UBC Theses and Dissertations

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UBC Theses and Dissertations

Tilt up concrete wall panels Weiler, Gerald Joseph 1980

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T I L T UP CONCRETE WALL PANELS by GERALD J O S E P H WEILER B . S c . ( H o n o r s ) , Q u e e n ' s U n i v e r s i t y a t K i n g s t o n , O n t a r i o , 1970 A t h e s i s s u b m i t t e d i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r t h e d e g r e e o f M a s t e r o f A p p l i e d Sc ience i n The F a c u l t y o f G r a d u a t e S t u d i e s D e p a r t m e n t o f C i v i l E n g i n e e r i n g We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d 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 March, 1980 g p G e r a l d J o s e p h W e i l e r , 1980 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make i t freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. G. W e i l e r Department nf C i v i l E n g i n e e r i n g The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date A p r i l 28, 1980 i i . ABSTRACT The d e s i g n o f t i l t up c o n c r e t e w a l l p a n e l s was s t u d i e d i n t h i s p a p e r . D e s i g n c h a r t s w e r e d e v e l o p e d t o a s s i s t t h e e n g i n e e r i n t h e a n a l y s i s o f p a n e l s u n d e r l o a d . C o m p u t e r s i m u l a t i o n o f t h e c o n c r e t e s e c t i o n was u s e d t o o b t a i n t h e c h a r t d a t a . A c o m p u t e r s t u d y o f t h e e f f e c t o f a number o f p a r a m e t e r s on t h e l o a d c a r r y i n g c a p a c i t y o f w a l l p a n e l s was m a d e . L o a d i n g , s e c t i o n p r o p e r t i e s and s u p p o r t c o n d i t i o n s w e r e v a r i e d i n i s o l a t i o n i n an a t t e m p t t o o b t a i n g e n e r a l t r e n d s o f how e a c h i n f l u e n c e s t h e s t r e n g t h c h a r a c t e r i s t i c of- a c o n c r e t e w a l l p a n e l . A r ecommended d e s i g n p r o c e d u r e h a s b e e n i n c l u d e d w h i c h u t i l i z e s t h e c h a r t s d e v e l o p e d . i i i . T I L T UP CONCRETE WALL PANELS T A B L E OF CONTENTS P a g e A b s t r a c t i 1 . INTRODUCTION 1 2 . THE A N A L Y T I C A L MODEL 2 2 . 1 G e n e r a l C o n s i d e r a t i o n s 2 . 2 S e c t i o n S t i f f n e s s 2 . 3 W a l l P a n e l A n a l y s i s 2 . 4 L o a d C a p a c i t y C h a r t s 2 . 5 C o n s t a n t S t i f f n e s s M e t h o d 3 . D E S C R I P T I O N OF I N V E S T I G A T I O N S 24 3 . 1 G e n e r a l 3 . 2 L o a d i n g 3 . 3 End E c c e n t r i c i t y 3 . 4 C o n c r e t e P r o p e r t i e s 3 . 5 R e i n f o r c i n g S t e e l 3 . 6 C a p a c i t y R e d u c t i o n F a c t o r 3 . 7 S e c t i o n T h i c k n e s s 3 . 8 P a n e l H e i g h t 3 . 9 End F i x i t y 4 . DESIGN METHOD 45 4 . 1 D e s c r i p t i o n o f D e s i g n P r o c e d u r e 4 . 2 L o a d C a p a c i t y C h a r t s 4 . 3 L o a d i n g C o n d i t i o n s 4 . 4 M a t e r i a l P r o p e r t i e s 4 . 5 E f f e c t i v e P a n e l H e i g h t 4 . 6 E f f e c t o f C r e e p & I n i t i a l D e f l e c t i o n s 4 . 7 C a p a c i t y R e d u c t i o n F a c t o r s 4 . 8 I n - P l a n e S h e a r 4 . 9 P a n e l s w i t h O p e n i n g s 4 . 1 0 I s o l a t e d F o o t i n g s TABLE OF CONTENTS - C o n t ' d . 5 . . COMPARISON OF RESULTS 5 . 1 E x p e r i m e n t a l V e r i f i c a t i o n o f C o m p u t e r P r o g r a m 5 . 2 PCA D e s i g n A i d 5 . 3 A C I / C S A R e c o m m e n d a t i o n s 6 . PROPOSED CHANGES TO A C I / C S A CODES 7 . L I S T OF REFERENCES A P P E N D I X A - N o t a t i o n A P P E N D I X B - L o a d C a p a c i t y C h a r t s A x i a l L o a d / U n m a g n i f i e d Moment A P P E N D I X C - A v e r a g e S t i f f n e s s C h a r t s A P P E N D I X D - L o a d C a p a c i t y C h a r t s A x i a l L o a d / L a t e r a l L o a d A P P E N D I X E - D e s i g n E x a m p l e s INTRODUCTION T i l t up c o n c r e t e w a l l p a n e l s h a v e b e e n e m p l o y e d i n a v a r i e t y o f b u i l d i n g t y p e s o v e r t h e p a s t s e v e r a l y e a r s . The r e c e n t i n t r o d u c t i o n o f a number o f r e f i n e m e n t s i n l i f t i n g h a r d w a r e and t e c h n i q u e s , c o m b i n e d w i t h i m p r o v e m e n t s ' i n a r c h i t e c t u r a l f i n i s h e s h a v e a l l o w e d t h i s t y p e o f c o n s t r u c t i o n t o d i s p l a c e many o f t h e more c o n v e n t i o n a l a p p r o a c h e s t o b u i l d i n g s y s t e m s . The mos t common a p p l i c a t i o n h a s b e e n i n l o a d b e a r i n g w a l l s f o r w a r e h o u s i n g and l i g h t i n d u s t r i a l s t r u c t u r e s . The s t a n d a r d 140 mm p a n e l c a n be u s e d f o r w a l l s i n e x c e s s o f 8 m e t e r s i n h e i g h t s u p p o r t i n g w i n d l o a d s , r o o f l o a d s and i n - p l a n e s h e a r f o r c e s . B e c a u s e l a t e r a l d e f l e c t i o n s due t o w i n d l o a d i n g a r e f r e q u e n t l y l a r g e , e f f e c t s o f s l e n d e r n e s s . m u s t be c o n s i d e r e d . D e s i g n a i d s t h a t a r e now a v a i l a b l e h a v e b e e n i n a d e q u a t e f o r t h e r a n g e o f d e s i g n c o n d i t i o n s e n c o u n t e r e d and p r o v i d e l i t t l e g u i d a n c e f o r s i t u a t i o n s f a l l i n g o u t s i d e t h e i r s c o p e . T h i s p a p e r d e a l s p r i m a r i l y w i t h s t a b i l i t y c o n s i d e r a t i o n s o f l o a d b e a r i n g p a n e l s s p a n n i n g v e r t i c a l l y b e t w e e n l a t e r a l s u p p o r t s . I t i s b a s e d on c o m p u t e r s i m u l a t i o n o f t h e c o n c r e t e s e c t i o n u n d e r l o a d and p r o v i d e s a r a t i o n a l b a s i s on w h i c h t o s e l e c t t h e m o s t s u i t a b l e d e s i g n . E v e r y a t t e m p t was made t o a v o i d t h e u s e o f e m p i r i c a l f o r m u l a s w h e r e e x t r a p o l a t i o n f r e q u e n t l y l e a d s t o e r r o r . 2 . 2 . THE A N A L Y T I C A L MODEL 2 . 1 G e n e r a l C o n s i d e r a t i o n s In t h e d e v e l o p m e n t o f l o a d c a p a c i t y c h a r t s f o r c o n c r e t e w a l l p a n e l s , i t i s i m p o r t a n t t o h a v e an a c c u r a t e a n a l y t i c a l m o d e l o f t h e c o n c r e t e s e c t i o n . Once c u r v a t u r e s a r e o b t a i n e d f o r a g i v e n c o m b i n a t i o n o f a x i a l c o m p r e s s i o n a n d b e n d i n g momen t , t h e d e f l e c t e d s h a p e o f a p a n e l u n d e r l o a d c a n be c o m p u t e d . A x i a l l o a d i s a p p l i e d t o t h e t o p o f t h e p a n e l a t some e c c e n t r i c i t y , i n c o m b i n a t i o n w i t h a u n i f o r m l a t e r a l l o a d . As t h e a x i a l l o a d i s i n c r e a s e d , d e f l e c t i o n s and moments a l s o i n c r e a s e u n t i l no a d d i t i o n a l l o a d c a n be s u s t a i n e d . The d e s i g n c h a r t s a r e b a s e d on t h e p e a k v a l u e o f a x i a l l o a d and t h e c o r r e s p o n d i n g maximum a p p l i e d moment . 2 . 2 S e c t i o n S t i f f n e s s M o m e n t - c u r v a t u r e r e l a t i o n s h i p s f o r t h e c o n c r e t e s e c t i o n a r e o b t a i n e d by n u m e r i c a l i n t e g r a t i o n o f t h e s t r e s s d i s t r i b u t i o n f o r a g i v e n s t r a i n c o n d i t i o n . The f o l l o w i n g a s s u m p t i o n s h a v e b e e n m a d e : a . C o n c r e t e h a s a w e l l d e f i n e d s t r e s s s t r a i n c u r v e w h i c h a p p l i e s t o b o t h a x i a l - and f l e x u r a l l o a d , s u c h a s t h e one shown i n F i g u r e 2 . 1 . b . R e i n f o r c i n g s t e e l h a s a b i l i n e a r s t r e s s s t r a i n c u r v e as a l s o shown i n F i g u r e 2 . 1 . c . S e c t i o n s o r i g i n a l l y p l a n e and n o r m a l t o t h e n e u t r a l s u r f a c e r e m a i n s o . d . P e r f e c t b o n d e x i s t s b e t w e e n s t e e l and c o n c r e t e . FIGURE 21 STRESS -STRA IN PROPERTIES REINFORCING S T E E L Es = 200000 MPa f s = - fy for e s <~6y f s = E s e s f o r - e y < e s < e y f s = fy for H > ey 4 . F o l l o w i n g t h e a s s u m p t i o n s t h a t p l a n e s e c t i o n s r e m a i n p l a n e , t h e s t r a i n d i s t r i b u t i o n c a n be d e f i n e d i n t e r m s o f two p a r a m e t e r s ; c u r v a t u r e and p o s i t i o n o f t h e n e u t r a l a x i s . C o r r e s p o n d i n g t o e a c h s t r a i n d i s t r i b u t i o n , t h e r e i s an e q u i l i b r i u m a x i a l l o a d and moment a s shown i n F i g u r e 2 . 2 . By c o n s i d e r i n g a g r e a t many s u c h s t r a i n d i s t r i b u t i o n s , a m o m e n t - c u r v a t u r e r e l a t i o n s h i p f o r a g i v e n a x i a l l o a d c a n be o b t a i n e d by i n t e r p o l a t i o n b e t w e e n d a t a p o i n t s . The t e c h n i q u e i n v o l v e s a s y s t e m a t i c g e n e r a t i o n o f d a t a p o i n t s c o v e r i n g t h e a p p l i c a b l e r a n g e o f s t r a i n c o n f i g u r a t i o n s . F i r s t o f a l l , t h e c u r v a t u r e i s h e l d c o n s t a n t w h i l e t h e p o s i t i o n o f t h e n e u t r a l a x i s i s v a r i e d i n s m a l l i n c r e m e n t s f r o m a p p r o x i m a t e l y 5% o f t h e d e p t h t o t w i c e t h e d e p t h o f t h e s e c t i o n . A t e a c h i n c r e m e n t , t h e e q u i l i b r i u m a x i a l l o a d and moment a r e c o m p u t e d . N o t e t h a t t h e moment i s a l w a y s c a l c u l a t e d w i t h r e s p e c t t o t h e c e n t r e l i n e o f t h e s e c t i o n . T h i s i s an a r b i t r a r y d e c i s i o n , b u t one t h a t d i c t a t e s t h a t a l l e x t e r n a l l o a d s a r e a p p l i e d a t an e c c e n t r i c i t y m e a s u r e d w i t h r e s p e c t t o t h i s c e n t r e l i n e . N e x t , t h e c u r v a t u r e i s v a r i e d o v e r a r a n g e t h a t w i l l e n c o m p a s s t h e e n t i r e i n t e r a c t i o n d i a g r a m . F o r e a c h v a l u e o f c u r v a t u r e , t h e n e u t r a l a x i s d e p t h s a r e v a r i e d and a n o t h e r l i n e o f c o n s t a n t c u r v a t u r e i s o b t a i n e d . A c o m p u t e r p l o t o f t y p i c a l c u r v e s i s shown i n F i g u r e 2 . 3 . Once t h e l o a d moment d a t a h a s b e e n g e n e r a t e d f o r a d e s i r e d s e c t i o n , i t i s a s i m p l e m a t t e r t o f i n d t h e m o m e n t - c u r v a t u r e r e l a t i o n s . A t a n y s p e c i f i e d l e v e l o f a x i a l c o m p r e s s i o n , t h e moment a t e a c h c o n s t a n t c u r v a t u r e l i n e i s o b t a i n e d b y d i r e c t i n t e r p o l a t i o n . F i g u r e 2 . 4 i s a c o m p u t e r p l o t o f s e v e r a l m o m e n t - c u r v a t u r e l i n e s f r o m t h e d a t a o f F i g u r e 2 . 3 . F I G U R E 2.2 DEVELOPMENT OF CONCRETE SECTION PROPERTIES SECTION Strain Parameters : STRAIN e c s y"cd Concrete Stress = f c Steel Stress = f s Force in concrete Moment w.tt. top Force in steel Total axial force es, =y"(cd-d|) FORCES eS2=y"(cd-d2) From stress - strain relations C - f b f c d z • C z = j b f c z d z z * C z / C Fs= ( f s - f c ) A s P= C •+ F S 1 + F s z Total moment w.rt. centerline axis: Moment M « C ( h / 2 - z ) + F s , ( h / 2 - d , ) + F S 2 ( h / 2 - d 2 ) FIGURE 2.3 SECTION INTERACTION PROPERTIES o g-| h - 5 . 5 " b =12" f c = 4000 PSI f y= 60000 PSI A s * . 3 1 IN 2 d .= 2.75" o o t o . o C M . o 03. IN 7 . «8-l .—I X F I G U R E 2 . 4 MOMENT CURVATURE RELATIONS P= I 40 p=||2 O.D 0.04 0.08 0.12 T T 0.16 0.2 0.24 CURVATURE ( X l O " 2 ) 8 . The d e s i r e d c u r v a t u r e f o r a s p e c i f i e d c o m b i n a t i o n o f a x i a l l o a d a n d moment i s a v a i l a b l e by i n t e r p o l a t i o n on t h e momen t -c u r v a t u r e l i n e s . M o d e r n d i g i t a l c o m p u t e r s c a n r e a d i l y g e n e r a t e a n d s t o r e t h i s i n f o r m a t i o n f o r u s e i n d e f l e c t i o n c a l c u l a t i o n s o f a w a l l p a n e l u n d e r l o a d . 2 . 3 W a l l P a n e l A n a l y s i s The p u r p o s e o f t h e a n a l y s i s i s t o o b t a i n a r e l a t i o n s h i p b e t w e e n a p p l i e d l o a d s and maximum b e n d i n g moment i n t h e w a l l p a n e l . I t i s t h e m a g n i t u d e o f t h e maximum moment f o r a g i v e n a x i a l / l a t e r a l l o a d c o m b i n a t i o n t h a t i s o f i n t e r e s t , s i n c e i t a l l o w s us t o a s s e s s t h e a v a i l a b l e c a p a c i t y r e m a i n i n g . The l o a d i n g c o n f i g u r a t i o n a d o p t e d , a s shown i n F i g u r e 2 . 