . f . ) = 124.3 f t . kips " T o t a l = 6 1 1 - 0 f t - k l p S s , 611.0 (12,000) = 3 5 8 .,3 req 1,900 3 S, _ approximately = 450 i n . holes 10 3/4" x 49 1/2"; A = 532.1 i n . 2 ; W = 126 p . l S = 4,390 i n . 3 > 4,308 i n . 3 — » O.K. E x t e r i o r s t r i n g e r : M = .37 M = .37(748.8) = 277.1 f t . kips XL max M^L = (for W = 298 p . l . f . ) = 93.1 f t . kips M = 370.2 f t . kips T o t a l c - 3 7 0 . 2 ( 1 2 , 0 0 0 ) _ 3 S r e q " 1,900 ~ 2 ' 3 3 8 i n * 3 ^holes a D r > r o x i m a t e l y = 400 i n . . 6 3/4 " x 49 1/2 " ; A = 334.1 i n . 2 ; W = 79 p . l . f S = 2 ,756.0 i n . 3 > 2,738 i n . 3 — > O.K. > 118 C h e c k f o r s h e a r s t r e s s e s ; V a c c o r d i n g to TC t a b l e s , L/Lt -o— "ztr V ( l ) V(2) V ( 3 ) V ( 4 ) i I : + w n 2 T j . a 2N " 2LT ( L 1 " a L 2 + 3 > + W n 2 _2. " "217 ( L 1 + a L 2 " a -> + W L 2 + W / T o ^ L i v e l o a d ^ = ^ = 1 2 . 5 f t . 4 A 3d = 3(A) = 12 f t . — * g o v e r n s /CL' \/f' . l b i 4 ; 14' i i. i X- ( O V 1 max _ 20(1A + 18) + 25(3A + 38) 50 = A8.8 k i p s I n t e r i o r s t r i n g e r : V L L = .65 (A8.8) = 31.72 k i p s V ( A ) D L = - ^ p ( 5 0 ) = 9.95 k i p s T o t a l = A 1 . 6 7 k i p s T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 110. 119 E x t e r i o r s t r i n g e r : V T T = .37(48.8) = 18.06 k i p s V ( 4 ) D L = ^ ? p ( 5 0 ) = 7.45 k i p s V T o t a l - 25.51 k i p s f v - 1 , 5 . . 4 : _ 1 0 ) = 1 1 4 p s i c 1 4 5 p 5 1 - ^ ° " R e a c t i o n s ( f o r e f f e c t o n c a n t i l e v e r e d b e a m ) . P o s i t i o n ( a ) : / / / y \ / P L J I—i I y- K . R - 1 0 < 1 0 > + 2 5 < 2 6 + 3 0 ) + 2 0 ( 4 6 + 5 0 ) - 68.4 k i p s c 50 P o s i t i o n (b) •A J A -> L - s o ' /- R = 20 (26 + 30) + 25(46 + 50) = 70.4 k i p s —> g o v e r n s 50 I n t e r i o r s t r i n g e r : R = 0.65(70.4) = 45.76 k i p s c E x t e r i o r s t r i n g e r : R = 0.37(70.4) = 26.05 k i p s c > 120 C a n t i l e v e r e d beam - p a r t B C . P o s i t i o n (a) X- i Ao 1 4o' 6 :<J -X R , + 2 5 < 3 0 + 3 A > + 2 0 < 5 n > = 5 4 . 8 k i p c c 50 1 M » 2 0 ( 1 1 ) + 5 4 . 8 ( 1 5 ) = 1 , 0 4 2 f t . k i p s max P o s i t i o n (b) * i 59 ' •f- '6 X. 4 G ' B £~o' X M = P a = 1 5 ( 7 0 . 