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Building Damage Caused by Deflection of Reinforced Concrete
Building Components
Mayer, H.; Rusch, H.
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NATIONAL RESEARCH COUNCIL OF C A N A D A T e c h n i c a l T r a n s l a t i o n 1 4 1 2 T i t l e : B u i l d i n g damage c a u s e d by d e f l e c t i o n o f r e i n f o r c e d c o n c r e t e b u i l d i n g c o m p o n e n t s ( B a u s c h a d e n a l s F o l f e d e r D u r c h b i e g u n g von S t a h l b e t o n - B a u t e i l e n ) A u t h o r s : H o r s t Mayer a n d H u b e r t RCsch R e f e r e n c e : D e u t s c h e r A u s s c h u s s f G r S t a h l b e t o n , H e f t 1 9 3 , B e r l i n 1 9 6 7 . 90 p . T r a n s l a t o r : J . H . R a i n e r , B u i l d i n g P h y s i c s S e c t i o n , D i v i s i o n o f B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l
PREFACE
The problem of deflection damage in reinforced concrete structures has been of interest to the Division of Building Research in connection with its technical support role to the Associate Committee on the National Building
Code. The widespread occurrence of loss of serviceability
and visual cases of damage in concrete structures, particularly in connection with partition walls supported by concrete
members, emphasizes the importance of studying the causes which contribute to this phenomenon.
The extensive survey of damage and subsequent analysis carried out and reported by the Testing Institute for Materials and Structures of the Technical University, Munich, Germany, represents an important contribution to an understanding of the cause of deflection damages in reinforced
concrete buildings. The remedial or preventive measures which
are suggested, both in the design phase as well as during con- struction, should prove to be of interest to designers, builders, and researchers concerned with the uses of reinforced concrete.
The translation has been prepared by J.H. Rainer, Research Officer, Building Physics Section, Division of
Building Research, and checked and revised by D.A. Sinclair, Chief Translator, National Science Library, National Research Council.
Ottawa May 1970
N.B. Hutcheon Director, DBR/NRC
FOREWORD
Damage i n a f i n i s h e d s t r u c t u r e c a n u s u a l l y be t r a c e d t o u n s a t i s f a c t o r y c o n s t r u c t i o n m e t h o d s . The e v i d e n c e s o f damage a n d t h e i r
c a u s e s a r e n u m e r o u s . The t y p e s o f damage t r e a t e d i n t h i s r e p o r t , how-
e v e r , c o n s t i t u t e a s p e c i a l c a t e g o r y . A s a r u l e t h e y o c c u r r e d d u e t o u n e x p e c t e d l y l a r g e d e f l e c t i o n s o f r e i n f o r c e d c o n c r e t e c o m p o n e n t s t h a t h a v e i n t h e l a s t few y e a r s b e e n o b s e r v e d w i t h i n c r e a s i n g f r e q u e n c y . A l r e a d y i n 1 9 5 8 t h e German R e i n f o r c e d C o n c r e t e A s s o c i a t i o n f o u n d i t d e s i r a b l e t o i n v e s t i g a t e t h e c a u s e s o f e x c e s s i v e d e f l e c t i o n s o f r e i n f o r c e d c o n c r e t e b u i l d i n g c o m p o n e n t s a n d t o a d o p t s u i t a b l e m e a s u r e s .