5 , c o n s i s t s o f a one d i m e n s i o n a l beam ( u n i a x i a l b e n d i n g ) p i n n e d a t e a c h end w i t h a u n i f o r m l a t e r a l l o a d a l o n g t h e e n t i r e l e n g t h a n d a n e c c e n t r i c a x i a l l o a d a t one ( u p p e r ) e n d . F rom t h i s m o d e l , i t i s p o s s i b l e t o d e d u c e t h e p e r f o r m a n c e o f many o t h e r d e s i g n c o n d i t i o n s . A p o s i t i v e e c c e n t r i c i t y i s d e f i n e d a s t h a t t e n d i n g t o i n c r e a s e t h e e f f e c t o f l a t e r a l l o a d and n e g a t i v e e c c e n t r i -c i t y a s t e n d i n g t o d e c r e a s e t h e l a t e r a l l o a d e f f e c t . The maximum b e n d i n g moment d o e s n o t n e c e s s a r i l y o c c u r a t m i d -h e i g h t n o r d o e s i t n e c e s s a r i l y c o i n c i d e w i t h t h e p o i n t o f maximum l a t e r a l d e f l e c t i o n . As p r e v i o u s l y m e n t i o n e d , o n l y t h e m a g n i t u d e o f t h e maximum moment i s d e s i r e d . The p r o c e d u r e u s e d t o o b t a i n l o a d moment r e l a t i o n s f o r a w a l l p a n e l i s shown p i c t o r i a l l y i n F i g u r e s 2 . 6 t h r o u g h 2 . 9 . I t i s e s s e n t i a l l y a Newmark t y p e m e t h o d i n w h i c h b o u n d a r y c o n d i t i o n s a r e a s s u m e d a t one end and t h e e q u i l i b r i u m FIGURE 2.5 CONCRETE WALL PANEL MODEL DEFLECTED SHAPE BENDING MOMENT 10 FIGURE 2.6 COLUMN DEFLECTION CURVE W P i + i i i - l Ax Moment •- M Deflection = y Slope y ' = d y / d x Curvature y " = d 2 y / d x 2 yi = y i - i - y ' i - i A x + y / ' 2 ( A x ) 2 y ' i s y ' l - i + y V i A x Mj= yi P-t- M w i y"i= f ( M j ) from moment-curvature relations M wi ' Moment due to lateral load FIGURE 2.7 FAMILY OF C.D.C.'s P a Constant W = Constant Initial slope at base is incremented FIGURE 2.8 E C C E N T R I C I T Y M O M E N T R E L A T I O N S P l < P 2 < P 3 < P4 < P5 MAXIMUM M O M E N T M FIGURE 2.9 L O A D M O M E N T R E L A T I O N S MAXIMUM M O M E N T M 12 . e q u a t i o n i s i n t e g r a t e d i n s e g m e n t s a l o n g t h e member by m a k i n g some a s s u m p t i o n on t h e v a r i a t i o n o f c u r v a t u r e w i t h i n t h e s e g m e n t . T h u s , t h e i n t e r n a l f o r c e s a r e c o m p u t e d f o r v a r i o u s d e f l e c t e d s h a p e s a n d b o u n d a r y c o n d i t i o n s . I n F i g u r e 2 . 6 , t h e s l o p e o f t h e C . D . C . ( c o l u m n d e f l e c t i o n c u r v e ) a t t h e b o t t o m i s a s s u m e d and t h e r e s u l t i n g d e f l e c t e d s h a p e c o m p u t e d a t d i s t i n c t n o d e s a l o n g t h e h e i g h t . The r e s u l t i n g d e f l e c t i o n a t t h e t o p i s t h e e c c e n t r i c i t y r e q u i r e d f o r e q u i l i b r i u m u n d e r t h a t c o m b i n a t i o n o f l a t e r a l a n d a x i a l l o a d . The s t a r t i n g s l o p e i s i n c r e m e n t e d a s shown i n F i g u r e 2 . 7 , u n t i l t h e end e c c e n t r i c i t y d e c r e a s e s b e l o w some s p e c i f i e d m in imum v a l u e . I n mos t c a s e s , t h e e n d e c c e n t r i c i t y w i l l a t f i r s t i n c r e a s e a s t h e b o t t o m s l o p e i s i n c r e a s e d and t h e n d e c r e a s e t o e v e n t u a l l y become n e g a t i v e . F o r a s e r i e s o f f i x e d a x i a l l o a d s , we o b t a i n e c c e n t r i c i t y -moment r e l a t i o n s a s i n F i g u r e 2 . 8 . A t a n y d e s i r e d end e c c e n t r i c i t y , t h e a x i a l l o a d P and c o r r e s p o n d i n g maximum moment M a r e f o u n d by i n t e r p o l a t i o n b e t w e e n t h e d a t a p o i n t s . The r e s u l t i s a l o a d moment c u r v e s i m i l a r t o t h a t shown i n F i g u r e 2 . 9 . N o t e t h a t t h e a x i a l l o a d c a p a c i t y i s s o m e t i m e s r e a c h e d p r i o r t o a c t u a l m a t e r i a l f a i l u r e and t h e moment t h a t o c c u r s a t t h i s p o i n t i s somewhat l e s s t h a n u l t i m a t e . The a c t u a l m a g n i t u d e o f t h i s moment a t o r n e a r t h e p e a k a x i a l l o a d c a p a c i t y i s v e r y s e n s i t i v e t o s l i g h t v a r i a t i o n s i n t h e l o a d i n g c o n d i t i o n s and m a t e r i a l p r o p e r t i e s . 13 . The maximum a p p l i e d moment - t h a t i s t h e moment due t o a l l a p p l i e d l o a d i n g s , b u t e x c l u d i n g P - d e l t a m a g n i f i c a t i o n s -i s w e l l d e f i n e d a t p e a k a x i a l l o a d and i s t h e b a s i s on w h i c h t h e l o a d c a p a c i t y c h a r t s w e r e d e v e l o p e d . 2 . 4 L o a d C a p a c i t y C h a r t s The m a i n c o n s i d e r a t i o n s i n t h e d e v e l o p m e n t o f l o a d c a p a c i t y c h a r t s ( s e e A p p e n d i x B) a r e t h a t t h e y s h o u l d h a v e t h e f o l l o w i n g p r o p e r t i e s : a . Be s i m p l e t o u s e a n d a l l o w a c o m p a r i s o n o f a l t e r n a t e d e s i g n s t o be p e r f o r m e d q u i c k l y and e a s i l y . b . A c c u r a t e l y r e p r e s e n t t h e p e r f o r m a n c e o f w a l l p a n e l s w i t h a m in imum number o f d e s i g n c o n s t r a i n t s . c . C o v e r a b r o a d r a n g e o f d e s i g n c o n f i g u r a t i o n s t o m i n i m i z e t h e amoun t o f i n t e r p o l a t i o n o r e x t r a p o l a t i o n . d . T a k e a d e q u a t e a c c o u n t o f m a t e r i a l v a r i a b i l i t y a n d p o o r w o r k m a n s h i p . The l a y o u t o f t h e c h a r t s was b a s e d on c o m p u t a t i o n s f o r t h e a x i a l l o a d c a p a c i t y o f a p a n e l w i t h a s p e c i f i c c o n c r e t e s e c t i o n and f i x e d l e n g t h . The p e a k v a l u e o f l o a d , a p p l i e d a t a p o s i t i v e e n d e c c e n t r i c i t y , was f o u n d f o r v a r i o u s l e v e l s o f l a t e r a l w i n d p r e s s u r e . F i g u r e 2 . 1 0 shows t h e l o a d moment c u r v e s f o r a p a n e l s u b j e c t t o s e v e r a l l e v e l s o f l a t e r a l l o a d . The c u r v e s m a r k e d Wo, , e t c . show t h e v a l u e o f t h e maximum m a g n i f i e d moment v e r s u s a x i a l l o a d f o r e a c h l a t e r a l l o a d W. The p o i n t s m a r k e d B i n d i c a t e t h e l i m i t o f u s e f u l c a p a c i t y a f t e r w h i c h t h e d e s c e n d i n g l o a d p a t h i s u n s t a b l e . I n c u r v e s a n d , m a t e r i a l f a i l u r e o c c u r r e d a t p o i n t s A b e f o r e i n s t a b i l i t y 0_ < MAX MOMENT M FIGURE 2.11 LOAD MOMENT CURVES MAX MOMENT M 15 . FIGURE 2.12 DOUBLE END ECCENTRICITY DEFLECTED SHAPE BENDING MOMENT 16 . was r e a c h e d . The d o t t e d l i n e s C C . . . C r e p r e s e n t s t h e maximum u n m a g n i f i e d moment c o r r e s p o n d i n g t o t h e p o i n t s A o r B . The d e s i g n e r e n t e r s t h e c h a r t w i t h t h e a x i a l l o a d a n d t h e maximum u n m a g n i f i e d momen t ; i f t h i s p o i n t l i e s t o t h e l e f t o f C C . . . C , t h e d e s i g n i s s a f e . O t h e r d e s i g n c u r v e s f o r t h e same p a n e l b u t d i f f e r e n t l e n g t h s a r e shown i n F i g u r e 2 . 1 1 . An end e c c e n t r i c i t y o f o n e - h a l f t h e p a n e l t h i c k n e s s was a d o p t e d a s a c u t o f f p o i n t i n t h e p r e p a r a t i o n o f t h e c h a r t s . T h i s i s c o n s i d e r e d t o be a m i n i m u m , p a r t i c u l a r l y when a x i a l l o a d i s l a r g e and l a t e r a l l o a d moment i s s m a l l . I n mos t i n s t a n c e s , h o w e v e r , t h e l a t e r a l l o a d moment a t o r n e a r m i d -h e i g h t o f t h e p a n e l i s g r e a t e r t h a n t h e e n d moment a n d t h i s r e s t r i c t i o n i s o f no c o n s e q u e n c e . F i g u r e 2 . 1 2 shows t h e d e f l e c t e d s h a p e s a n d moment d i a g r a m o f a p a n e l w i t h e q u a l e c c e n t r i c i t i e s a t e a c h e n d . The end c o n d i t i o n s a r e s u c h t h a t t h e v e r t i c a l l o a d and t h e maximum u n m a g n i f i e d moment a r e t h e same a s f o r t h e s i n g l e e c c e n t r i -c i t y c a s e i n F i g u r e 2 . 5 . I t w i l l be s e e n t h a t t h e r e i s a s m a l l d i f f e r e n c e i n t h e maximum m a g n i f i e d m o m e n t s ; t h e m a g n i f i c a t i o n b e i n g s l i g h t l y l e s s i n t h e c a s e o f s i n g l e e c c e n t r i c i t y . I n F i g u r e 2 . 1 3 , t h e c u r v e A i s o b t a i n e d on t h e b a s i s o f s i n g l e e c c e n t r i c i t y , w h i l e c u r v e B i s b a s e d on d o u b l e e c c e n t r i c i t y . C u r v e C i s t h e same a s c u r v e A w i t h t h e c a p a c i t y r e d u c t i o n f a c t o r i n c l u d e d . I t was f e l t t h a t , i n p r a c t i c e , s i n g l e e c c e n t r i c i t y i s u s u a l l y t h e c a s e and t h e c u r v e s f o r t h e c h a r t s w e r e o b t a i n e d on t h a t b a s i s . T h a t i s t o s a y , t h e v e r t i c a l l o a d a p p l i e d a t a n e c c e n t r i c i t y a t t h e t o p e q u a l t o t h e h a l f t h i c k n e s s o f t h e p a n e l i s c o m b i n e d w i t h t h e l a t e r a l l o a d w h i c h w o u l d c a u s e f a i l u r e . 17 . FIGURE 2.13 LOAD MOMENT CURVES 0 M U M u MAX MOMENT M 18 . A l l t h e d e s i g n c h a r t s o f A p p e n d i x B i n c l u d e t h e c a p a c i t y r e d u c t i o n f a c t o r as r ecommended by A C I / C S A c o d e s . T h i s means t h a t t h e c o m p u t e d a x i a l l o a d and moment c a p a c i t i e s a r e r e d u c e d by 0 . 9 t o 0 . 7 d e p e n d i n g on t h e l e v e l o f a p p l i e d a x i a l l o a d . I n a d d i t i o n , t h e c a l c u l a t e d s e c t i o n s t i f f n e s s i s r e d u c e d by t h e same c a p a c i t y r e d u c t i o n f a c t o r . T h i s h a s t h e e f f e c t o f i n c r e a s i n g d e f l e c t i o n s and l o w e r i n g l o a d c a p a c i t i e s ; i t i s , h o w e v e r , c o n s i s t e n t w i t h t h e r e q u i r e m e n t s of the ACI/CSA codes . Curve C of F i g u r e 2.13 i l l u s t r a t e s the ex ten t to which l oad c a p a c i t y i s decreased by a p p l i c a t i o n of the c a p a c i t y r e d u c t i o n f a c t o r . Th i s i s d i s c u s s e d i n g rea te r d e t a i l i n S e c t i o n 3 . 6 . 2 . 5 C o n s t a n t S t i f f n e s s M e t h o d T r a d i t i o n a l l y , h a n d c a l c u l a t i o n s f o r d e f l e c t i o n a n d s t a b i l i t y o f b e a m - c o l u m n s a s s u m e d a c o n s t a n t v a l u e f o r t h e s e c t i o n s t i f f n e s s E I a l o n g t h e member l e n g t h , r e g a r d l e s s o f l o a d i n g o r d e g r e e o f c u r v a t u r e . A l t h o u g h i t i s a p p a r e n t t h a t a c o n s t a n t E I f o r c o n c r e t e c o v e r i n g a l l c o n d i t i o n s i s n o t c o r r e c t , i t i s p o s s i b l e t o o b t a i n r e a s o n a b l y a c c u r a t e r e s u l t s by a s s u m i n g an a v e r a g e o r e f f e c t i v e v a l u e f o r t h i s s t i f f n e s s a l o n g t h e l e n g t h o f t h e member a t a f i x e d l e v e l o f a x i a l l o a d and maximum b e n d i n g momen t . A good e s t i m a t e o f t h i s d e s i r e d v a l u e o f a v e r a g e s t i f f n e s s E I i s t h e s e c a n t m o d u l u s t o t h e c u r v a t u r e - m o m e n t c u r v e , a v g o r i n e f f e c t , t h e i n v e r s e o f t h e s l o p e o f a l i n e c o n n e c t i n g a n y p o i n t on t h e c u r v e t o t h e o r i g i n ( s e e F i g u r e 2 . 1 4 ) . T y p i c a l v a l u e s o f E I h a v e b e e n c o m p u t e d and p l o t t e d i n F i g u r e 2 . 1 5 f o r s e l e c t e d a x i a l c o m p r e s s i o n s . A l s o s e e A p p e n d i x C . FIGURE 2.14 MOMENT CURVATURE LINES P= IOk p=5 k P= 2 k P= 0 k 20 . The p r o c e d u r e u s e d t o c o m p u t e t h e maximum moment due t o a p p l i e d l o a d i n g i s a s f o l l o w s : a . S e t t h e e f f e c t i v e h e i g h t o f p a n e l ( u s u a l l y t h e c l e a r d i s t a n c e b e t w e e n s u p p o r t s ) . b . Compu te a x i a l l o a d a t t h e c r i t i c a l s e c t i o n ( u s u a l l y m i d - h e i g h t ) . c . Compu te t h e maximum moment Mo due t o a l l a p p l i e d l o a d i n g s i n c l u d i n g w i n d l o a d , end e c c e n t r i c i t y and i n i t i a l o u t o f s t r a i g h t n e s s ( s e e F i g u r e s 2 . 1 6 t h r o u g h 2 . 