4 ) = 1 ,056 f t . k i p s — * • g o v e r n i n g p o s i t i o n max I n t e r i o r s t r i n g e r : KLL = 0 . 6 5 ( 1 , 0 5 6 ) = - 6 8 6 . 4 f t . k i p s = ( f o r W == 428 p . l . f . ) = - 2 0 8 . 6 f t . k i p s M T o t a l = - 8 9 5 . 0 f t . k i p s s , 8 9 5 - ^ ^ ° ° ° ) - 5 , 6 5 2 i n . 3 r e q 1 ,900 3 S, , a p p r o x i m a t e l y = 700 i n . h o l e s 10 3 / 4 " x 6 0 " ; A = 645 i n . 2 ; W = 152 p . l . f . ; S = 6 , 4 5 0 i n . 3 > 6 , 3 5 2 i n . 3 — > - 0 . K . 121 E x t e r i o r s t r i n g e r : = 0 . 3 7 ( 1 , 0 5 6 ) = - 3 9 0 . 7 f t . k i p s M _ L = ( f o r w = 334 p . l . f . ) = - 1 6 2 . 8 f t . k i p s M _ o t a l = - 5 5 3 . 5 f t . k i p s s , 5 5 3 : 5 < " ^ 0 0 0 > - 3 , 4 9 6 i n . 3 r e q 1 ,900 3 S, , a p p r o x i m a t e l y = 650 i n . h o l e s . 8 3 / 4 " x 6 0 " ; A = 5 2 5 . 0 i n . 2 ; W = 124 p . l . f . ; S = 5 , 2 5 0 i n . 3 > 3 , 4 9 6 i n . 3 — * O . K . ( c h o s e n f o r same h e i g h t as i n t e r i o r s t r i n g e r ) Check f o r s h e a r s t r e s s e s : L i v e l o a d . V = R o f s u s p e n d e d beam = 7 0 . 4 k i p s J_JJ_I I n t e r i o r s t r i n g e r : V _ 4 5 . 7 6 k i p s V ( 3 ) _ L - = 1 6 . 4 k i p s V T o t a l " 6 2 " 1 6 k i p S f v = 1 - 5 ( 6 2 , 1 6 0 ) = 1 4 4 6 p s . < 1 4 5 p s . _ _ > 0 > K < E x t e r i o r s t r i n g e r : V T T = 2 6 . 0 5 k i p s V ( 3 ) _ L = • 3 1 2 ( 8 0 ) = 1 2 . 4 8 k i p s V T o t a l = 3 8 ' 5 3 k l p S 122 C a n t i l e v e r e d beam - p a r t A B . £/i:Jo' ' 'Y l/i --2?' A d _ 2 0 ( 1 6 + 20) - 25 (4 ) = x - ^ - d - 2 0 - 3 . 4 4 - 1 6 . 5 6 f t . M max _ 2 _• P e - 9 0 ( 1 6 . 5 6 ) 2 L L L "~ 40 = 5 1 7 . 0 2 f t . k i p s I n t e r i o r s t r i n g e r : = 0 . 6 5 ( 5 1 7 . 0 2 ) = 3 3 6 . 0 6 f t . k i p s M ( l ) DL M T o t a l 1 1 . 4 2 f t . k i p s 3 4 7 . 4 8 f t . k i p s S - 3 4 7 - 4 8 ^ - ° ° 0 ) = 2 , 1 9 4 i n . : r e q 1 ,900 3 S. . a p p r o x i m a t e l y = 300 i n . h o l e s 10 3 / 4 " x 37 1 / 2 " ; A = 4 0 3 . 1 i n . ; W = 9 5 . 2 p . l . f . ; ' O . K . S = 2 , 5 1 9 . 5 i n . 3 > 2 , 4 9 4 i n . 3 E x t e r i o r s t r i n g e r : M L L = - 3 7 ( 5 1 7 . 0 2 ) = 1 9 1 . 3 f t . k i p s M. T o t a l S = 2 0 0 . 4 ( 1 2 , 0 0 0 ) = 1 ,266 i n r e q 1 ,900 9 . 1 f t . k i p s 2 0 0 . 