I t was shown t h a t t h e d e f l e c t i o n c a l c u l a t i o n s commonly u s e d u n t i l t h e n w e r e u n s u i t a b l e s i n c e a n u n c r a c k e d s e c t i o n ( S t a t e I ) was a s s u m e d a n d c r e e p a n d s h r i n k a g e o f t h e c o n c r e t e h a d b e e n n e g l e c t e d . D u r i n g t h e d e l i b e r a t i o n s i t became a l s o a p p a r e n t t h a t i t was t h e n n o t p o s s i b l e t o recommend r e l i a b l e m e t h o d s o f a n a l y s i s a n d r e l e v a n t l i m i t i n g v a l u e s f o r a maximum p e r m i s s i b l e d e f l e c t i o n . I n o r d e r t o remove t h i s u n c e r t a i n t y v a r i o u s r e s e a r c h p r o g r a m s w e r e c a r r i e d o u t , o n e o f w h i c h i s t h e s u b s e q u e n t c o l l e c t i o n a n d a n a l y s i s o f o b s e r v e d c a s e s o f b u i l d i n g damage. The f i n a n c i a l s u p p o r t f o r t h i s i n v e s t i g a t i o n was p r o v i d e d by t h e F e d e r a l M i n i s t r y o f H o u s i n g a n d C i t y C o n s t r u c t i o n , t o whom s p e c i a l t h a n k s a r e e x t e n d e d h e r e w i t h . Warm t h a n k s a r e d u e a l s o t o t h e members o f t h e T a s k F o r c e o n D e f l e c t i o n s o f t h e German R e i n f o r c e d C o n c r e t e A s s o c i a t i o n , p a r t i c u l a r l y t o P r o f e s s o r s D r . - I n g . G . F r a n z , D r . - I n g . S . H a s e n j g g e r , D r . - I n g . F . L e o n h a r d t , D r . - I n g . A . Mehmel, a n d D r . - I n g . K . P i e p e r . We a r e p a r t i c u l a r l y g r a t e f u l t o a l l f e d e r a l a n d s t a t e o f f i c i a l s a s w e l l a s t h e numerous p r i v a t e c o n c e r n s a n d e n g i n e e r i n g d e s i g n o f f i c e s f o r t h e i r a c t i v e s u p p o r t i n t h e a c q u i s i t i o n o f p l a n s a n d c a l c u l a t i o n s
n e e d e d f o r t h e e r a l u a t i o n o f o b s e r v e d b u i l d i n g damage. Only t h e i r co-
o p e r a t i o n p e r m i t t e d a r e l i a b l e a n d a l m o s t c o m p l e t e t r e a t m e n t o f a l l t y p e s o f d e f l e c t i o n damage.
RES UME
Le r a p p o r t concerne l t 6 t u d e d t u n g r a n d nombre d l i n c i - d e n t s c o n s t a t k s s u r d e s c o n s t r u c t i o n s e n b 6 t o n arm6 e t a y a n t pour c a u s e e s s e n t i e l l e l a d 6 f o r m a b i l i t 6 e x c e s s i v e des 616ments f l 6 c h i s . Parmi l e s 1 8 1 d 6 c l a r a t i o n s d l i n c i d e n t s , o b t e n u e s p a r une e n q u s t e ,
115
s o n t suffisamment compl6 t e s pour p e r m e t t r e une a n a l y s e
.
Les cons6-
quences d f u n i n c i d e n t k t a n t p a r f o i s m u l t i p l e s , e l l e s peuvent s t r e c l a s s 6 e s dans l e s c a t e g o r i e s n u i v a n t e s : 106 c a s : d 6 s o r d r e s dans l e s c l o i s o n s e t murs de r e f end ; 60 c a s : flGche t r o p i m p o r t a n t e du p l a n c h e r ; 39 c a s : f i s s u r a t i o n d e s blkments e n b k t o n armk; 29 c a s : f i s s u r e s h o r i z o n t a l e s l t a p p u i d l u n p l a n c h e r ;
13
c a s : e n d u i t s e t r e v s t e m e n t s endommagks;1 2 c a s : dommages p a r t i c u l i e r s diis awr d 6 f o r m a t i o n s ;
259 dommages d i s t i n c t s , r e l e v 6 s s u r 1 8 1 c a s d t i n c i d e n t s ,
Les d k s o r d r e s dans l e s c l o i s o n s endommagkes l e s p l u s f r k q u e n t s r 6 s u l t e n t de l a f l e x i b i l i t 6 d i f f b r e n t e de l a c l o i s o n e t de s o n s u p p o r t , l a c l o i s o n formant un panneau r i g i d e vis-A-vis de l r 6 l k m e n t d l a p p u i f l e x i b l e en b 6 t o n arm6 d o n t l a d 6 f o r m a t i o n augmente e n c o r e s o u s l l e f f e t du r e t r a i t e t du f l u a g e . A f i n d l 6 v i t e r c e s d k s o r d r e s , i l con- v i e n t de r 6 d u i r e l a f l e x i b i l i t k d e s p o u t r e s - s u p p o r t s s u i v a n t une formule i n d i q u 6 e dans c e t expos6 ou de c h o i s i r un g e n r e de c l o i s o n q u i s o i t i n d i f f 6 r e n t aux a f f a i s s e m e n t s d i f f b r e n t i e l s de son s u p p o r t .