1 8 ) . d . E s t i m a t e t h e f i n a l t o t a l momen t ; i . e . i n i t i a l moment p l u s P - d e l t a e f f e c t s . e . F rom t h e e f f e c t i v e s t i f f n e s s c h a r t , f i n d E I f o r t h e a v g g i v e n a x i a l l o a d and maximum moment . f . Compute c r i t i c a l l o a d P ' a n d m a g n i f i c a t i o n f a c t o r ( s e e F i g u r e 2 . 1 9 ) . g . Compu te t o t a l moment M^ = M^ h . C h e c k E I and r e c o m p u t e M i f n e c e s s a r y . a v g t The e f f e c t o f s e l f - w e i g h t i s a p p r o x i m a t e d by a s s u m i n g t h a t o n e - h a l f t h e p a n e l w e i g h t a c t s a t t h e t o p a s c o n c e n t r i c a x i a l l o a d ( s e e F i g u r e 2 . 2 0 ) . N o t e t h a t d e f l e c t i o n s a t t h e t o p due t o f l e x i b i l i t y o f t h e r o o f d i a p h r a g m do n o t c o n t r i b u t e t o t h e P - d e l t a moment m a g n i f i c a t i o n u n l e s s t h e r e i s some f i x i t y a t e i t h e r s u p p o r t ( s e e F i g u r e 2 . 2 1 ) . T h i s m e t h o d o f a n a l y s i s g i v e s r e s u l t s t h a t c o m p a r e f a v o u r a b l y w i t h a d e t a i l e d c o m p u t e r a n a l y s i s o f t h e d e f l e c t e d s h a p e . I t d o e s t e n d t o be somewhat cumbe rsome f o r d e s i g n , a s a t r i a l and e r r o r s o l u t i o n i s r e q u i r e d . E x a m i n a t i o n o f t h e c h a r t s c a n , h o w e v e r , p r o v i d e a u s e f u l means o f e v a l u a t i o n o f t h e e f f e c t o f c h a n g e s i n m a t e r i a l p r o p e r t i e s o r s e c t i o n c o n -f i g u r a t i o n s . FIGURE 2.16 L A T E R A L LOAD F IGURE 2.17  END MOMENT ^ _ M 0 L For y w > > y m P' M = max. moment Maximum moment Max. deflection • _ 5 M L 2 y * ' 4 8 E T ~ Moment at midheight M m = M 0 / 2 Deflection at midheight y m = FIGURE 2.18  INITIAL DEFLECTION Moment M = 0 Deflection y i = Estimated (initial out-of-straightness) FIGURE 2.19 P-DELTA EFFECTS Total deflection y t = y w + y - m + y i + y p = M t /P '+ y'j ,y p= additional deflection due to axial load M~ = total moment = M w +M m + P y' t M t = M w + ^ + | r M t + P y j = Mw+Mm + Py j F IGURE 2.20 S E L F WEIGHT P s = total weight of panel y t= total deflection due to all effects X = C.of G. of panel H = horiz. reaction = P S X / L Moment at midheight M = HL/2+ -ff (y t ~ X ) = p s y t / 2 F IGURE 2.21 ROOF D E F L E C T I O N y r / 2 y r = roof deflection H = P y r / L Moment at midheight M = HL/2 + P (yyy>/2 ) = py t 24 . 3 . D E S C R I P T I O N OF I N V E S T I G A T I O N S 3 . 1 G e n e r a l The b e h a v i o r o f c o n c r e t e w a l l p a n e l s h a s b e e n i n v e s t i g a t e d f o r a w i d e v a r i e t y o f l o a d i n g c o n d i t i o n s a n d m a t e r i a l p r o -p e r t i e s . The c o m p u t e r p r o g r a m s u s e d f o r t h i s p u r p o s e a r e c a p a b l e o f p r e d i c t i n g t h e c u r v a t u r e s a n d d e f l e c t i o n s t o a h i g h d e g r e e o f a c c u r a c y w i t h a m in imum number o f s i m p l i f y i n g a s s u m p t i o n s . The b i g a d v a n t a g e i n c o m p u t e r i z e d a n a l y t i c a l m e t h o d s o v e r a c t u a l p r o t o t y p e t e s t i n g , o t h e r t h a n t h e c o s t f a c t o r , i s t h e a b i l i t y t o l o o k a t t h e e f f e c t o f v a r y i n g i s o l a t e d p a r a -m e t e r s w h i l e t h e r e m a i n d e r a r e h e l d c o n s t a n t . I n t h e f o l l o w i n g s e c t i o n s , a p a r a m e t r i c s t u d y i s made o f t h e e f f e c t s o f v a r y i n g l o a d i n g c o n d i t i o n s , m a t e r i a l p r o p e r t i e s and p a n e l d i m e n s i o n s . A s t a n d a r d c o n f i g u r a t i o n was a d o p t e d as a b a s i s o f c o m p a r i s o n w h i c h r e p r e s e n t s an a v e r a g e p r a c t i c a l c a s e : 5 V p a n e l t h i c k n e s s , 2 0 ' u n s u p p o r t e d h e i g h t , p i n n e d s u p p o r t s , 4 " a x i a l l o a d e c c e n t r i c i t y , 30 P S F l a t e r a l l o a d . 3 .2 L o a d i n g The e f f e c t o f t h e i n t e r - r e l a t i o n b e t w e e n a x i a l a n d l a t e r a l l o a d s on t h e s t r u c t u r a l p e r f o r m a n c e o f t h i n w a l l p a n e l s i s t h e m a i n p u r p o s e o f t h e s e i n v e s t i g a t i o n s . L a t e r a l l o a d s u s u a l l y t a k e t h e f o r m o f w i n d p r e s s u r e s t h a t a r e u n i f o r m l y d i s t r i b u t e d a l o n g t h e h e i g h t , b u t w i l l s o m e t i m e s t a k e t h e f o r m o f a s e r i e s o f p o i n t f o r c e s e x e r t e d by w i n d o w o r d o o r f r a m e s . O v e r h a n g i n g f e a t u r e s s u c h as f a s c i a f r a m i n g may a l s o p r o v i d e a s o u r c e o f l a t e r a l l o a d i n g u s u a l l y r e s u l t i n g i n a c o u p l e . 2 5 . A x i a l l o a d s a r e v e r t i c a l f o r c e s a p p l i e d a t t h e t o p o f t h e p a n e l a n d s o m e t i m e s a t some l o c a t i o n a l o n g t h e h e i g h t . E x t e r n a l l o a d s s u c h a s r e a c t i o n s f r o m r o o f o r f l o o r members a r e u s u a l l y a p p l i e d e c c e n t r i c a l l y w i t h r e s p e c t t o t h e c e n t r e l i n e of t h e c r o s s s e c t i o n . S e l f - w e i g h t c o n t r i b u t e s a s i g n i f i c a n t p o r t i o n o f t h e a x i a l l o a d and i s c o n s i d e r e d t o be c o n c e n t r i c a l l y a p p l i e d . A d d i t i o n a l a x i a l l o a d s may a l s o o c c u r a s a r e s u l t o f i n - p l a n e f o r c e s . F o r t h e common t i l t - u p a p p l i c a t i o n w h e r e u n s u p p o r t e d h e i g h t s e x c e e d 18 f e e t and r o o f l o a d s a r e i n t h e o r d e r o f 1000 t o 1500 P L F , t h e c o n t r i b u t i o n made by w i n d p r e s s u r e i s e a s i l y t h e l a r g e s t i n f l u e n c e on f i n a l b e n d i n g moments i n t h e w a l l p a n e l . W i t h t h e a d d e d e f f e c t s o f a x i a l l o a d and s l e n d e r n e s s m a g n i f i c a t i o n s o f momen t , t h e e x p e c t e d mode o f f a i l u r e w o u l d be one o f i n s t a b i l i t y . C o n v e r s e l y , f o r s h o r t p a n e l s o f 10 t o 12 f o o t h e i g h t s , t h e e f f e c t o f l a t e r a l w i n d l o a d i s c o n s i d e r a b l y l e s s and f a i l u r e w o u l d l i k e l y o c c u r a s a r e s u l t o f e x c e s s i v e b e n d i n g a t t h e e c c e n t r i c s u p p o r t , p a r t i c u l a r l y when l a r g e a x i a l l o a d s a r e a p p l i e d . The c h a r t s o f A p p e n d i x D g i v e a g o o d g e n e r a l i n d i c a t i o n o f how t h e c a p a c i t y o f a p a n e l i s a f f e c t e d by c h a n g e s i n a x i a l and l a t e r a l l o a d . L i n e a r i n t e r p o l a t i o n b e t w e e n t h e p l o t t e d p a r a m e t e r s w i l l g i v e a c c u r a c i e s s u f f i c i e n t f o r d e s i g n p u r p o s e s . I f r e q u i r e d , t h e c u r v e s may be e x t r a p o l a t e d b e y o n d t h e l a t e r a l l o a d s g i v e n by s i m p l y e x t e n d i n g t h e given l i n e s to the i n t e r s e c t i o n of the zero a x i a l l o a d l i n e . The v a l u e o f a l a t e r a l l o a d a t t h i s p o i n t i s g i v e n by 8Muo W = w h e r e Muo i s t h e u l t i m a t e moment a t z e r o a x i a l l o a d L i s t h e d i s t a n c e b e t w e e n s u p p o r t s 26 . The e f f e c t o f s e l f - w e i g h t was n o t i n c l u d e d i n t h e c h a r t s o f A p p e n d i x D b u t c a n b e a p p r o x i m a t e l y a c c o u n t e d f o r by a s s u m i n g t h a t o n e - h a l f o f t h e w e i g h t i s a p p l i e d ( c o n c e n t r i c a l l y ) a t t h e t o p . T h i s h a s b e e n v e r i f i e d by a n a l y z i n g a p a n e l w i t h a c t u a l s e l f - w e i g h t and t h e n w i t h z e r o w e i g h t b u t an e q u i v a l e n t a x i a l l o a d o f o n e - h a l f t h e w e i g h t o f t h e p a n e l a t t h e t o p . The r e s u l t s a r e v i r t u a l l y i d e n t i c a l . I t m i g h t a p p e a r more a c c u r a t e t o a p p l y a s v e r t i c a l l o a d a t t h e t o p , t h e w e i g h t o f p a n e l a b o v e t h e p o i n t o f maximum moment , b u t t h i s i s a l m o s t a l w a y s a b o u t e q u a l t o o n e - h a l f t h e p a n e l w e i g h t w h e r e s l e n d e r n e s s m a g n i f i c a t i o n s become s i g n i f i c a n t . 3 . 3 End E c c e n t r i c i t y V a r i a t i o n s i n end e c c e n t r i c i t y a t t h e t o p o f a p a n e l h a v e a s u b s t a n t i a l e f f e c t on t h e l o a d c a r r y i n g c a p a c i t y a s c a n be s e e n by t h e two c h a r t s o f F i g u r e 3 . 1 . F o r s m a l l e c c e n t r i c i t i e s t h e p e a k l o a d c a p a c i t y i s h i g h , w i t h a s u b s t a n t i a l r a n g e o f u n s t a b l e e q u i l i b r i u m b e f o r e a c t u a l m a t e r i a l f a i l u r e . I f t h e a x i a l l o a d s a r e a l l o w e d t o a p p r o a c h t h e i n d i c a t e d max imum, t h e r e e x i s t s t h e d a n g e r o f " s n a p t h r o u g h b u c k l i n g " i n w h i c h t h e p a n e l may jump f r o m t h e s t a b l e t o u n s t a b l e p o r t i o n o f t h e c u r v e . T h i s may be i n i t i a t e d by u n e x p e c t e d e x t e r n a l e f f e c t s l i k e s u d d e n i m p a c t o r h i g h w i n d g u s t s . The c o n s e q u e n c e w o u l d be a s u d d e n and t o t a l l o s s o f l o a d c a p a c i t y . T h i s phenomenon e s s e n t i a l l y d o e s n o t o c c u r when e c c e n t r i c i t i e s a r e a t l e a s t h / 2 and t h e l a t e r a l l o a d s e x c e e d l O P S F ( 0 . 5 2 k N / m ) . F o r t h e s e c o n d i t i o n s , t h e l o a d moment c u r v e i n c r e a s e s s t e a d i l y t o a maximum j u s t p r i o r t o u l t i m a t e moment c a p a c i t y . FIGURE 3.1b LOAD MOMENT CURVES 4CH MOMENT (in-k) 28 . T h i s s i t u a t i o n i s more p r e d i c t a b l e a n d t h e d a n g e r s i n c o l l a p s e c a n be a d e q u a t e l y g u a r d e d a g a i n s t by c a r e f u l s e l e c t i o n o f l o a d i n g s a n d c a p a c i t y r e d u c t i o n f a c t o r s . N e g a t i v e e c c e n t r i c i t i e s p r o d u c e a d o u b l e c u r v a t u r e c o n d i t i o n r e s u l t i n g i n l o w e r d e f l e c t i o n s a n d h i g h e r l o a d c a p a c i t i e s . F a i l u r e i s o f t e n t h e r e s u l t o f e x c e s s i v e b e n d i n g moment a t t h e e c c e n t r i c s u p p o r t a n d c a n be p r e d i c t e d by a s i m p l e s t r e n g t h c a l c u l a t i o n . F o r t h e c a s e w h e r e t h e f a i l u r e mode i s one o f i n s t a b i l i t y due t o p o s i t i v e b e n d i n g ( h i g h p a n e l s w i t h f u l l w i n d l o a d a n d s m a l l n e g a t i v e end e c c e n t r i c i t i e s ) , t h e r e i s u s u a l l y an a b r u p t l o s s o f l o a d c a p a c i t y w e l l b e f o r e m a t e r i a l f a i l u r e . 3 . 4 C o n c r e t e P r o p e r t i e s F o r t h e p u r p o s e o f t h e s e i n v e s t i g a t i o n s , t h e c o n c r e t e s t r e s s s t r a i n r e l a t i o n was a s s u m e d t o t a k e t h e s h a p e shown i n F i g u r e 2 . 1 . I t i s c o n s i d e r e d t h a t t h i s i s a s u f f i c i e n t l y r e a l i s t i c r e p r e s e n t a t i o n o f t h e a c t u a l c u r v e . C o m p r e s s i v e S t r e n g t h F o r a l l d e s i g n c h a r t s o f A p p e n d i x B , t h e 28 d a y c o m p r e s s i v e s t r e n g t h was a s s u m e d t o be 25 MPa ( 3 6 2 0 P S I ) . T h i s i s n o r m a l l y a m in imum r e q u i r e m e n t f o r a d e q u a t e r e s i s t a n c e a g a i n s t f l e x u r a l c r a c k i n g d u r i n g t h e p a n e l l i f t i n g o p e r a t i o n . The e f f e c t o f v a r y i n g c o n c r e t e s t r e n g t h on t h e a v e r a g e s t i f f n e s s p r o p e r t i e s i s shown f o r one s p e c i f i c c a s e i n F i g u r e 3 . 2 ( a ) . F o r t h e mos t p a r t , t h e u l t i m a t e moment c a p a c i t y i s n o t g r e a t l y a f f e c t e d by c h a n g e s i n c o n c r e t e c o m p r e s s i v e s t r e n g t h . The s t i f f n e s s d o e s seem t o i n c r e a s e w i t h i n c r e a s i n g c o m p r e s s i v e s t r e n g t h up t o a b o u t 4000 P S I . A f t e r t h i s , t h e r e i s v e r y l i t t l e i n c r e a s e . 29 . FIGURE 3 . 2 a A V E R A G E ST IFFNESS FOR VARIATIONS IN C O N C R E T E S T R E N G T H 100 H M O M E N T ( i n - k ) FIGURE 3.2 b LOAD MOMENT RELAT IONS FOR  VARIATIONS IN CONCRETE S T R E N G T H 0 10 2 0 3 0 4 0 5 0 6 0 7 0 M O M E N T ( i n - k ) 3 0 . The e f f e c t o f c o m p r e s s i v e s t r e n g t h c h a n g e s on l o a d c a p a c i t y i s shown i n F i g u r e 3 . 