4 f t . k i p s 3 3 S, , a p p r o x i m a t e l y = 250 i n h o l e s 123 8 3 / 4 " x 37 1 / 2 " ; A = 3 2 8 . 1 I n . 2 ; W = 7 7 . 5 p . l . f . ; S = 2 , 0 5 0 . 8 i n . 3 > 1 ,266 i n . 3 —> O . K . ( c h o s e n f o r t h e same h e i g h t as i n t e r i o r s t r i n g e r ; w i d t h g i v e n by p a r t BC) C h e c k f o r s h e a r a t R , . A L / 4 = 10 f t . ; 3d = 9 f t . ^ g o v e r n s \ r . yy ••••• |*> ?-> l _ L i _ L L I •4C v = 20 (7 + 11) 25(27 + 3 1 1 = ^ ^ I n t e r i o r s t r i n g e r : V T T = . 6 5 ( 4 5 . 2 5 ) = 2 9 . 4 1 k i p s LtLi v ( 1 ) d l . -215g0) + (15)2) ^ } 1 ± J y v V 3 2 . 5 3 k i p s T o t a l f v = 1 , 5 . ( 3 2 ? 5 3 0 ) - = 121 p s i < 145 p s i — * 0 . K . 4 0 J . 1 E x t e r i o r s t r i n g e r : V T T = . 3 7 ( 4 5 . 2 5 ) = 1 6 . 7 4 k i p s v m = - 3 ( ( 4 0 ) 2 - 1 5 ( 8 0 ) + ( 1 5 ) 2 ) „ 2 > 3 A k . p s v ( i ) D L 2 ( 4 0 ) 1— V 1 9 . 0 8 k i p s T o t a l f v =  1 - ^ 9 , 0 8 0 ) = 8 7 p s i < 145 p s i - O . K . 1 124 R e a c t i o n s : L i v e l o a d . ?= 7<=>.<t £ 7 R . = 4 - •J9 \C a ~ is' X- P a 7 0 . 4 ( 1 5 ) , , / , . " 40 = - 2 - 1 4 k i p S P_ = L 1 to1 /T . \ 7 0 . 4 ( 5 5 ) 0 _ o , . ( L . + a) = — 7 7 7 ^ — = 9 6 . 8 k i p s 40 A': L* J — L so' / 20(49 + 45) , . , „ . . • C = — 5 0 = 3 7 . 6 k i p s _ 2 5 ( 4 0 + 36) + 1 0 ( 2 0 ) 3 7 . 6 ( 5 5 ) _ R_ - A Q + 40 . 1 U * , Z R 1 P ^ I n t e r i o r s t r i n g e r : R_ = . 6 5 ( 1 0 4 . 2 ) = 6 7 . 7 3 k i p s E x t e r i o r s t r i n g e r : R_ = . 3 7 ( 1 0 4 . 2 ) = 3 8 . 5 5 k i p s 3 Dead l o a d ( c a l c u l a t i o n a c c o r d i n g t o TC t a b l e s ) . g o v e r n s 3 T i m b e r C o n s t r u c t i o n : C a n a d i a n I n s t i t u t e o f T i m b e r C o n s t r u c t i o n , 1963 ( O t t a w a , C a n a d a ) , p . 1 1 0 . 125 R A = 2L7 ^ L l 2 " a L 2 + a ^ R B = l : ( L i + a ) ( L i + L 2 - a ) I n t e r i o r s t r i n g e r ,410 R A = 2 ( 4 0 ) [ ( 4 0 ) " 1 5 ( 8 0 ) + ( 1 5 ) ] = 3 ' 2 0 k i P s 41 0 \ = 2 ( t o ) ( 5 5 > ( 1 0 5 ) = 2 9 - 6 0 k i P s E x t e r i o r s t r i n g e r : . 3 1 0 2 ? R A = 2 ( 4 0 ) t ( 4 0 ) " 1 5 ( 8 0 ) + ( 1 5 ) ] = 2 , 4 2 k i P s 3 1 0 *B = 2 ( 4 0 ) ( 5 5 ) ( 1 0 5 ) = 2 2 , 3 8 k i p s T o t a l r e a c t i o n s a t " A " : - \ L = 2 ( 3 . 