Les 6lBments
A
f a i b l e h a u t e u r e t soumisA
de f o r t e sc h a r g e s s o n t l a c a u s e e s s e n t i e l l e de dommages p a r d 6 f o r m a t i o n ex-
c e s s i v e ~ . I1 f a l l a i t s u r t o u t r e d o u t e r d e s d k s o r d r e s pour l e s p l a n c h e r s r e c t a n g u l a i r e s p o r t a n t dans l e s dewr s e n s , pour l e s q u e l s l e r6glement
allemand a u t o r i s a i t jusqul a l o r s une h a u t e u r p l u s r k d u i t e que pour l e s
p l a n c h e r s ne p o r t a n t que dans un s e n s . Pour l a f l 6 c h e a d m i s s i b l e d l u n
p l a n c h e r on a adopt6 l a v a l e u r de f =
L/300,
Tous l e s a u t r e s g e n r e s de d 6 s o r d r e s d 6 c o u l e n t e s s e n -
t i e l l e m e n t de f a u t e s commises dans l t k t u d e du p r o j e t ou dans l l e x 6 c u t i o n
du bGtiment. Le p r k s e n t r a p p o r t c i t e e t d k c r i t p l u s i e u r s dommages
c a r a c t k r i s t i q u e s .
E n s u i t e v i e n t un b r e f r6sumk d e s e x p k r i e n c e s f a i t e s
6
1 1 6 t r a n g e r e t une s p B c i f i c a t i o n d e s p r i n c i p e s de b a s e6
r e s p e c t e r a f i n d l k v i t e r d e s i n c i d e n t s p a r d k f o r m a t i o n s e x c e s s i v e s .CONTENTS 1. Introduction (Synopsis)
2. Statement of the Problem
Page 1
3.
Region Covered by the Survey of Structural Damage4 . Types of Structural Damage Which Have Occurred
5.
The Types of Flexural Component Which Produced the MostFrequent Cases of Damage
5.1 Number of Participating Types of Building Components 5.2 Comparison of the Behaviour of One-Way Slabs With
Two-Way Slabs
6.