2 ( b ) . A d e c r e a s e f r o m 4000 P S I t o 2000 P S I r e d u c e s t h e p e a k a x i a l l o a d by a b o u t 25% and an i n c r e a s e f r o m 4000 P S I t o 6000 P S I i n c r e a s e s t h i s a x i a l l o a d by 15%. T e n s i l e S t r e n g t h C o n s i d e r a t i o n o f c o n c r e t e t e n s i l e s t r e n g t h w i l l a d d t o t h e o v e r a l l s t i f f n e s s o f t h e s e c t i o n a t l o w b e n d i n g moment b u t w i l l n o t r e s u l t i n any s i g n i f i c a n t i n c r e a s e s a t u l t i m a t e . A c o m p a r i s o n o f t h e a v e r a g e s t i f f n e s s f o r 0 , 300 P S I and 600 P S I u l t i m a t e t e n s i l e c a p a c i t y i s shown i n F i g u r e 3 . 3 . A c h e c k on a x i a l l o a d c a p a c i t y f o r t h e same t h r e e c a s e s r e v e a l e d no d i f f e r e n c e s , p r e s u m a b l y b e c a u s e t h e s t i f f n e s s e s a r e i n d i s t i n g u i s h a b l e a t h i g h e r m o m e n t s . 3 . 5 R e i n f o r c i n g S t e e l A b i - l i n e a r e l a s t o - p l a s t i c s t r e s s s t r a i n c u r v e was a d o p t e d f o r t h e r e i n f o r c i n g s t e e l a s shown i n F i g u r e 2 . 1 . The s t e e l i s a s s u m e d t o e l o n g a t e i n d e f i n i t e l y a t a c o n s t a n t s t r e s s a f t e r r e a c h i n g t h e s p e c i f i e d y i e l d . P e r f e c t b o n d b e t w e e n c o n c r e t e and s t e e l i s a s s u m e d s u c h t h a t s t r a i n i n t h e s t e e l i s a l w a y s p r o p o r t i o n a l t o c u r v a t u r e . T h i s i m p l i e s a u n i f o r m d i s t r i b u t i o n o f c r a c k s on t h e t e n s i o n f a c e w i t h no s l i p p a g e a t t h e c r a c k s . The a s s u m p t i o n i s g e n e r a l l y b e l i e v e d t o be v a l i d f o r d e f o r m e d r e i n f o r c i n g b a r s o f y i e l d s t r e n g t h up t o a b o u t 60 k s i . 70CH 650-6 0 0 H 5 5 0 -500 -4 5 0 -4 0 0 -350" 3 0 0 -2 5 0 -200-1 5 0 -100 50 H 0 F IGURE 3.3 A V E R A G E S T I F F N E S S FOR VAR IAT IONS IN C O N C R E T E TENS ION 10 2 0 M O M E N T 30 1 4 0 5 0 ( i n - k ) I— 6 0 70 32 . Y i e l d S t r e s s A l t h o u g h t h e s t e e l y i e l d s t r e s s f o r a l l t h e i n v e s t i g a t i o n s was s e t a t 60 K S I , t h e e f f e c t o f l o w e r o r h i g h e r y i e l d s was i n v e s t i g a t e d . F i g u r e 3 . 4 ( a ) shows t h e s t i f f n e s s v a r i a t i o n s f o r 4 0 , 60 a n d 80 K S I y i e l d a n d f o r t h e f i c t i t i o u s c a s e o f i n f i n i t e y i e l d s t r e n g t h . The u l t i m a t e moment c a p a c i t y i n c r e a s e s w i t h i n c r e a s i n g y i e l d , a s w o u l d be e x p e c t e d a t l o w l e v e l s o f a x i a l c o m p r e s s i o n , b u t t h e a v e r a g e s t i f f n e s s d o e s n o t c h a n g e . A c o m p a r i s o n o f a x i a l l o a d c a p a c i t y f o r v a r i o u s y i e l d s i n r e i n f o r c e m e n t i s shown i n F i g u r e 3 . 4 ( b ) . The i n c r e a s e i n l o a d c a p a c i t y c a n be a t t r i b u t e d t o t h e a d d i t i o n a l u l t i m a t e moment a t h i g h e r y i e l d s . B e c a u s e o f t h e v a r i a t i o n s i n t h e s e r e s u l t s due t o a x i a l c o m p r e s s i o n , t h e r e d o e s n o t a p p e a r t o be a n y s a t i s f a c t o r y r e l a t i o n a v a i l a b l e f o r m o d e l l i n g t h e e f f e c t o f l o w e r o r h i g h e r y i e l d s t r e s s . H o w e v e r , f o r t h e n o r m a l r a n g e o f a x i a l l o a d i n g s f o r t i l t - u p w a l l p a n e l s (0 t o 2000 P L F ) , a x i a l l o a d c a p a c i t y a p p e a r s t o v a r y i n r o u g h l y a l i n e a r f a s h i o n w i t h y i e l d s t r e s s o f t h e s t e e l . A r e a o f R e i n f o r c e m e n t V a r i a t i o n s i n t h e a r e a s o f s t e e l u s e d i n a s e c t i o n a p p e a r to a f f e c t t h e s e c t i o n s t i f f n e s s on an a p p r o x i m a t e l y l i n e a r b a s i s . The c h a r t s o f A p p e n d i x C i n d i c a t e t h a t t h e a s s u m p t i o n o f a l i n e a r v a r i a t i o n w o u l d be s u f f i c i e n t l y , a c c u r a t e f o r c h a n g e s o f t h e o r d e r o f ±15%. The a x i a l l o a d c a p a c i t y i s a l s o a f f e c t e d by c h a n g e s i n a r e a s o f s t e e l and a g a i n , t h e r e l a t i o n i s a l m o s t l i n e a r ( s e e A p p e n d i x B ) . FIGURE 3 . 4 0 AVERAGE STIFFNESS FOR FIGURE 3.4 b  AXIAL LOAD FOR VARIATIONS IN YIELD M O M E N T ( i n - k ) 34 . L o c a t i o n o f R e i n f o r c e m e n t L o c a t i o n o f r e i n f o r c i n g s t e e l i n t h e s e c t i o n h a s a p r o n o u n c e d e f f e c t on t h e l o a d c a r r y i n g c a p a c i t y o f t h e p a n e l . F o r a 5h" s e c t i o n w i t h o n l y one l a y e r o f r e i n f o r c e m e n t , v a r i a t i o n s i n p l a c e m e n t o f ± 1 / 8 " c a u s e d c h a n g e s i n s t i f f n e s s o f a b o u t 10% and i n p e a k a x i a l l o a d by 13% ( s e e F i g u r e 3 . 5 ) . A p a n e l w i t h two l a y e r s o f s t e e l ( F i g u r e 3 . 6 ) showed s t i f f n e s s v a r i a t i o n s o f 4% a n d l o a d v a r i a t i o n s o f 7% f o r t h e same 1 / 8 " t o l e r a n c e . I n b o t h c a s e s , t h e c o n s e q u e n c e o f s m a l l c h a n g e s i n l o c a t i o n o f t h e s t e e l a p p e a r t o be a p p r o x i m a t e l y p r o p o r t i o n a l t o a t l e a s t t h e s q u a r e o f t h e e f f e c t i v e d e p t h o f s t e e l . P r e s t r e s s i n g P r e s t r e s s i n g o f t h e r e i n f o r c i n g s t e e l c a n r e s u l t i n l a r g e i n c r e a s e s i n b e n d i n g s t i f f n e s s , p a r t i c u l a r l y f o r l o w l e v e l s o f a x i a l l o a d i n g t o w h i c h m o s t w a l l p a n e l s a r e n o r m a l l y s u b j e c t e d . A c o m p a r i s o n b e t w e e n a p r e s t r e s s e d and n o n -p r e s t r e s s e d w a l l p a n e l i s shown i n F i g u r e 3 . 7 . P r e s t r e s s i n g a l l o w s f o r f u l l a d v a n t a g e t o be t a k e n o f t h e i n c r e a s e d s t i f f n e s s a t h i g h e r a x i a l c o m p r e s s i o n w i t h o u t t h e e x t e r n a l i n s t a b i l i t y due t o P - d e l t a e f f e c t s . S i n c e t h i s p a p e r i s c o n c e r n e d w i t h t h e n o n - p r e s t r e s s e d c o n d i t i o n , no f u r t h e r d i s c u s s i o n o f p r e s t r e s s i n g w i l l be m a d e . 3 . 6 C a p a c i t y R e d u c t i o n F a c t o r The c a p a c i t y r e d u c t i o n f a c t o r 0 a s r ecommended by t h e A C I / C S A c o d e s ( r e f . 2 and 3) s h o u l d be u s e d t o d e c r e a s e t h e c o m p u t e d l o a d c a p a c i t i e s . The p u r p o s e o f t h i s r e d u c t i o n i s t o a l l o w f o r v a r i a t i o n s i n m a t e r i a l p r o p e r t i e s and p o o r w o r k m a n s h i p . FIGURE 3,5o AVERAGE STIFFNESS FOR VARIATIONS IN REINFORCING 1 1 1 1 1 I I T 0 10 20 30 40 50 60 70 MOMENT ( i n - k ) FIGURE 3.5 b AXIAL LOAD FOR VARIATIONS IN S T E E L LOCATION MOMENT ( i n - k ) 0 10 20 30 4 0 50 60 70 8 0 9 0 100 M O M E N T ( in-k) MOMENT ( i n - k ) 38 . The amoun t o f r e d u c t i o n i n c r e a s e s w i t h i n c r e a s i n g a x i a l l o a d and r e f l e c t s t h e f a c t t h a t f a i l u r e due t o c r u s h i n g o f c o n c r e t e i s l e s s p r e d i c t a b l e t h a n y i e l d i n g o f r e i n f o r c i n g s t e e l . The c o d e s a l s o s u g g e s t t h a t t h e s t i f f n e s s u s e d t o c o m p u t e d e f l e c t i o n s a n d t h u s , t h e t o t a l m o m e n t s , s h o u l d a l s o be r e d u c e d b y t h e 0 f a c t o r . The e f f e c t o f 0 on a v e r a g e s t i f f -n e s s i s shown i n F i g u r e 3 . 8 . I f t h i s r e d u c e d s t i f f n e s s i s u s e d ( i n a c t u a l f a c t c u r v a t u r e i s i n c r e a s e d by t h e i n v e r s e o f 0 ) , t h e c o m p u t e d l o a d c a p a c i t i e s w i l l n a t u r a l l y be l e s s a s i n d i c a t e d i n F i g u r e 3 . 9 . L i n e A i s t h e d e s i g n l o a d c u r v e f o r a p a n e l w i t h no r e d u c t i o n i n s e c t i o n s t i f f n e s s , and l i n e B i s t h e same p a n e l w i t h 0 a p p l i e d t o t h e c u r v a t u r e o n l y . L i n e C i s t h e f i n a l r e s u l t w h e r e 0 i s u s e d t o r e d u c e t h e a x i a l l o a d and moment c o m p u t e d f o r l i n e B . The e f f e c t o f t h i s d o u b l e r e d u c t i o n i s s u b s t a n t i a l as c a n be s e e n i n F i g u r e 3 . 9 , b u t i s c o n s i d e r e d n e c e s s a r y p a r t i c u l a r l y i n v i e w o f t h e e f f e c t s o f s m a l l v a r i a t i o n s i n p l a c e m e n t o f r e i n f o r c i n g s t e e l ( s e e S e c t i o n 3 . 5 ) . 3 . 7 S e c t i o n T h i c k n e s s P a n e l t h i c k n e s s s h o u l d be c o n s i d e r e d a l o n g w i t h p l a c e m e n t o f r e i n f o r c e m e n t when a s s e s s i n g t h e e f f e c t s on b e n d i n g s t i f f n e s s and l o a d c a p a c i t y . As was i l l u s t r a t e d i n s e c t i o n 3 . 5 , r e i n f o r c i n g s t e e l p l a c e d i n two l a y e r s c a n g r e a t l y i m p r o v e t h e p e r f o r m a n c e o v e r a s i n g l e l a y e r o f s t e e l i n t h e m i d d l e o f a s e c t i o n o f t h e same t o t a l t h i c k n e s s . 3 9 . F I G U R E 3 . 8  E F F E C T OF 0 ON A V E R A G E S T I F F N E S S MOMENT ( i n - k ) 40 . FIGURE 3 . 9  E F F E C T OF 0 ON LOAD MOMENT CURVES MOMENT ( i n - k ) 4 1 . S i n c e m o s t o f t h e t i l t - u p p a n e l s p r o d u c e d a r e r e i n f o r c e d w i t h o n l y one c e n t r a l l a y e r , i t i s w o r t h w h i l e t o i n v e s t i g a g e t h e e f f e c t o f v a r y i n g t h e c o n c r e t e t h i c k n e s s w h i l e h o l d i n g t h e r e i n f o r c e m e n t c o n s t a n t . F i g u r e 3 . 1 0 ( a ) c o m p a r e s t h e s t i f f -n e s s o f a 5h, 6 , 6%, 7 and lh i n c h p a n e l w i t h t h e same t o t a l a r e a o f s t e e l i n t h e c e n t r e o f t h e c r o s s s e c t i o n . The t r e n d i n d i c a t e d i s t h a t s t i f f n e s s i n c r e a s e s a t a r a t e a p p r o x i m a t e l y p r o p o r t i o n a l t o t h e s q u a r e o f t h e p a n e l t h i c k -n e s s o r more c o r r e c t l y by t h e s q u a r e o f t h e e f f e c t i v e d e p t h " d " t o t h e r e i n f o r c e m e n t . U l t i m a t e moment a l s o i n c r e a s e s b u t o n l y l i n e a r l y w i t h t h e d e p t h . The e f f e c t on a x i a l l o a d c a p a c i t y i s shown i n F i g u r e 3 . 1 0 ( b ) . The i n c r e a s e i n t h e p e a k a x i a l l o a d c a n be a t t r i b u t e d t o b o t h t h e i n c r e a s e i n s e c t i o n s t i f f n e s s a s w e l l a s t o t h e i n c r e a s e i n u l t i m a t e moment . I t a p p e a r s t o be a f u n c t i o n o f t h e d e p t h t o t h e r e i n f o r c e m e n t r a i s e d t o a p o w e r o f a t l e a s t 3 and p o s s i b l y a s much a s 3 . 5 . T h i s , o f c o u r s e , w o u l d v a r y w i t h p a n e l h e i g h t , end e c c e n t r i c i t y and l a t e r a l l o a d . I t w o u l d be c o n s e r v a t i v e , h o w e v e r , t o s a y t h a t i n c r e a s e s i n a x i a l l o a d c a p a c i t y a r e a f u n c t i o n o f t h e s q u a r e o f p a n e l t h i c k n e s s r a t i o s f o r t h e same o v e r a l l h e i g h t . C o n v e r s e l y , o f c o u r s e , t h i s means a r e d u c t i o n i n p r o p o r t i o n a l t o s q u a r e o r more o f t h e t h i c k n e s s , p a n e l i s a c c i d e n t l y c a s t a b i t t o o t h i n . c a p a c i t y i f t h e FIGURE 3.10a A V E R A G E S T I F F N E S S FOR VAR IAT IONS IN S E C T I O N T H I C K N E S S 14 F IGURE 3 . 1 0 b A X I A L L O A D FOR VAR IAT IONS IN T H I C K N E S S 43. 3.8 Panel Height The l i m i t a t i o n s on panel h e i g h t , or more g e n e r a l l y height to t h i c k n e s s r a t i o s , are of i n t e r e s t to a l l engineers and have o f t e n been the t o p i c of lengthy debates by code committees and b u i l d i n g o f f i c i a l s . There have been attempts to set upper bounds on slenderness r a t i o s based on the codes w r i t t e n f o r other m a t e r i a l s such as s t r u c t u r a l s t e e l . Slenderness r a t i o s such as unsupported h e i g h t / t h i c k n e s s or h e i g h t / r a d i u s of g y r a t i o n of the gross concrete s e c t i o n are meaningless without c o n s i d e r a t i o n of the amount and l o c a t i o n of r e i n f o r c i n g s t e e l , the l e v e l of a x i a l compression, end e c c e n t r i c i t i e s and l a t e r a l l o a d . The c h a r t s i n Appendix D i n d i c a t e that v a r i a t i o n s i n end e c c e n t r i c i t y and l a t e r a l l o a d can g r e a t l y a f f e c t the load c a r r y i n g p r o p e r t i e s of the p a n e l . Two l a y e r s of r e i n f o r c i n g s t e e l i n s t e a d of one c e n t r a l l a y e r w i l l almost double the c a p a c i t y f o r the same o v e r a l l panel t h i c k n e s s . 