2 0 ) + 2 ( 2 . 4 2 ) - 2 . 1 4 = 9 . 1 0 k i p s T o t a l r e a c t i o n s a t " B " : Vtal = + I n t e r i o r s t r i n g e r : R T o t a l = 6 7 . 7 3 + 2 9 . 6 0 = 9 7 . 3 3 k i p s E x t e r i o r s t r i n g e r : ^ o t a l = 3 8 , 5 5 + 2 2 , 3 8 = 6 0 , 9 3 k i p s " V " s u p p o r t s ( s o l v e d as s h o r t c o l u m n s ) . I n t e r i o r s t r i n g e r : A = 9 7 , 3 3 0 2 r e q 1 ,400 7 0 i n - B a s e o f c o l u m n 1 2 " x 10 3 / 4 " = 129 i n . 2 > 70 i n . 2 — > O . K . E x t e r i o r s t r i n g e r : 6 0 , 9 3 0 . . . 2 A = ^—TrTTT = 44 i n . r e q 1 ,400 B a s e o f c o l u m n 1 2 " x 8 3 / 4 " = 105 i n . 2 > 44 i n . 2 — > O . K . > 126 CONCRETE- ABUTMENTS: B a c k f i l l s o i l c o n d i t i o n s same as c o n s i d e r e d i n A p p e n d i x I I . A b u t m e n t s c a l c u l a t e d f o r R _ L - R ^ a t A ( s e e a b o v e ) . B a s e o f a b u t m e n t s is s o l i d r o c k . 0 = 3 2 ° 3 0 ' ; w = 135 p . c . f . ; K = . 3 0 2 N o r t h A b u t m e n t -y- 6), S-.r ' 7.s- Yd* ; \ : 0 W v-$j7!y//;$yr,} / : 0 h T o t a l = 1 2 ' 0 + 1 - 7 = 1 3 - 7 f t - p m Icwh 2 _ . 3 0 2 ( . 1 3 5 ) ( 1 3 . 7 ) 2 = ^ 8 2 k ± p s M = 3 . 8 2 ^ ~ = 1 7 - 4 7 f t - k i P s s o i l 3 W e i g h t c o m p o n e n t s : w = 5 . 5 ( 1 2 . 0 ) ( . 1 5 ) = 9 . 9 0 k i p s w 2 = 2 . 0 ( 6 . 6 ) ( . 1 5 ) = 1 .98 k i p s *DI = = 9 . 1 0 W 3 w i d t h 1 6 . 0 w, T o t a l .57 k i p s = 1 2 . 4 5 k i p s H± = 9 . 9 ( 4 . 7 5 ) = 4 7 . 0 3 f t . k i p s M 2 = 1 . 9 8 ( 1 . 0 ) = 1 .98 f t . k i p s M 3 = . 5 7 ( 1 . 5 ) ,86 f t . k i p s "r o t a l "rot.- " M X t a l s o i l 3 2 . 4 0 1 2 . 4 5 4 9 . 8 7 f t . k i p s 4 9 . 8 7 - 1 7 . 4 7 = 3 2 . 4 f t . k i p s = 2 . 6 0 f t . > 2 . 3 3 f t . > O . K . " T o t a l ( x ) 1 127 S o u t h A b u t m e n t h = 13.0 + 1.7 = 14.7 f t . .302M35)(14.7) 2 = 4.40 k i p s 2 4.40(14.7) 0 1 „ ,„ . . M . , = Ti - 21.5£ f t . k i p s s o i l 3 W e i g h t c o m p o n e n t s : ŵ^ = 6(13) (.15) = 11.70 k i p s / l n . f t . w 2 = 2(7.6)(.15) = 2.28 k i p s / l n . f t . W, T o t a l .57 k i p s / l n . f t . 14.55 k i p s / l n . f t . M 2 = 1(2.28) = 2.28 f t . k i p s M 3 = 1.5(.57) = .86 f t . k i p s "T o t a l = 61.64 f t . k i p s MSj , - M _ _ J 1 = 61.64 - 21.58 = 40.06 f t . k i p s C o t a l s o i l 40.06 14.55 = 2.75 f t . > 2.67' O . K . 