The Effective Slenderness Ratio of Reinforced ConcreteFlexural Members That Have Contributed to Damage
7. Theoretical Determination of the Probable Deflection of the Reinforced Concrete Support Members Involved in a Case of Damage
7.1 Characteristic Values, Loads, Internal Forces and Deformation Constants
7.2 Calculation of Terminal Deflection Values
7.3 Magnitude of Deflections Which Initiated Damage 7.4 Coefficients of Deformation Which Were Calculated
Simultaneously With the Deflection
8. Factors Responsible for the Occurrence of Deflection Damage 8.1 'Theoretically Possible Sources of Damage
8.2 Actual Causes of Damage
8.3 Connection Between Origin and Type of Damage 9. Evlauation of Partition Wall Damage
9.1 Types of Partition Wall Damage Observed
9.2 Limiting Values for the Initiation of Partition Wall Cracks
9 . 3 Means of Preventing Partition Wall Cracks in the Future
10. Evaluation of Excessive Slab Deflections 10.1 Magnitude of Permissible Slab Deflection
10.2 Measures by Which Excessive Deflections Can Be Prevented
11. Evaluation of Observed Cracks in Reinforced Concrete Building Components
12. Evaluation of Horizontal Cracks in the Vicinity of Slab Supports
Evaluation of Damage to Plaster and Finishes Evaluation of Deflection Damage in Isolated Cases Results of Questionnaire on Deflection Damage in Other
Countries
15.1 Reports of Cases of Damage
15.2 Studies of Deflection Damage in Other Countries 15.3 Deflection Limitations of Reinforced Concrete
Components in Various Countries Summary
Figures and Table 1 References
List of Symbols
Appendix
-
List of Tables of the Most Important Data on Each Individual Case of DamageSketches and Drawings for the Various Cases of Damage Photographs
BUILDING DAMAGE CAUSED BY DEFLECTION OF REINFORCED CONCRETE BUILDING COMPONENTS
1. INTRODUCTION ( S y n o p s i s )
I n t h i s r e p o r t v a r i o u s t y p e s o f damage t o b u i l d i n g s h a v e
b e e n c o l l e c t e d a n d e v a l u a t e d . The damage was c a u s e d p r i m a r i l y by
e x c e s s i v e d e f l e c t i o n o f r e i n f o r c e d c o n c r e t e s t r u c t u r a l p a r t s . I n r e s - p o n s e t o a q u e s t i o n n a i r e , 1 8 1 c a s e s o f damage w e r e r e p o r t e d : 1 1 5 o f t h e s e c o u l d b e e v a l u a t e d s a t i s f a c t o r i l y . I n m o s t c a s e s a number o f c a u s e s c o n t r i b u t e d t o t h e damage. A l t o g e t h e r t h e f o l l o w i n g c a s e s w e r e r e p o r t e d : 1 0 6 r e p o r t s o f damage t o t h e p a r t i t i o n w a l l s 60 r e p o r t s o f e x c e s s i v e s a g g i n g i n t h e c e i l i n g 39 r e p o r t s o f c r a c k s i n t h e r e i n f o r c e d c o n c r e t e s t r u c t u r a l p a r t s 29 r e p o r t s o f h o r i z o n t a l c r a c k s i n t h e r e g i o n o f t h e c e i l i n g s u p p o r t s 1 3 r e p o r t s o f damage t o p l a s t e r a n d w a l l c o v e r i n g 1 2 r e p o r t s o f d e f l e c t i o n o f i s o l a t e d c a s e s t o t a l o f 259 r e p o r t s i n 1 8 1 c a s e s .
The damage t o t h e p a r t i t i o n walls r e s u l t s f r o m t h e f l e x -
i b i l i t y o f t h e r e i n f o r c e d c o n c r e t e p a r t s s u p p o r t i n g t h e r i g i d w a l l s . The d e f o r m a t i o n o f t h e s u p p o r t s i n c r e a s e s i n t i m e o w i n g t o c r e e p a n d s h r i n k a g e . The damage c a n b e a v o i d e d e i t h e r by i n c r e a s i n g t h e t h i c k n e s s o f t h e s u p p o r t s - t h e f u n c t i o n o f s p a n - l e n g t h i s p r e s e n t e d i n t h e f o r m u l a - o r by c o n s t r u c t i n g a s u i t a b l e p a r t i t i o n w a l l . The s a g g i n g a p p e a r s m a i n l y i n s l e n d e r , h i g h l y - s t r e s s e d s t r u c t u r a l p a r t s . The p a r t s o f t h e c e i l i n g w i t h c r o s s e d r e i n f o r c e m e n t s a r e p a r t i c u l a r l y s u s c e p t i b l e t o damage. U n t i l r e c e n t l y , t h e s p e c i f i c - a t i o n s f o r r e i n f o r c e d c o n c r e t e i n Germany a l l o w e d a g r e a t e r d e g r e e o f s l e n d e r n e s s f o r t h e s e p a r t s t h a n f o r c e i l i n g s r e i n f o r c e d i n o n l y o n e d i r e c t i o n . The d e g r e e o f s a g g i n g p e r m i t t e d i s f = L / 3 0 0 . I n a l l o t h e r c a s e s damage was c a u s e d m a i n l y by e r r o r s i n d e s i g n o r c o n s t r u c t i o n . A number o f c a s e s o f c h a r a c t e r i s t i c damage a r e p r e s e n t e d a n d d e s c r i b e d . F i n a l l y , a s u r v e y w i l l b e g i v e n o f f i n d i n g s f r o m a b r o a d a n d a l i s t o f i m p o r t a n t r e q u i r e m e n t s t o p r e v e n t f u r t h e r dam- a g e t h r o u g h s a g g i n g .