3 . 9 End F i x i t y Often a w a l l panel i s continuous over one or more i n t e r i o r supports such as f l o o r and foundations and can be considered as p a r t i a l l y r e s t r a i n e d at one end. This w i l l u s u a l l y r e s u l t i n an i n c r e a s e d a x i a l load c a p a c i t y above the simply supported c o n d i t i o n . The computer programs developed were not g e n e r a l l y a p p l i -cable i n a s s e s s i n g the e f f e c t of end f i x i t y f o r the f o l l o w i n g reasons: 44 . a . H o r i z o n t a l d e f l e c t i o n s a t t h e t o p ( r o o f ) w i l l now i n d u c e s e c o n d a r y moments i n t o t h e p a n e l . (In s imply supported pane l s the moment i s independent of roo f d e f l e c t i o n . ) b . L a t e r a l r e s t r a i n t p r o v i d e d by t h e f o o t i n g i s a l w a y s q u e s t i o n a b l e a n d may be i n s u f f i c i e n t t o p r e v e n t s m a l l d i s p l a c e m e n t s . c . R o t a t i o n a l s t i f f n e s s o f o t h e r members f r a m i n g i n t o t h e j o i n t i s u n k n o w n . d . The e f f e c t o f l a t e r a l s o i l p r e s s u r e f o r p a n e l s e x t e n d i n g b e l o w f l o o r s l a b l e v e l i s d i f f i c u l t t o a s s e s s . e . S e l f - w e i g h t o f t h e p a n e l c o m p l i c a t e s t h e a n a l y s i s f u r t h e r p a r t i c u l a r l y f o r a . and b . As a r e s u l t , t h e e f f e c t o f end f i x i t y c a n a t b e s t o n l y be a p p r o x i m a t e d . A p o p u l a r a p p r o a c h i s t o a s s u m e some r e d u c e d o r e f f e c t i v e l e n g t h a n d t h e n t o a n a l y z e t h e p a n e l as s i m p l y s u p p o r t e d . The e f f e c t i v e l e n g t h o f an e l a s t i c beam c o l u m n f i x e d a g a i n s t r o t a t i o n a t e a c h end w o u l d be o f t h e o r d e r o f 50% o f t h e t o t a l d i s t a n c e b e t w e e n s u p p o r t s . N o r m a l l y , o n l y one end i s r e s t r a i n e d and t h i s c a n n o t be c o n s i d e r e d a s 100% f i x e d . I t i s , t h e r e f o r e , common p r a c t i c e t o a s s u m e n o t l e s s t h a n a b o u t 85% o f t h e u n s u p p o r t e d s p a n a l t h o u g h i n m o s t c a s e s a f u l l 100% i s c o n s e r v a t i v e l y a d o p t e d f o r a l l c o n d i t i o n s . 45 . 4 . DESIGN METHOD 4 . 1 D e s c r i p t i o n o f D e s i g n P r o c e d u r e The s t r e n g t h o f t h i n c o n c r e t e w a l l p a n e l s s u b j e c t e d t o c o m b i n e d a x i a l and l a t e r a l l o a d s c a n be o b t a i n e d by a d e t a i l e d c o m p u t e r a n a l y s i s w h i c h t a k e s i n t o a c c o u n t t h e v a r i a t i o n s i n s e c t i o n s t i f f n e s s w i t h a x i a l c o m p r e s s i o n and b e n d i n g . S i n c e t h i s i s n o t a l w a y s r e a d i l y a v a i l a b l e t o t h e d e s i g n e r , an a p p r o x i m a t e h a n d a n a l y s i s i s d e s i r e d . The m e t h o d p r e s e n t e d i n t h i s m a n u a l c o n s i s t s o f a s e r i e s o f d e s i g n c h a r t s c o v e r i n g a b r o a d r a n g e o f p a n e l t h i c k n e s s e s and r e i n f o r c i n g c o n f i g u r a t i o n s . The maximum moment due t o f a c t o r e d a p p l i e d l o a d i n g and d e s i g n e c c e n t r i c i t y , b u t e x c l u d i n g s l e n d e r n e s s e f f e c t s i s c a l c u l a t e d and c o m p a r e d t o t h e a l l o w a b l e v a l u e s p l o t t e d on t h e c h a r t s . The s e c t i o n p r o p e r t i e s c a n t h e n be a d j u s t e d u n t i l a s a t i s f a c t o r y d e s i g n i s r e a c h e d . 4 . 2 L o a d C a p a c i t y C h a r t s A t o t a l o f 48 d e s i g n c h a r t s h a s b e e n p r e p a r e d t o a s s i s t i n t h e d e s i g n o f t i l t - u p w a l l p a n e l s ( A p p e n d i x B ) . A l l l o a d s and s e c t i o n p r o p e r t i e s a r e i n t e r m s o f S I ( m e t r i c ) u n i t s . E a c h c h a r t i s a p p l i c a b l e t o a u n i q u e c r o s s s e c t i o n . T h r e e t h i c k n e s s e s w e r e s e l e c t e d : 140 mm, 165 mm and 190 mm w i t h t h e r e i n f o r c i n g s t e e l p l a c e d i n one l a y e r i n t h e m i d d l e o f t h e s e c t i o n ( A l t o A24 ) o r i n two l a y e r s 20 mm c l e a r o f e a c h f a c e ( B l t o B 2 4 ) . The a r e a o f r e i n f o r c i n g r a n g e s f r o m 300 mm 2 t o 1 400 mm, i n a 1 000 mm w i d e s e c t i o n . 46 . A 28 d a y c o n c r e t e c y l i n d e r s t r e n g t h o f 25 MPa was u s e d . The y i e l d s t r e s s o f t h e r e i n f o r c i n g s t e e l c o n f o r m s t o t h e new m e t r i c s t a n d a r d o f 400 M P a . E a c h c h a r t c o n t a i n s i n t e r a c t i o n c u r v e s f o r f a i l i n g v a l u e s o f a p p l i e d a x i a l l o a d and u n m a g n i f i e d moment f o r a number o f u n s u p p o r t e d h e i g h t s . The d e s i g n p r o c e d u r e c o n s i s t s o f e n t e r i n g t h e c h a r t w i t h t h e a x i a l l o a d a p p l i e d a t t h e p o i n t o f maximum moment ( u s u a l l y a b o u t m i d - h e i g h t ) . I f t h e moment g i v e n b y t h e c h a r t f o r t h e d e s i g n h e i g h t i f p a n e l i s g r e a t e r t h a n t h e maximum moment due t o a l l e f f e c t s i n c l u d i n g w i n d and e c c e n t r i c i t y and i n i t i a l o u t - o f - s t r a i g h t n e s s , b u t e x c l u d i n g s l e n d e r n e s s m a g n i f i c a t i o n s , t h e n t h e s e c t i o n c a n be c o n s i d e r e d a d e q u a t e . N o t e t h a t a l l l o a d s a r e u l t i m a t e ( f a c t o r e d ) a n d t h e c a p a c i t y r e d u c t i o n f a c t o r 0 h a s b e e n i n c l u d e d i n t h e c h a r t s . F o r a more d e t a i l e d d e s c r i p t i o n o f t h e d e v e l o p m e n t o f t h e s e c h a r t s , s e e S e c t i o n 2 . 4 . 3 L o a d i n g C o n d i t i o n s a . L a t e r a l l o a d s : u s u a l l y w i n d p r e s s u r e s c o n t r o l t h e d e s i g n a l t h o u g h s e i s m i c a c c e l e r a t i o n s may i n some c a s e s be s i g n i f i c a n t . L o c a l c o d e s s h o u l d be c o n s u l t e d , b u t i n no c a s e s h o u l d a l a t e r a l p r e s s u r e o f l e s s t h a n 0 . 5 2 k N / m be u s e d ( p o s i t i v e o r n e g a t i v e ) . b . A x i a l l o a d s : t h e s e a r e u s u a l l y u n i f o r m l y d i s t r i b u t e d l i n e l o a d s a l o n g t h e t o p o f t h e p a n e l . F o r l i g h t p o i n t l o a d s a t s m a l l e c c e n t r i c i t i e s , i t i s s u f f i c i e n t t o s u b s t i t u t e an e q u i v a l e n t u n i f o r m l y d i s t r i b u t e d l o a d by 4 7 . d i v i d i n g the load by the spacing. Where a x i a l load i s la r g e (50 kN), the width of i n f l u e n c e should be l i m i t e d to the load l e n g t h plus approximately 12 times the panel t h i c k n e s s . E c c e n t r i c i t i e s : a x i a l loads w i l l always be a p p l i e d at some e c c e n t r i c i t y to the c e n t r e l i n e a x i s of the panel, e i t h e r i n t e n t i o n a l l y or due to bea r i n g i r r e g u l a r i t i e s . A minimum e c c e n t r i c i t y of one-half the panel t h i c k n e s s i s recommended f o r design computation where the e f f e c t i s a d d i t i v e to the wind load and zero where a r e d u c t i o n of t o t a l moment would otherwise occur. E c c e n t r i c i t y at the bottom i s assumed to be zero. S e l f - w e i g h t : the e f f e c t of panel s e l f - w e i g h t on moment m a g n i f i c a t i o n can be approximated by assuming that a p o r t i o n of the t o t a l weight acts at the top as a con-c e n t r i c a x i a l l o a d . Since the c r i t i c a l s e c t i o n u s u a l l y occurs at or s l i g h t l y above mid-height, i t i s c o n s e r v a t i v e to use one-half of the t o t a l panel weight. Load combinations: there are f i v e load combinations that may be considered, a c c o r d i n g to the N a t i o n a l B u i l d i n g Code of Canada, and each should be i n v e s t i g a t e d s e p a r a t e l y U = 1.4D + 1.7W U = 1.4D + 1.8E U = 1.4D + 1.7L U = 0.75 (1.4D + 1.7L + 1.7W) U = o.75 (1.4D + 1.7L + 1.8E) U s u a l l y the f i r s t c o n d i t i o n w i l l c o n t r o l the design although the t h i r d i s s i g n i f i c a n t f o r short panels with l a r g e e c c e n t r i c a x i a l l o a d s . 48 . F o r t h e common c a s e o f l a r g e w i n d l o a d moments and s m a l l a x i a l l o a d s , t h e maximum moment w i l l o c c u r v e r y n e a r m i d - h e i g h t o f t h e p a n e l . As t h e a x i a l l o a d and end moment i n c r e a s e , t h i s p o i n t w i l l s h i f t t o w a r d s t h e t o p . The d e s i g n c h a r t s r e q u i r e t h a t t h e maximum moment , w h e r e v e r i t may o c c u r , be p l o t t e d a g a i n s t a x i a l l o a d . 4 . 4 M a t e r i a l P r o p e r t i e s The s e l e c t i o n o f m a t e r i a l p r o p e r t i e s s h o u l d be b a s e d l a r g e l y on l o c a l c o n d i t i o n s and p r a c t i c e , and i s u s u a l l y g o v e r n e d by c o s t c o n s i d e r a t i o n s . The s p e c i f i e d 28 day c o n c r e t e s t r e n g t h s h o u l d be i n t h e o r d e r o f 30 t o 35 MPa s u c h t h a t s u f f i c i e n t f l e x u r a l s t r e n g t h i s a v a i l a b l e f o r l i f t i n g . Many c o n t r a c t o r s w i l l a s k f o r f l e x u r a l s t r e n g t h t e s t s j u s t p r i o r t o l i f t i n g t o c o n f i r m t h e s t r e n g t h r e q u i r e m e n t s . The c o m p r e s s i v e s t r e n g t h o f c o n c r e t e i s r e l a t i v e l y u n i m p o r t a n t as l o n g a s a m in imum o f 25 MPa a t 28 d a y s i s r e a c h e d . The g r a d e o f r e i n f o r c i n g s t e e l s h o u l d a l w a y s be h a r d g r a d e , 400 MPa u n l e s s i t i s o n l y r e q u i r e d f o r t e m p e r a t u r e s t r e s s e s . M i x i n g g r a d e s o f t h e same s i z e o f r e b a r on one j o b s i t e s h o u l d be a v o i d e d . The u s e o f l i g h t w e i g h t a g g r e g a t e s c a u s e s a d e c r e a s e i n l o a d c a p a c i t y i n t h e o r d e r o f a b o u t 5%, h o w e v e r d u e . t o t h e r e d u c e d s e l f - w e i g h t t h e s e p a n e l s w i l l u s u a l l y c a r r y g r e a t e r r o o f and w i n d l o a d s t h a n i f n o r m a l w e i g h t c o n c r e t e i s u s e d . 49 . E f f e c t i v e P a n e l H e i g h t I t i s r e c o m m e n d e d t h a t a l l p a n e l s be c o n s i d e r e d a s p i n n e d a t e a c h e n d u n l e s s t h e b o t t o m s u p p o r t i s f i x e d so t h a t a l l r o t a t i o n i s p r e v e n t e d . I n t h a t c a s e , a r e d u c e d e f f e c t i v e l e n g t h may be u s e d i n t h e o r d e r o f a b o u t 85% t o 90% o f t h e c l e a r d i s t a n c e b e t w e e n a c t u a l s u p p o r t s . P r a c t i c a l l i m i t s on t h e u n s u p p o r t e d h e i g h t o f a w a l l p a n e l mus t be b a s e d on s e c t i o n t h i c k n e s s , r e i n f o r c i n g c o n f i g u r -a t i o n and l o a d i n g c o n d i t i o n . F i g u r e 4 . 1 may be u s e d a s a g u i d e when m a k i n g p r e l i m i n a r y s e l e c t i o n s o f p a n e l d e s i g n s . T h i s d i a g r a m h a s b e e n e s t a b l i s h e d on t h e b a s i s o f t h e f o l l o w i n g c o n d i t i o n s : a . C o n c r e t e s t r e n g t h 25 M P a . b . R e i n f o r c i n g s t e e l y i e l d 400 M P a . 2 2 c . S t e e l a r e a 800 mm /m i n t h e c e n t r e o r 800 mm /m e a c h f a c e (20 mm c l e a r ) . 2 d . . W i n d l o a d Wu = 1 . 7 5 k N / m ( p o s i t i v e ) . 2 e . A x i a l l o a d Pu = 6 . 5 k N / m p l u s h s e l f - w e i g h t x 1 . 