128 B I L L OF MAIN MATERIAL AND PRELIMINARY COST ESTIMATE R u n n i n g d e c k , t i e s , w h e e l g u a r d and g u a r d r a i l (From A p p e n d i x I I ) ll'tl9 (162 f t . ) = $ 1 0 , 4 1 0 S t r i n g e r s : C a n t i l e v e r e d beams A r e a o f beams i n p r o f i l e (37 1 /2" x 2 1 ' ) + 1/2 (37 1 /2" + 6 0 ' ) 20 + 1/2 ( 6 0 ' + 49 1 /2") 15 = 2 1 5 . 3 1 f t . 2 I n t e r i o r s t r i n g e r s 4 (10 3 / 4 " ) 2 1 . 5 . 3 1 f t . 2 = 772 c u . f t . ? E x t e r i o r s t r i n g e r s 4 (8 3 / 4 " ) 2 1 5 . 3 1 f t . = 628 c u . f t . Suspended beams I n t e r i o r s t r i n g e r s 2 (10 3 / 4 " x 49 1 /2" x 5 0 ' ) = 369 c u . f t . E x t e r i o r s t r i n g e r s 2 (6 3 / 4 " x 49 1 /2" x 5 0 ' ) = 232 c u . f t . " V " s u p p o r t s A t B A r e a i n p r o f i l e 1/2 ( 1 2 " + 30") 9 . 7 5 = 1 7 . 1 f t . 2 2 I n t e r i o r s u p p o r t 2 (10 3 / 4 " x - 1 7 . 1 f t . ) = 30 c u . f t . E x t e r i o r s u p p o r t 2 (8 3 / 4 " x 1 7 . 1 f t . 2 ) = 2 5 c u . f t . A t E A r e a i n p r o f i l e 1/2 ( 1 2 " + 40") 1 4 . 7 5 ' = 3 1 . 9 6 f t . 2 I n t e r i o r s u p p o r t 2 (10 3 / 4 " x 3 1 . 9 6 f t . 2 ) = 57 c u . f t . 2 E x t e r i o r s u p p o r t 2 (8 3 / 4 " x 3 1 . 9 6 f t . ) = 47 c u . f t . 129 D i a p h r a g m s 24 (6 3 / 4 " x 3 3 " x 5 ' ) = 186 c u . f t . 9 (6 3 / 4 " x 4 5 " x 5 ' ) = 95 c u . f t . 2 (6 3 / 4 " x 54" x 5 ' ) = 25 c u . f t . T o t a l = 2 , 4 6 6 c u . f t . (? $27 = $ 6 6 , 5 8 2 C o n c r e t e A b u t m e n t s N o r t h A b u t m e n t : ZJJ ( [ 4 . 5 x 12] + [ 1 . 5 x 6 . 6 ] ) 16 = 3 7 . 9 c u . y d . S o u t h A b u t m e n t : — ( [ 5 . 5 x 13] + [ 1 . 5 x 7 . 6 ] ) 16 = 4 9 . 1 c u . y d . F o u n d a t i o n s u n d e r " V " s u p p o r t s _ 1 27 ( 1 . 5 x 1.0 x 16) 2 = 1.8 c u . y d . T o t a l = 8 8 . 8 c u . y d . @ $250 = $ 2 2 , 2 0 0 T o t a l f i l l 726 CCY = 1 ,075 LCY @ $ 2 . 2 0 = $ 2 , 3 6 5 T o t a l f o r c a n t i l e v e r e d b r i d g e = $ 1 0 1 , 5 5 7 F i g u r e 7.1 - Cant ( l e v e r e d beam h i < ^ ; . 1 e 1 I n . n 9ft f t - .

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