STATEMENT OF THE PROBLEM
I n r e c e n t d e c a d e s c a s e s o f s t r u c t u r a l damage i n n e w l y c o n s t r u c t e d b u i l d i n g s h a v e b e e n o b s e r v e d w i t h i n c r e a s i n g f r e q u e n c y a n d a r e t h o u g h t t o h a v e a r i s e n f r o m e x c e s s i v e d e f l e c t i o n o f r e i n f o r c e d c o n - c r e t e b u i l d i n g c o m p o n e n t s . S u c h damage became a p p a r e n t o n l y a f t e r a c e r t a i n p e r i o d o f u s e , o r became more p r o n o u n c e d w i t h t i m e . T h u s , p a r t i t i o n w a l l s p l a c e d on f l e x i b l e r e i n f o r c e d c o n c r e t e s l a b s c r a c k e d ;
the slabs themselves frequently exhibited large deflections which were considered unsightly or led to depressions in which water accumulated and
caused damage to the roof membrane. In addition, other types o f damage
were reported as is shown in greater detail in Section 4.
These types of damage had previously not been observed to
such an extent. Their causes must therefore lie in the technical applic-
ation of progressively higher concrete and steel stresses, and the use of
large spans and slenderer members. Consequently, under working load the
reinforced concrete flexural members no longer remain chiefly in State I* but in a majority of cases have already passed into State 11* with a
cracked tension zone. Simultaneously, the creep deformation of the
concrete has increased.
These developments mean, therefore, that the previously satisfactory rules, which were based on decades of experience, must now be expanded and the deformation behaviour of the building components must henceforth be carefully considered so that damaging consequence to other
build in^
components can be avoided by suitable design measures.These considerations led the German Reinforced Concrete Association (DAfStb) in 1958, even before the new revision of the German Reinforced Concrete Code DIN 1045 had been concluded, to propose a temporary change in the hitherto applicable provisions. How- ever, during the deliberations it became apparent that it was neither possible to give a characteristic value for the permissible deflection magnitude that would be valid for all uses, nor did sufficiently reliable documents exist for the prediction of the expected deflections.
In order to avoid further instances o f damage, or at least to diminish their extent, the Association decided despite these uncertainties, to propose new rules for the deflection limits of re- inforced concrete building components in an addendum to DIN 1045. This
supplementary specification has been in use since 1959. It is based
mainly on a limitation of the deflection slenderness ratio R/h of the building component, depending on the concrete and steel stresses. Un-
fortunately, this sometimes resulted in uneconomical slab thicknesses and did not always prevent the undesirable cracking of partition walls.
Thus further studies were needed in order to provide a
reliable basis for eventual control. Various research programs were
initiated, beginning in 1959, by the Materials Testing Laboratory for
Structures of the Technical University, Munichn*. First of all, measure-
ments were made of the time-dependent deflections of completed reinforced
concrete flexural members (see Ref. 1). This work was intended to yield
numerical values which would describe the actual behaviour of structures, and thus make it possible to determine the constants needed for the
structural analysis.