4 . f . End e c c e n t r i c i t y e = o . g . I n i t i a l d e f l e c t i o n 20 mm. E f f e c t o f C r e e p and I n i t i a l D e f l e c t i o n s L o n g t e r m d e f l e c t i o n s c a u s e d by c r e e p a r e n o t n o r m a l l y c o n s i d e r e d s i n c e d e a d l o a d d e f l e c t i o n s a r e u s u a l l y q u i t e s m a l l c o m p a r e d t o t h o s e f r o m w i n d l o a d . I n i t i a l o u t - o f - s t r a i g h t n e s s c a u s e d by v a r i a t i o n s i n s h r i n k a g e o r by c a s t i n g on u n e v e n f l o o r s l a b s c a n be a p p r o x i m a t e d by a d d i n g a s m a l l d e f l e c t i o n a t m i d - h e i g h t i n t h e o r d e r o f 20 mm 50 FIGURE 4.1 CONCRETE WALL PANEL HEIGHT - THICKNESS RELATIONS x CD UJ X Q UJ y— or o o_ a. CO z 3 2 X < ' i 1 1 1 r 100 120 140 160 180 200 220 240 260 280 PANEL THICKNESS (mm) PM*6.5kN/m fC= 25 MPa fy= 400 MPQ W u=i.75kN/m 2 h/2 •Ar-As= 800 mm 2 20mm » 4 •As= 800mm 2 20mm SECTION A SECTION B 51 . D e f l e c t i o n s a t r o o f l e v e l due t o t h e f l e x i b i l i t y o f t h e r o o f d i a g h r a g m h a v e no i n f l u e n c e on s l e n d e r n e s s e f f e c t s u n l e s s t h e r e i s f i x i t y a t e i t h e r t h e t o p o r b o t t o m o f t h e p a n e l . 4 . 7 C a p a c i t y R e d u c t i o n F a c t o r s I n t h e A C I d e s i g n p r o c e d u r e , t h e f a c t o r e d moments a r e i n c r e a s e d by t h e moment m a g n i f i e r and c o m p a r e d w i t h t h e u l t i m a t e moment r e d u c e d by t h e c a p a c i t y r e d u c t i o n f a c t o r . B e c a u s e v a r i a t i o n i n m a t e r i a l p r o p e r t i e s a n d d i m e n s i o n s i n f l u e n c e s t i f f n e s s and t h e r e f o r e s l e n d e r n e s s e f f e c t s , t h e c a p a c i t y r e d u c t i o n f a c t o r a p p e a r s a s e c o n d t i m e i n t h e moment m a g n i f i e r . A p a r a l l e l p r o c e d u r e h a s b e e n f o l l o w e d i n t h e p r e s e n t w o r k : i n c o m p u t i n g t h e e f f e c t s o f s l e n d e r -n e s s , t h e moment r o t a t i o n r e l a t i o n s h i p o r s t i f f n e s s o f t h e s e c t i o n was r e d u c e d by t h e c a p a c i t y r e d u c t i o n f a c t o r . The l a t t e r was s u b s e q u e n t l y a p p l i e d a s e c o n d t i m e t o r e d u c e b o t h a x i a l l o a d a n d moment b e f o r e p r e p a r a t i o n o f t h e c h a r t s . The a c t u a l v a l u e o f 0 was b a s e d on t h e r e c o m m e n d a t i o n by A C I 318 a n d CSA A 2 3 . 3 0 = 0 . 9 - 2 . 0 — ^ 0 . 7 f ' c A g 4 . 8 I n - P l a n e S h e a r I n - p l a n e s h e a r i s o n l y s i g n i f i c a n t f o r h i g h , n a r r o w p a n e l s w i t h s u b s t a n t i a l s h e a r l o a d s a p p l i e d a t t h e t o p . T h i s s o m e -t i m e s o c c u r s i n v e r y l o n g b u i l d i n g s w h e r e end w a l l s a r e r e q u i r e d t o r e s i s t t h e l a t e r a l s h e a r f o r c e s f r o m t h e r o o f d i a p h r a g m . I n t h e s e c a s e s , t h e s t a b i l i t y o f t h e c o m p r e s s i v e edge i n b u c k l i n g p e r p e n d i c u l a r t o t h e p l a n e o f t h e p a n e l i s t h e m a i n p o i n t o f i n t e r e s t a s a c t u a l s h e a r s t r e s s e s . w o u l d r a r e l y be e x c e s s i v e . 5 2 . F i g u r e 4 . 2 shows t h e p r o p o s e d m e t h o d o f a n a l y s i s by w h i c h t h e s h e a r l o a d i s c o n v e r t e d i n t o an e f f e c t i v e s e l f - w e i g h t a t t h e o u t e r c o m p r e s s i v e e d g e . I n m o s t c a s e s , t h i s w o u l d i n v o l v e a p p l y i n g h a l f o f t h e t o t a l e f f e c t i v e s e l f - w e i g h t t o t h e t o p o f t h e p a n e l . I f t h i s e d g e i s s t a b l e u n d e r t h e c o m b i n a t i o n o f e f f e c t i v e s e l f - w e i g h t p l u s l a t e r a l w i n d l o a d , t h e n no f u r t h e r b r a c i n g i s n e c e s s a r y . I f n o t , a t h i c k e n e d edge beam may be a d d e d . The s i m p l e s t m e t h o d , h o w e v e r , i n v o l v e s c o n n e c t i n g t h e p a n e l s t o g e t h e r so t h a t t h e c o m p r e s s i o n e d g e o f one p a n e l i s t i e d t o t h e t e n s i o n edge o f a n o t h e r and t h e c o m p l e t e w a l l a c t s a s a u n i t . When a p a n e l s u b j e c t e d t o l a r g e i n - p l a n e s h e a r s a l s o h a s l a r g e o p e n i n g s , t h e e f f e c t o f i n - p l a n e f r a m e a c t i o n mus t be c o n s i d e r e d . I n a l l c a s e s , o v e r t u r n i n g and s l i d i n g s h o u l d be c h e c k e d and t i e s p r o v i d e d t o t h e f o o t i n g o r f l o o r s l a b as r e q u i r e d . 4 . 9 P a n e l s w i t h O p e n i n g s P a n e l s w i t h o p e n i n g s c a n be a n a l y z e d by two d i m e n s i o n a l f i n i t e e l e m e n t m e t h o d s , b u t t h i s i s u s u a l l y e x p e n s i v e a n d t i m e c o n s u m i n g , and i s r a r e l y j u s t i f i e d . An a p p r o x i m a t e one d i m e n s i o n a l a n a l y s i s w i l l g i v e r e s u l t s t h a t a r e s u f f i c i e n t l y a c c u r a t e f o r mos t d e s i g n s and c a n be a d a p t e d t o h a n d c a l c u l a t i o n s . Where o p e n i n g s o c c u r , t h e l a t e r a l and a x i a l l o a d s ( i n c l u d i n g s e l f - w e i g h t ) on t h e e n t i r e p a n e l mus t be c a r r i e d by t h e c o n t i n u o u s v e r t i c a l l e g s e a c h s i d e o f t h e o p e n i n g ( s e e F i g u r e 4 . 3 ) . O f t e n i t i s o n l y n e c e s s a r y t o i n c r e a s e t h e l o a d s a c t i n g on t h e l e g s by t h e r a t i o o f t h e t o t a l p a n e l w i d t h t o t h e l e g w i d t h , a l t h o u g h some d e s i g n e r s may a l t e r n -a t i v e l y w i s h t o u s e p o i n t l o a d s e x e r t e d by w i n d o w and d o o r f r a m e s . 53 . FIGURE 4.2 IN-PLANE SHEAR B C C + C V Compression due to self weight (per unit length) C C = W C X Max. comp. due to in-plane shear V (per unit length) C v = V X - 6 / B 2 Total comp. = C C + C V = (W C + 6 V / B 2 ) X Equiv. self weight Compressive ( p e r u n i t a r e a ) Edge % - W c + 6 V / B 2 5 4 . FIGURE 4 . 3 PANELS WITH OPENINGS B Effective leg width Max. A= 12 h Load on each leg Ratio R = (C+2A)/2A Axial = PR Lateral = WR Self weight = W CR 55 . The w i d t h o f t h e l e g a s s u m e d t o be c a r r y i n g t h e s e a d d i t i o n a l l o a d s s h o u l d be r e s t r i c t e d t o a b o u t 12 t i m e s t h e p a n e l t h i c k n e s s i n o r d e r t o a v o i d t h e p o s s i b i l i t y o f l o c a l b u c k l i n g a t t h e e d g e o f t h e o p e n i n g . F o r v e r y w i d e o p e n i n g s i n e x c e s s o f 5 m, i t i s o f t e n n e c e s s a r y t o p r o v i d e a t h i c k e n e d p i l a s t e r a t e a c h v e r t i c a l e d g e and a h o r i z o n t a l h e a d e r beam a t t h e t o p ( a n d b o t t o m ) o f t h e o p e n i n g . 4 . 1 0 I s o l a t e d F o o t i n g s I s o l a t e d o r i n t e r m i t t e n t f o o t i n g s a r e n o r m a l l y e m p l o y e d i n s i t u a t i o n s w h e r e p i l i n g i s s p e c i f i e d . O t h e r w i s e , i t h a s b e e n f o u n d t h a t c o n t i n u o u s s t r i p f o o t i n g s p r o v i d e a more d e s i r a b l e means o f p a n e l s u p p o r t . An i s o l a t e d f o o t i n g a t e a c h end o f t h e p a n e l c a u s e s a b u i l d u p o f h i g h c o m p r e s s i v e s t r e s s n e a r t h e p o i n t o f s u p p o r t . The s i t u a t i o n c a n be s a t i s f a c t o r i l y s i m u l a t e d i n much t h e same way a s i n - p l a c e s h e a r by a d d i n g an e f f e c t i v e s e l f - w e i g h t and c h e c k i n g t h e p a n e l i m m e d i a t e l y a b o v e t h e f o o t i n g . I t i s common t o assume t h a t t h e l o a d s p r e a d s o u t a t an a n g l e o f a b o u t 3 0 ° t o t h e v e r t i c a l . A l t e r n a t i v e l y , t h e a x i a l c o m p r e s s i o n c a n be a s s u m e d t o i n c r e a s e l i n e a r l y f r o m t h e t o p t o b o t t o m o f t h e p a n e l a s shown i n F i g u r e 4 . 4 . The e f f e c t i v e p a n e l s e l f w e i g h t w o u l d b e : e c c _ ( b / 2 a - 1) ( w e i g h t p e r u n i t a r e a ) L O n e - h a l f o f t h e t o t a l e f f e c t i v e s e l f w e i g h t w o u l d t h e n be a p p l i e d a t t h e t o p o f t h e p a n e l . 5 5 a . FIGURE 4.4 ISOLATED FOOTINGS i Design Strip o p W rL -ir »». (P b/2a »*-PANEL ELEVATION LOAD DIAGRAM ON DESIGN STRIP 56 . 5 . COMPARISON OF RESULTS 5 . 1 E x p e r i m e n t a l V e r i f i c a t i o n o f C o m p u t e r P r o g r a m The p r o g r a m d e v e l o p e d f o r t h i s p u b l i c a t i o n was b a s e d on t h e same p r i n c i p l e s a s one u s e d p r e v i o u s l y f o r p r e s t r e s s e d c o n c r e t e w a l l p a n e l s . T h a t p r o g r a m was e x p e r i m e n t a l l y c o n f i r m e d by t e s t i n g ( R e f . 4) and by c o m p a r i s o n w i t h a l i m i t e d amount o f d a t a f r o m t e s t s by o t h e r s . 5 . 2 PCA D e s i g n A i d The PCA d e s i g n a i d f o r t i l t - u p w a l l p a n e l s ( R e f . 5) c o n t a i n s c h a r t s f o r maximum a x i a l l o a d on w a l l p a n e l s w i t h f i x e d end e c c e n t r i c i t i e s and l a t e r a l l o a d s . A d i r e c t c o m p a r i s o n i s made f o r t h e f o l l o w i n g s e l e c t e d e x a m p l e : T a b l e s B l a n d B2 h = 5k" b = 1 2 " d = 2 . 7 5 " A = 0 . 0 0 2 5 x 12 x 5k = 0 . 1 6 5 i n 2 s e c c = 2 . 7 5 " f o r w = 30 p s f PCA C o m p u t e d k L / h L ( f t ) C o e f f . P (K) P (K) u u m a x v max ' 20 9 . 1 7 0 . 0 9 6 2 5 . 3 2 7 . 5 30 1 3 . 7 5 . 0 . 0 2 8 7 . 4 7 . 5 40 1 8 . 3 3 0 . 0 0 7 1 .8 . 1 . 9 50 2 2 . 9 2 u n s t a b l e u n s t a b l e 57 . The m a t e r i a l p r o p e r t i e s w e r e i d e n t i c a l i n b o t h c a s e s , i n c l u d i n g t h e c o n c r e t e s t r e s s s t r a i n c u r v e . The r e s u l t s o b t a i n e d a r e i n c l o s e a g r e e m e n t , w i t h t h e d i f f e r e n c e s b e i n g a t t r i b u t a b l e t o t h e d e g r e e o f r e f i n e m e n t i n c o m p u t i n g s e c t i o n p r o p e r t i e s o r i n s i z e o f l o a d i n c r e m e n t s on t h e w a l l p a n e l m o d e l . The PCA r e s u l t d o e s n o t c o n t a i n an a l l o w a n c e f o r r e d u c e d s t i f f n e s s by means o f t h e c a p a c i t y r e d u c t i o n f a c t o r and i s t h e r e f o r e e x p e c t e d t o y i e l d o v e r a l l h i g h e r l o a d c a p a c i t i e s . ( T h i s r e d u c t i o n was o m i t t e d i n t h e " c o m p u t e d " v a l u e f o r t h e p u r p o s e o f t h e a b o v e c o m p a r i s o n . ) 5 . 3 A C I / C S A R e c o m m e n d a t i o n s A r e v i e w o f t h e A C I / C S A r e c o m m e n d a t i o n s ( R e f . 2 , S e c t i o n 1 0 ; R e f . 3 , S e c t i o n 8) f o r member s t i f f n e s s as a p p l i e d t o t h e d e s i g n o f l o a d b e a r i n g w a l l p a n e l s i n d i c a t e s t h a t t h e y c a n -n o t be u s e d f o r mos t t i l t - u p d e s i g n . The c o d e e q u a t i o n s a r e d e r i v e d f o r h i g h a x i a l l o a d s a n d s m a l l e c c e n t r i c i t i e s a n d a r e r e s t r i c t e d t o k L u / r v a l u e s l e s s t h a n 100 ( k L u / h : l e s s t h a n a b o u t 3 0 ) . A good number o f t i l t - u p w a l l p a n e l s a r e now b e i n g b u i l t w h e r e k L u / h i s 50 o r m o r e , and a x i a l l o a d s t r e s s e s a r e g e n e r a l l y s m a l l i n r e l a t i o n t o l a t e r a l l o a d b e n d i n g s t r e s s e s . The A C I / C S A c o d e s r e q u i r e a d e t a i l e d e v a l u a t i o n o f s l e n d e r n e s s f o r t h e s e c o n d i t i o n s b u t o f f e r v e r y l i t t l e t o g u i d e t h e d e s i g n e r . The d e s i g n a p p r o a c h d e s c r i b e d i n t h i s p a p e r m e e t s t h e r e q u i r e -m e n t s o f t h e c o d e s w i t h r e s p e c t t o t h e d e t a i l e d a n a l y s i s , and i n a d d i t i o n a l l o w s t h e d e s i g n e r t o a s s e s s t h e e f f e c t s o f a l l t h e f a c t o r s t h a t may c o n t r i b u t e t o f a i l u r e . 58 . 6. PROPOSED CHANGES TO ACI/CSA CODES As was i n d i c a t e d i n S e c t i o n 5.3, t h e p r e s e n t ACI/CSA c o d e s do n o t c o n t a i n a d e q u a t e p r o v i s i o n f o r t h e d e s i g n o f t i l t - u p w a l l p a n e l s . I n most c a s e s t h e l i m i t i n g s l e n d e r n e s s r a t i o s a r e w e l l b e l o w t h a t commonly e m p l o y e d , r e q u i r i n g t h a t a d e t a i l e d a n a l y s i s be p e r f o r m e d t o v e r i f y t h e s t a b i l i t y c o n d i t i o n . The d e s i g n c h a r t s p r e s e n t e d i n A p p e n d i x B meet t h e r e q u i r e m e n t s f o r a d e t a i l e d a n a l y s i s and may be u s e d f o r d e s i g n , s u b j e c t t o t h e l i m i t a t i o n s g i v e n i n S e c t i o n 4. I n l i e u o f t h e d e s i g n c h a r t m e thod, a s t r e n g t h c a l c u l a t i o n c a n be made where t h e m a g n i f i e d moment i s o b t a i n e d f o r a g i v e n l o a d i n g c o n d i t i o n . The d i f f i c u l t y l i e s i n o b t a i n i n g a r e a l i s t i c e s t i m a t e o f s e c t i o n s t i f f n e s s E I . T h i s s h o u l d n o r m a l l y be b a s e d on a c r a c k e d s e c t i o n w i t h f u l l c o n s i d e r -a t i o n o f t h e e f f e c t o f a x i a l l o a d . U n f o r t u n a t e l y , t h e c a l c u l a t i o n s a r e t o o i n v o l v e d f o r most d e s i g n o f f i c e s u n l e s s a c o m p u t e r o r p r o g r a m m a b l e c a l c u l a t o r i s u s e d . Owing t o t h e f a c t t h a t t h e a x i a l l o a d i s r e l a t i v e l y l i g h t , i t i s u s u a l l y s u f f i c i e n t ( and c o n s e r v a t i v e ) t o compute t h e s t i f f n e s s f o r t h e c a s e o f z e r o a x i a l l o a d o n l y and t h e n a p p l y i t t o a l l l o a d c o n d i t i o n s . I t c a n be shown t h a t t h e s t i f f n e s s o f a r e c t a n g u l a r c o n c r e t e s e c t i o n w i t h a s i n g l e l a y e r o f r e i n f o r c i n g s t e e l ( i n t h e m i d d l e ) i s as f o l l o w s : E I E bC 2 (d - C,/3)/2 c d d 6.1 E 33W 1.5 c c b w i d t h o f s e c t i o n d d e p t h t o r e i n f o r c i n g s t e e l •5 9 . C , = d e p t h t o n e u t r a l a x i s d r-2 - a + Ma + Ada „ . - 2nAs 2 ; a = —r A = a r e a o f s t e e l s n m o d u l a r r a t i o = E s / E c F o r a . s y m m e t r i c a l s e c t i o n w i t h two l a y e r s o f r e i n f o r c i n g s t e e l : E I E b C 2 ( d , - C J / 3 ) / 2 + E A ( d P - d , ) (C , - d , ) 6 . 2 c d c d s s ^ ^ d 1 The s e c o n d t e r m i s u s u a l l y l e s s t h a n 5% o f t h e f i r s t a n d t h e e q u a t i o n c a n be r e d u c e d t o : E I E b C 2 (d ; - C , / 3 ) 1 2 6 . 3 C Q Q i d = d e p t h o f t e n s i o n r e i n f o r c e m e n t C : = - 2 a + J ( 2 a ) 2 + 4 a h 2 a = as b e f o r e h = t o t a l d e p t h o f . s e c t i o n T h e s e f o r m u l a a r e b a s e d on t h e c r a c k e d s e c t i o n i n w h i c h c o n c r e t e and s t e e l s t r e s s e s a r e a p p r o x i m a t e l y l i n e a r w i t h s t r a i n and r e i n f o r c i n g s t e e l h a s n o t y e t y i e l d e d . F o r t h i s t y p e o f s e c t i o n , t h e c o n c r e t e s t r a i n i s o f t h e o r d e r o f 0 . 0 0 1 when g r a d e 60 r e i n f o r c i n g y i e l d s ( s t r a i n = . 0 0 2 1 ) . A c o m p a r i s o n o f t h e p r e d i c t e d s t i f f n e s s by e q u a t i o n s 6 . 1 and 6 . 3 c a n be made w i t h t h e c h a r t s o f A p p e n d i x C . F o r e x a m p l e , a 5h" p a n e l r e i n f o r c e d i n t h e m i d d l e w i t h 0 . 3 0 n 6 2 i n / f t . c o m p u t e d E I = 4 0 . 8 x 10 P - i n ( s e e c h a r t C3 f o r c o m p a r i s o n ) . A 5 V p a n e l w i t h two l a y e r s o f r e i n f o r c e m e n t 0 . 3 0 i n / f t . 6 2 e a c h f a c e g i v e s a c o m p u t e d E I = 1 1 7 . 3 x 10 P - i n ( s e e c h a r t C 9 ) . T h u s , t h e c r a c k e d s e c t i o n s t i f f n e s s e s a s c a l c u l a t e d by e q u a t i o n s 6 . 1 and 6 . 3 c a n be u s e d i n t h e a b o v e f o r m u l a s f o r moment m a g n i f i c a t i o n g i v i n g r e a s o n a b l y a c c u r a t e b u t c o n s e r v a t i v e r e s u l t s . The m a g n i f i c a t i o n f a c t o r o b t a i n e d w i t h t h e s e s t i f f n e s s v a l u e s s h o u l d n o t e x c e e d 1 . 5 s i n c e d e f l e c t i o n s become l a r g e and i n s t a b i l i t y i s e m i n e n t . A t h i g h e r l e v e l s o f a x i a l c o m p r e s s i o n , t h e c a p a c i t i e s p r e d i c t e d by t h i s m e t h o d w o u l d r e s u l t i n i n c r e a s i n g l y u n e c o n o m i c a l d e s i g n s and d e s i g n c h a r t s s u c h a s t h o s e i n A p p e n d i x B s h o u l d be c o n s u l t e d . 61 . L I S T OF REFERENCES 1 . G a l a m b o s , T . V . , " C o l u m n D e f l e c t i o n C u r v e s " , L e c t u r e N o . 9 , P l a s t i c D e s i g n o f M u l t i - S t o r e y F r a m e s , F r i t z E n g i n e e r i n g L a b o r a t o r y R e p o r t N o . 2 7 3 - 2 0 , L e h i g h U n i v e r s i t y , 1 9 6 5 . 2 . A C I C o m m i t t e e 3 1 8 , " A C I S t a n d a r d B u i l d i n g Code R e q u i r e m e n t s f o r R e i n f o r c e d C o n c r e t e ( A C I 3 1 8 - 7 7 ) " , A m e r i c a n C o n c r e t e I n s t i t u t e , D e t r o i t , M i c h i g a n , 1 9 7 7 . 3 . CSA C A N 3 - A 2 3 . 3 - M 7 7 , " C o d e f o r t h e D e s i g n o f C o n c r e t e S t r u c t u r e s f o r B u i l d i n g s " , 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 , 1 9 7 7 . 4 . A l c o c k , W . J . , and N a t h a n , N . D . , "Moment M a g n i f i c a t i o n T e s t s o f P r e s t r e s s e d C o n c r e t e C o l u m n s " , P C I J o u r n a l , J u l y - A u g u s t , 1 9 7 7 . 5 . K r i p a n a r a y a n a n , K . M . , " T i l t - u p L o a d - B e a r i n g W a l l s " , The P o r t l a n d Cement A s s o c i a t i o n P u b l i c a t i o n EBO 7 4 . 0 1 D , 1 9 7 4 . O t h e r R e l e v a n t P u b l i c a t i o n s 1 . M a c G r e g o r , J . G . , O e l h a f e n , U . H . and H a g e , S . E . , " A R e - e x a m i n a t i o n o f t h e E I v a l u e f o r S l e n d e r C o l u m n s " P u b l i c a t i o n S P - 5 0 - 1 , The A m e r i c a n C o n c r e t e I n s t i t u t e . 2 . N a t h a n , N . D . , " S l e n d e r n e s s o f P r e s t r e s s e d C o n c r e t e B e a m - C o l u m n s " , P C I J o u r n a l , V . 1 7 , N o . 6 , N o v e m b e r -D e c e m b e r , 1972 . A P P E N D I X A N o t a t i o n g r o s s a r e a o f c o n c r e t e s e c t i o n a r e a o f r e i n f o r c i n g s t e e l w i d t h o f p a n e l c o m p r e s s i v e f o r c e d e p t h o f n e u t r a l a x i s d e p t h t o r e i n f o r c i n g s t e e l e c c e n t r i c i t y c o n c r e t e s t r a i n s t e e l s t r a i n c o n c r e t e e l a s t i c m o d u l u s s t e e l e l a s t i c m o d u l u s s t r e s s i n c o n c r e t e s t r e s s i n s t e e l t o t a l d e p t h o f c o n c r e t e s e c t i o n h e i g h t o f w a l l p a n e l b e n d i n g moment m o d u l a r r a t i o a x i a l f o r c e on p a n e l l a t e r a l l o a d on p a n e l s e l f w e i g h t o f p a n e l e f f e c t i v e p a n e l s e l f w e i g h t l a t e r a l d e f l e c t i o n s l o p e o f c u r v e c u r v a t u r e c a p a c i t y r e d u c t i o n f a c t o r A P P E N D I X B LOAD C A P A C I T Y CHARTS A X I A L L O A D / U N M A G N I F I E D MOMENT CONCRETE WALL P A N E L DESIGN CHART £ \ Q < O < X < 2 Z3 2 X <£ 2 MATERIAL PROPERTIES f'c=25 MPa f y = 400 MPa h = 140 mm h/2 h / 2 160 . 140. 120. 100. 80. 60. 40 20. SECTION / ART l = 300 / / CH / A s / l/ L=( / \ \ m / — tj \ r 4 6 8 10 12 14 MAXIMUM MOMENT M 16 18 20 ( k N - m / m ) 22 24 CHART A 2 A s =400 mm/m 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CONCRETE WALL P A N E L DESIGN CHART -65 E \ z a < o X < z X < s MATERIAL PROPERTIES f c=25 MPa P f y = 400 MPa h =140 mm h/2 h/2 W 160 • 140. 120. 100. 80 . 60-40 . 20. 160 • 140. 120. 100. 80 . 60-40. 20. SECTION CHART A3 A s= 500 mm/m 0 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) CHART A 4 As= 600 mm/m 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL P A N E L DESIGN CHART O 2 4 6 8 10 12 14 16 18 20 22 24 _j MAXIMUM MOMENT M (kN-m/m) < 0 2 4 6 . 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) C O N C R E T E W A L L PANEL DES IGN C H A R T MATERIAL PROPERTIES f c = 25 MPa f y=400 MPa h/2 h = 140 mm - A s h/2 2 < O _J < < 400 330 2 300 < 2 250 200 SECTION CHART A 7 A S=I200 mrrrym 0 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CHART A 8 A s= 1400 mrrrvm 5 10 15 20 25 30 35 40 45 00 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL P A N E L DESIGN CHART 6 8 . E \ Q < O < X < 2 r> 2 X < 2 MATERIAL PROPERTIES fJ. = 25 MPa f y = 400 MPa h = 165 mm e . | P h/2 h / 2 W 160 . 140. 160 4 140. ± 120. 100. 80. 60. 40. 20. SECTION CHART A 9 A s= 300 mm/m 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CHART A 10 A s =400 mm/m 1 1 1 1 r 0 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CONCRETE WALL P A N E L . DESIGN CHART ,6 9 E \ z Q < O X < MATERIAL PROPERTIES f|-*25 MPa P f y = 400 MPa h = 165 mm h/2 - A s h / 2 W 160 . 140. 120. 100-80 • 160 . 140. S ZJ m 120. X < 100. 80. 60. 40-20. SECTION CHART A l l A s= 500 mm/m 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CHART A 12 A s= 600 mm/m 4 6 8 10 12 MAXIMUM MOMENT 18 20 22 (kN-m / m ) 24 CONCRETE WALL PANEL DESIGN CHART 70 £ \ < O _1 X < 2 ZJ 2 X •< 2 MATERIAL PROPERTIES f^=25 MPa f y = 400 MPa h = 165 mm 160 140 120 100 L A s= 800 mm/m 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CHART A 14 A s= 1000 mm/m 1 r 0 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) C O N C R E T E W A L L P A N E L D E S I G N C H A R T -71. MATERIAL PROPERTIES f c =25 MPa f y=400 MPa h/2 h = 165 mm h/2 W E 2 a < o < < 2 X < 400 SECTION CHART A 15 As= 1200 mrr^ /m 0 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CHART A 16 A s=|400 mmvm 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART E \ < O < X < s ZD 5 X < 2 MATERIAL PROPERTIES fc*25 MPa f y = 400 MPa h = 190 mm 160 160 140 120 100 A s= 300 mm/m 0 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CHART A IS A s= 400 mm/m 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) C O N C R E T E W A L L P A N E L D E S I G N C H A R T E \ Q < O _J < X < 2 ZD 2 X < MATERIAL PROPERTIES f'c=2S MPa P f y = 400 MPa h = 190 mm h/2 h / 2 L 160 • 1 4 0 . 1 2 0 . 100-8 0 • 6 0 . 4 0 . 2 0 . 160 • 1 4 0 . 1 2 0 . 1 0 0 . SECTION CHART A 19 A s= 500 mm/m 2 4 6 8 10 12 14 16 18 2 0 2 2 2 4 MAXIMUM MOMENT M ( k N - m / m ) CHART A 20 A s= 600 mm/m 4 6 8 10 12 14 16 18 2 0 2 2 2 4 MAXIMUM MOMENT M ( k N - m / m ) CONCRETE WALL PANEL DESIGN CHART ,7 E \ z a < o _i X < s 5 MATERIAL PROPERTIES fj- = 25 MPa f y = 400 MPa h = 190 mm 160 160 140 ZZ 120 X < 100 A s= 800 mm/m 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) CHART A 22 A s= 1000 mm/m i r 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M ( k N - m / m ) C O N C R E T E W A L L P A N E L D E S I G N C H A R T 75 2 -5C Q < O _J < < X < 2 MATERIAL PROPERTIES f c =25 MPa f y =400 MPa h = 190 mm h/2 /I h/2 ->»-W 400 350 300 250 • 200' 150 • 100 • 50 • 400' 350 • 300 250' 200 • 150 • 100 • 50 • SECTION . CHART A 23 . As= 1200 mrrfym 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CHART A 24 A s= 1400 mrrr/m Uo 0 5 10 15 20 25 30 35 4 0 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART 76. E \ z CL a < o < X < X < 2 MATERIAL PROPERTIES f c - 2 5 M P a A c f s « 4 0 0 MPa h « 140 mm 20 mm 20 mm W 140 SECTION CHART Bl A s = 3 0 0 mmym 2 4 6 8 10 12 14 16 18 20 2 2 24 MAXIMUM MOMENT M (kN-m/m) CHART B2 A s = 4 0 0 mm/m L i O 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) C O N C R E T E W A L L P A N E L DESIGN C H A R T O 2 4 6 8 10 12 1 4 16 18 2 0 2 2 2 4 MAXIMUM MOMENT M (KN-m/m) < x < 2 CONCRETE WALL PANEL DESIGN CHART 2 Q < O MATERIAL PROPERTIES f'c=25 MPa fy»400 MPa h = |40 rnm 2 0 m m -As 20 mm 1 W 400-SECTION CHART B5 As = 800 mm/m 10 15 20 25 30 MAXIMUM MOMENT 35 40 45 50 55 60 M (kN-m/m) T 5 CHART B6 A s= 1000 mmf/m 10 15 20 25 30 35 4 0 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) C O N C R E T E W A L L P A N E L DES IGN C H A R T 0 5 10 15 20 25 30 35 . 40 45 50 55 60 _j MAXIMUM MOMENT M (kN-m/m) < 0 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART 80. E Q < O < X < 2 2 X < MATERIAL PROPERTIES f c » 2 5 MPa A f S " 4 0 0 MPa h • 165 mm 20 mm - A s 20 mm W SECTION CHART B 9 A s=300 mrnyrn 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) CHART BIO A s = 400 rnmym 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) C O N C R E T E W A L L P A N E L D E S I G N C H A R T h MATERIAL PROPERTIES — f'c-25 MPa A s ^ it) fft /As fy-400 MPa 20mm 20 mm 81. Z Q < O _J < X < 2 X < 2 h * 165 mm W 4 0 0 . 350-300-2 5 0 • 200-150-100-50-0 • SECTION CHART Bl! A s = 500 mm2/m 0 5 10 15 20 25 30 35 4 0 45 50 55 6 0 MAXIMUM MOMENT M (kN-m/m) L=0 CHART BI2 A s =600 mm^m 10 15 20 25 30 35 4 0 45 50 55 6 0 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART O 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) < CONCRETE WALL PANEL DESIGN CHART 83. 