Translator's Notes:
*
StateI
represents the uncracked concrete sectionState I1 represents the cracked concrete section
**
German title: MaterialprUfunpamt fiir das Bauwesen der TechnischenThe s e c o n d p r o j e c t , d e s c r i b e d h e r e i n , i s t o i n v e s t i g a t e t h e e x t e n t a n d t y p e s o f b u i l d i n g damage w h i c h a c t u a l l y o c c u r as a con- s e q u e n c e o f d e f l e c t i o n s of r e i r l f o r c e d c o n c r e t e b u i l d i n g c o m p o n e n t s . The i n d i v i d u a l c a s e s o f damage h a v e b e e n a s s e s s e d u n d e r u n i f o r m c l a s s i f i c a t i o n s a n d a n a t t e n i p t h a s b e e n made t o e s t a b l i s h t h e t y u e
c a u s e s o f t h e damage. The f i n a n c i a l s u p p o r t came f r o m t h e F e d e r a l
M i n i s t r y :'ora B u i l d i n g C o n s t r u c t i o n , t o w h i c h w e e x t e n d o u r p a r t L c u l a r t h a n k s
.
F i n a l l y , a t h i r d s t u d y dete17mined m e t h o d s o f how d e r l e c -
t i o r s u n d e r a c t u a l c o n d i t i o r l s may b e c a l c u l a t e d
( 3 ) .
T h e s e s u g g e s t i o n s h a v e beell a p p l i e d t,o t h e c a s e s o f damage c o l l e c t , e d h e r e .3 .
REGIO1.J COVLRED BY THE SURVEY OF STRUCfI'URAL DAMAGEThe s u r v e y o f t h e d e f l e c t i o n damage el-~compassed m a i n l y t h e F e d e r a l R e p u b l i c o f G e r m m y . The s e n i o r b u i l d i n g a u t l i o r i t i e s o f t h e 11 F e d e r i i l s t a t e s d i s t r i b u t e d a c i r . c u l a r f r o m t h e M a t e r i a l s T e s t i n g 1 n s t i l ; u t e f o r S t r u c t u r e s o f t h e T e c h n i c a l U r l i v e ~ s i t y Munich t o a l l a p p r o p r i a t e b u i l d i n g i n s p e c t i o n o f f : i c e s , s t a t e b u l . l d i n g o f f i c e s a n d i n s p e c t i o n e n g i n e e r s . A t t h e same t i m e , a l l b u i l d i n g m a t e r i a l . t e s t i n g s t a t i o n s , s t a i : e b u i l d i n g s c h o o l s , i n : 3 t i t u t e s o f t e c h n i c a l u n i v e r s i t i e s a n d a l l c o n s u l t i i n g o f f i c e s who m i g h t p o s s i b l y h a v e b e e n c o n s u l t e d I n t h e evaluation o f d e f l e c t i o n damage w e r e c o n t a c t e d . A t o t a l o f a g p r o x i m a % e l y i ,0 0 0 q u e s t i o r l n a i r * e s w e r e d i s t r ' l b u t e d . I n d e p e n d e n t o f t h e s u r v e y o f t h e M a t e r i a l T e s t i n g J n s t L t u t e f o r S t r u c t u r e s o f t h e T e c h n i c a l U n i v e r s i 1 ; y M u n i c h , t h e E a u s t a h l g e w e b e GMBH* D u s s e l d o r f , i n t h e s r , r i n g o f 1 9 6 1 , h a d a l s o c a r r i e d o u t a s t a t i s t i c a l i r ~ v t l s t i g a t i o n o f d e f ' l e c t i o n damage. T h e s e r e s u l t s h a v e k i n d l y b e e n made a v a i l e b l e 50 u s ' o r f u r t h e r e v e l u a t i o n . T h i ~ , e f f o r t c o n c e r n e d l t s e l f w i t h t h e b u i l d i n g c o o p e r a t i v e s , p a r t i c u l a r - l y i n t h e s t a t e s o f I i o r d r h e i n - W e s t f a l e n a n d N i e d e r s a c h s e n . Of t h e 1 0 5 b u i l d i n g c o o p e r a t i v e s z u r v e y e d , o n l y two d e f l e c t i o n damage w e r e
r e p o r t e d . They weye i n c l u d c d i n t h e damagc a n a l - y s i s c a r r i e d o u t h e r e i n . F'our o t h e r o : ? g a n i z a t ? - o n s knew o f "some c a s e s " . However, f u r t h e r . d e t a i l s c o u l d n o t b e o b y a i n e d . T h r e e c o o p e r a t i v e s h a d m i s t a k e n l y r e p o r t e d
o t h e r b u l - l d i n g danrage t o b e d u e ?.o e x c e s s r j v e d e f l e c t i o n s .