2 CL Q < O < X < 2 ZD X < 2 MATERIAL PROPERTIES f'c»25 MPa fy-400 MPa h =165 mm 20mm k> el 20 mm 400 4 SECTION CHART B 15 A s= 1200 mm/Tn 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CHART B 16 A s= 1400 mm^ m 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART 3 4 . E Q < O _J _J < < 2 ZD 2 X < 2 MATERIAL PROPERTIES f c - 2 5 MPa f s ° 4 0 0 MPa h « 190 mm CHART B 17 A s = 300 mm/m 2 4 6 8 10 12 14 16 18 20 2 2 24 MAXIMUM MOMENT M (kN-m/m) CHART B 18 A s= 400 mmVm 2 4 6 8 10 12 14 16 18 20 22 24 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART • Q < O MATERIAL PROPERTIES fc = 25 MPa fy-400 MPa h * 190 mm 400 A s =500 mm/m 5 10 15 20 25 30 35 40 43 50 55 60 MAXIMUM MOMENT M (kN-m/m) X < 2 2 X < 2 CHART B 20 ' A s = 600 mm2' m -l ! r 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART 86. O 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) 0 5 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CONCRETE WALL PANEL DESIGN CHART z < O < X < 2 X < MATERIAL PROPERTIES f ' c = 25 MPa fy»400 MPa h » 190 mm 20 mm -As 20 mm W 400-350-300-250-200-150-100-50-400-350-300-250-200-150 • 100 50' SECTION CHART B 2 3 ,= 1200 mm7m 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) CHART B 2 4 A s = |400mm7m 10 15 20 25 30 35 40 45 50 55 60 MAXIMUM MOMENT M (kN-m/m) A P P E N D I X C AVERAGE S T I F F N E S S CHARTS C O N C R E T E WALL P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S i l l * , f ' c = 4 0 0 0 PSI f y = 6 0 0 0 0 PSI 5.5" Hi. T A , 2.75" PTMU SECTION Ag-.IO m 2/ft 160 4 o o o c 40 i UJ i — i — i s 1 i r~— i —T— i r 0 10 20 30 40 50 60 70 80 90 100 110 M O M E N T M u in-k AS=.I5 m2/ft -4-10 20 30 40 50 60 70 80 90 100 110 M O M E N T Mu m-k C O N C R E T E WALL P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 9 0 . fc= 4000 PSI fy= 60000 PSI 5.5" T A. 2.75 PTMU SECTION i&o -4 o o o « UJ M O M E N T M, in-k AJJ-,20 \u z/U A s=.25 m2/ft 1 0 2 0 3 0 4 0 5 0 6 0 7 0 6 0 9 0 1 0 0 110 M O M E N T M u in-k C O N C R E T E W A L L P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S f c = 4 0 0 0 PS I f y » 6 0 0 0 0 PS I 5.5" = ° I in-k A j - .30 in< i t i 1—~ r — T 10 20 50 40 50 60 70 80 SO 100 110 M O M E N T M, A s =.35 i n ' 20 30 40 50 60 70 80 90 IOO 110 M O M E N T M, in-k C O N C R E T E W A L L P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 92 . fc= 4000 PSI fy » 60000 PSI 5.5" T A . 2.75 M, S E C T I O N A^.40 in 2/ff As=.45 ,n z/ft 20 30 40 50 60 70 80 90 100 110 M O M E N T M u in-k C O N C R E T E W A L L P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 93 f c = 4 0 0 0 PSI f y = 6 0 0 0 0 PSI 5.5" 160 -4 140 120 100 80 o o 2 60 c 40 T 20 UJ CO CO LU u_ U. p C O •z o 1-o UJ CO o A T A, to 2.75 S E C T I O N in-k A ^ ' 5 0 in 2 / f t —j { ^ j ! j p—-j-10 20 30 40 50 60 70 80 90 100 110 M O M E N T M, A s = . 5 5 in 2/Yt 100 110 M O M E N T M u in-k CONCRETE WALL PANEL SECTION STIFFNESS PROPERTIES 94. f c = 4000 PSI f y - 6 0 0 0 0 PSI 5.5" o o o 1 U J cn L U z L L L L P co 2 O h-O LU CO 400 3/41 — > i J A, AJ 3/4" SECTION J I I i J ! I I C i 0 10 20 30 40 50 60 70 80 90 MOMENT Mu in-k Ag-jo in 2/ft 100 110 A s=.i5 i n 2 / f t 10 20 30 40 50 60 70 80 90 K>0 110 MOMENT Mu in-k C O N C R E T E W A L L P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S f ' c = 4 0 0 0 P S I f y - 6 0 0 0 0 P S I 5.5" 3/4' H r r Hi, As A, 3/4" < t — PTMU S E C T I O N M O M E N T M, in-k As- .20in 2/ft 10 20 30 40 50 60 70 80 90 100 110 A s=.25 m 2 / f t 10 20 30 40 50 60 70 eO 90 100 110 M O M E N T M u i n-k C O N C R E T E WALL P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 96 f ' c = 4 0 0 0 PSI f y » 6 0 0 0 0 P S I 5.5" o o o I LU CO CO LU z u. P CO o H o LU CO Aj A, M. 3/4" SECTION A 3-.30 i n 2 / f t 6 20 40 60 80 100 120 140 160 180 2*00 220 M O M E N T M u in-k A s = . 3 5 m 2 / f t 4 0 0 - r " 1 0 20 4*0 60 80 100 120 140 160 180 200 220 M O M E N T M u m-k C O N C R E T E WALL P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 97 f c = 4 0 0 0 PSI f y - 6 0 0 0 0 PSI 3/4 5.5" [ I T A, AJ 3/4" PTMU S E C T I O N A ^ - .4 0 i n 2 / f t o o o c 100 I L U 400 350 300 250 200 150 20 40 60 80 100 120 140 ISO ISO 200 220 M O M E N T M, in-k A s = . 4 5 t n 2/ft O 20 40 60 80 100 120 140 160 180 200 220 M O M E N T M u in-k C O N C R E T E WALL P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 98 f ' c = 4 0 0 0 PSI f y - 6 0 0 0 0 PSI 5.5" 400 -I 350 300 250 200 o o o OJ 150 c 100 i L U 3/4 — * -I I A» AJ _3/4" S E C T I O N .50 irfyft M O M E N T M, in-k As=.55 m 2 / f t 0 2 0 4 0 6 0 8 0 100 120 140 160 180 2 00 . 220 M O M E N T M u in-k C O N C R E T E W A L L P A N E L S E C T I O N S T I F F N E S S P R O P E R T I E S 99. f c = 4 0 0 0 PSI f y = 6 0 0 0 0 PSI 5.5"' 400 -4 o o o t U J CO CO U J u. u. CO O h-O UJ CO As-.60 !n2/ff i i i i t t i i 20 40 60 80 100 120 140 160 ISO 200 220 M O M E N T M, 'u in-k A s = .65 m 2 / f t 20 40 60 80 100 120 140 160 180 200 220 M O M E N T M u io-k A P P E N D I X D LOAD C A P A C I T Y CHARTS A X I A L L O A D / L A T E R A L LOAD C O N C R E T E W A L L P A N E L AXIAI 1 P A D C A P A C I T Y 101 h « 5.5 |N As= -10 I N 2 / FT f'c = 4 0 0 0 PSI fy = 6 0 0 0 0 PSI 4 0 —<x h/2 S E C T I O N i e W„ to m o o o a. Q o 25-— 20-< r-_J 3 15-10-e = 4. o o" f 20_ - 1 5 ^ i 10 2 0 3 0 40 50 60 70 80 90 100 110 W U P SF C O N C R E T E W A L L P A N E L -A X I A L L O A D C A P A C I T Y 102 . h -5 .5 As = . l5 I N V F T f'c=4000 PSI fy= 6 0 0 0 0 PSI 4 0 m o o o C L < O < UJ < H _ l 3 w „ 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100 110 WU P S F e = 4.oo C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 1 0 3 . h -'5.5 IN As= . 2 0 I N 2 / F T f c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI h/2 e S E C T I O N W„ m o o o 0-< O C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 104 C O N C R E T E W A L L P A N E L 105. A X I A L L O A D C A P A C I T Y O 10 20 30 40 50 60 70 80 90 100 110 < . - • - . W U PSF 25 0 10 20 30 40 50 60 70 80 90 100 110 Wu PS F CONCRETE WALL PANEL' AXIAL LOAD CAPACITY 106 I N V FT f c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI C O N C R E T E W A L L P A N E L ' A X I A L L O A D C A P A C I T Y 107 h = 5.5 |N As=.40 IN 2/ FT fc = 4 0 0 0 PSI fy= 60 000 PSI 'r-V h/2 I e 1a W„ SECTION co m o o o 3 Q < O UJ r-< _ l 3 CONCRETE WALL PANEL' AXIAL LOAD CAPACITY 108 . h -'5.5 IN As* -45 IN2/ FT f'c = 4 0 0 0 PSI fy= 60 000 PSI h/2 i e W„ SECTION m o o o 3 fx < O e = 4.oo t— < r-C O N C R E T E W A L L P A N E L -A X I A L L O A D C A P A C I T Y 1 0 9 . 0 10 20 30 40 50 60 70 80 90 100 f 10 Wu PSF e a 6 . o o " 0 10 20 30 40 50 60 70 80 90 100 110 W l ) P S F  C O N C R E T E W A L L P A N E L ' A X I A L L O A D C A P A C I T Y 110 h - 5.5 IN As=.55 I N 2 / F T f'c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI , A h/2 — / I e — A u W„ S E C T I O N C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 111 h * 5.5 |N A s * .10 I N 2 / FT f'c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI 5M" A 6 A S E C T I O N e u —<-W„ to CQ o o o 80-70 60-50 • 40 • 30 • 20 • 10-CL < O L= 10'. Ft. e=2.75' < s ZD 50 40 • 30 • 20 • 10--I e = 4.oo 30. 20-10 e«6.oo 10 20 30 40 50 60 70 80 90 100 110 W l i P S F CONCRETE WALL PANEL AXIAL LOAD CAPACITY 112 h -5.5 |N A s * .15 IN 2/ FT f'c = 4000 PSI fy= 60 000 PSI CONCRETE WALL PANEL AXIAL LOAD CAPACITY 113, h -'5.5 [N A s * . 2 0 I N 2 / F T f ' c = 4 0 0 0 PS! fy= 6 0 0 0 0 PSI e 5 / 4 " A.AJ; S E C T I O N CO m 80 70 60 50 40 e=2:75' 30. e-6.00 C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 114 h - '5.5 IN A s » . 2 5 I N 2 / FT f' c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI 8 /4 " A $ AJ I /y_ S E C T I O N e 80 70 60 50 m 40 o o o 3 CL < O L=I0' e=2.75' 10 20 30 40 50 60 70 80 90 100 110 W U PSF 30, e-6.oo" C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 115 . A s » . 3 0 I N 2 / FT f'c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 116. h - 5 . 5 |N A s * .35. I N 2 / FT f'c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI e 3 / 4 " A s A L W„ S E C T I O N CONCRETE WALL PANEL' AXIAL LOAD CAPACITY 117 h - 5 . 5 |N A s - . 40 . I N 2 / F T f'c = 4 0 0 0 PSI f'y = 6 0 0 0 0 PSI e h-v-5 / 4 " A, A, I /y -w „ SECTION C O N C R E T E W A L L P A N E L 1 1 8 . A X I A L L O A D C A P A C I T Y O 10 20 30 40 50 60 70 80 90 100 110 W U P S F O O 10 20 30 40 50 60 70 80 90 100 110 Wl) P S F  C O N C R E T E W A L L P A N E L A X I A L L O A D C A P A C I T Y 119 h - '5.5 IN A s * .50 . I N 2 / F T f c = 4 0 0 0 PSI fy= 6 0 0 0 0 PSI 8/4" 80-70 60 A^ S E C T I O N - i > u W„ L=IO'-e= 2.75' 3 0 4 •10' e°6.oo C O N C R E T E W A L L P A N E L -A X I A L L O A D C A P A C I T Y 120 h - 5 .5 |N As=.55 I N 2 / F T f ' c = 4 0 0 0 PSI f y = 6 0 0 0 0 PSI e 3 / 4 " A, A, W„ S E C T I O N C O N C R E T E W A L L P A N E L ' A X I A L L O A D C A P A C I T Y 121 CONCRETE WALL PANEL-AXIAL LOAD CAPACITY 122 CONCRETE WALL PANEL AXIAL LOAD CAPACITY 123 A P P E N D I X E DESIGN EXAMPLES 125. DESIGN EXAMPLE #1 S I M P L E P A N E L , J O I S T LOADING 8 . 5 m I.O -z-0 2.0 e o tfa aj 1.5 7.1 i»> C3rft G i v e n f ' c = 25 MPa ( n o r m a l w g t . ) f y = 400 MPa P a n e l t h i c k n e s s h = 140 mm P a n e l s u p p o r t e d a t r o o f j o i s t and f l o o r l e v e l s , J o i s t r e a c . W ind l o a d R = 7 . 5 D + 1 5 . O L = 2 2 . 5 kN +W » 0 . 5 5 x (2 x . 7 + . 3 ) = 0 . 9 4 k N / m ' -W = 0 . 5 5 x (2 z . 7 - . 3 ) = 0 . 6 1 A s s u m e : J o i s t l o a d a c t s l i k e U . D . L . P = 2 2 . 5 / 2 . 0 = 1 1 . 2 5 k N / m ( 3 . 7 5 D + 7 . 5 0 L ) L o a d ECC = 70 mm f o r - w i n d 0 mm f o r + w i n d I n i t . d e f ' n . & c r e e p Yo = 20 mm @ m i d h e i g h t Span = 6 . 8 m, p i n n e d - p i n n e d s u p p o r t R e i n f . i n c e n t r e o f s e c t i o n d = 70 mm C r i t i c a l l o a d c a s e : d e a d p l u s +ve w i n d A x i a l l o a d a t m i d h e i g h t P = 1 .4 x ( 3 . 7 5 + 24 x . 1 4 0 x 6 . 8 / 2 ) = 2 1 . 2 k N / m u Maximum a p p l i e d moment ~ M = 1 .7 x 0 . 9 4 x 6 . 8 / 8 + 2 1 . 2 x 0 . 0 2 0 = 9 . 6 6 k N - m / m a 7 From c h a r t A 5 , A g = 800 mm /m F o r P = 2 1 . 2 k N / m , L = 6 . 8 m u 7 M a x . M = 1 3 . 0 k N - m / m O . K . a P r o v i d e #15 @ 250 mm o / c , A = 800 mm /m s 126 . DESIGN EXAMPLE #2 PANEL WITH OPENING 8 . 5 rr. L-M. L E G . T J (7.14. o. 3m 7.1 rvx G i v e n : Same span and l o a d i n g as Example #1. T r u c k door o p e n i n g as shown R.H. L e g : Assume 1 . 0 m wide s t r i p c a r r i e d l o a d s from 1 / 2 w i d t h of o p e n i n g . A x i a l l o a d a t mid h e i g h t : P = 1 . 4 x ( 3 . 7 5 + 2 4 x . 1 4 0 x 6 . 8 / 2 ) x 1 . 7 5 + 1 . 0 C „ - . , u — Q = 5 8 . 3 kN/ Maximum a p p l i e d moment: M = 9 . 6 6 x 2 . 7 5 = 2 6 . 5 7 kN-m/m m From C h a r t B6 A = 1000 mm /m E.F. s For P = 58.3 kN/m, L = 6.8 m u Max. M = 27.5 kn-m/m O.K. a P r o v i d e 5 #15 E.F., A = 1000 mm s L.H. Leg - max. e f f e c t i v e w i d t h = 1.75 m P = 21 . 2 x 1 . 75 + 1 . 75 .„ . , .. , u j—Y$ = 42.4 kN/m M = 9.66 x 1 . 75 + 1 . 75 , Q „ . „ , a j — = 19.3 kN-m/m 2 From C h a r t B5, A = 800 mm /m E.F. Max. M = 24 SkN-m/m O.K. P r o v i d e #15 @ 250 mm E.F. A = 800 mm2/m E.F. s F o r 1.75 m w i d t h Remainder of L.H. Leg #15 @ 400 mm E.F. 127 . DESIGN EXAMPLE #3 EXTENSION BELOW FLOOR SLAB 8 - 5 m |.S m G i v e n : Same a s E x a m p l e #1 w i t h e x t e n s i o n b e l o w f l o o r s l a b . E f f e c t o f s o i l p r e s s u r e and r o o f d e f l e c t i o n i g n o r e d . A s s u m e : E f f e c t i v e s p a n = 0 . 8 5 x 6 . 8 = 5 . 7 8 m F o r D + W l o a d i n g : P = 2 1 . 2 k N / m ( f r o m E x a m p l e #1) u A s s u m e : M a x . s p a n moment = m a x . s u p p o r t moment = W L 2 / 1 1 . 6 M = 1 .7 x 0 . 9 4 x 6 . 8 2 / 1 1 . 6 + 2 1 . 2 x . 0 2 0 = 6 . 7 9 k N - m / m a F rom C h a r t A 2 , A = 400 mm /m CTR s F o r P = 2.1.2 L = 5 . 7 8 m u u M a x . M = 7 . 0 k N - m / m O . K . a P r o v i d e #15 @ 400 mm o / c , i n c e n t r e A = 5 0 0 m m / m s 128 . DESIGN EXAMPLE #4 ISOLATED FOOTING ~a cr—A—CJ T o • # — i l 0.3 m G i v e n : Same s p a n and l o a d i n g a s E x a m p l e #1 . P a n e l s u p p o r t e d on p a d f o o t i n g s a s s h o w n . Assume d i s t r i b u t i o n o f v e r t i c a l l o a d i n t o d e s i g n s t r i p a b o v e f o o t i n g i s l i n e a r f r o m t o p t o b o t t o m . E f f e c t i v e s e l f - w e i g h t i n d e s i g n s t r i p : W = . 1 4 0 x 24 + 3 . 7 5 + . 1 4 0 x 24 x 7 . 1 ( 8 . 5 - 1) e 7 . 1 ( 2 x . 6 ) = 3 . 3 6 + 2 3 . 6 4 = 2 7 . 0 k N / m 2 P u = 1 .4 (27 x 6 . 8 / 2 + 3 . 7 5 ) = 1 3 3 . 8 k N / m M = 9 . 6 6 kN -m/m ( f r o m E x a m p l e #1) a 2 F rom C h a r t B 5 , A g = 800 mm /m E . F . F o r P = 1 3 3 . 8 L = 6 . 8 m u M a x . M = 1 1 . 0 kN -m/m O . K . a P r o v i d e #15 @ 250 mm E . F . A = 800 mm 2 /m E . F . o v e r i s o l a t i n g f o o t i n g 

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