P. view o f t l i e r e g i o n s c o v e r e d by t h e s u r v e y i s g i v e n i n P i g . 1. The c i r c l e s s i g n i f y t h a t t h e o T g a n i z a t j o n s who w e r e q u e s t i o n e d
knew of' n o d e f ' e c t f o n damage. The c r o s s e s s y m b o l i z e t h a t o n e o r more
c a s e s o f d a ~ a g e liave b e e n r e p o r t e d . From t h e d i s t r i c t s w h i c h d o riot c c n t a i n a n y s y m b o l , n e i t l ~ e r a p o s i 1 . i v e : l o r a n e g a t i v e rinswer t o t h e s u r v e y was r e c e i v e d . I t mey w e l l b e c o n c l u d e d t h a t i n t i ~ i s c a s e n o
d e f l e c t : on damagc had b e e n known.
I n o r d e r t o o b t a i n a p i c t u r e o f t h e e x t e n t o f d e f l e c t i o n damage i n o t h e r c c u n t r i e s , a n a d d i t i o n a l 2 0 0 q u e s t , i o n n a i r e s wer.e d i r e c t e d t o t,he m a i n i n t e r n a t i o n a l i n s t f - t u t e s a n d t o well-known a u t l ~ o r i t , i e s a b r o a d . I n t h i s s u r v e y , a l l E u r o p e a n c o u n t r i e s i n c l u d i n g t h o s e o f t h e e a s t e r n b l o c k , w e r e j n c l u d e d , as w e l l as t h e niain c o u n t r i e s o f N o r t h a n d S o u t h Amer'ca, A u s t r a l i a , I n d i a a n d J a p a n . S e c t f o n 1 5 r e p o r t s b r i e f l y a b o u t t h e r e s u l t s o f t h i s :i.nl'or.mational s u r v e y . T r a n s l a t o l a ' s N o t e :
4 .
TYPES OF STRUCTURAL DAMAGE WflICH HAVE OCCURREDA t o t a l o f 1 8 1 c a s e s o f damage w e r e r e p o r t e d . F o r 1 1 5
o f t h e s e s u f f i c i e n t s u p p o r t i n g m a t e r i a l was made a v a i l a b l e f o r a r e -
c a l c u l a t i o n s o t h a t t h e y c o u l d b e e v a l u a t e d s a t i s f a c t o r i l y . I n 25 c a s e s
o n l y few d e t a i l s a r e known. About t h e r e m a i n i n g o n e s o n l y t h e f a c t t h a t
a d e f l e c t i o n damage h a d o c c u r r e d c o u l d b e e s t a b l i s h e d .
F i g u r e 2 c o n t a i n s a n e n u m e r a t i o n o f v a r i o u s damage
p o s s i b i l i t i e s a n d t h e c o r r e s p o n d i n g f r e q u e n c i e s o f t h e i r o c c u r r e n c e . A s c a n b e s e e n , two t y p e s o f damage p r e d o m i n a t e among t h e many c a s e s r e p o r t e d . One c a n , h o w e v e r , g r o u p t h e v a r i o u s p o s s i b i l i t i e s l o g i c a l l y i n t o s i x l a r g e r c a t e g o r i e s as h2.s a l r e a d y b e e n i n d i c a t e d i n t h i s f i g u r e . I n tile e v a l u a t i o n t h e s e w i l l b e d e s c r i b e d h e r e a f t e r i n more d e t a i l u n d e r t h e i n d i v i d u a l s e c t i o n s . P a r t i t i o n w a l l damage c o n s t i t u t e s t h e m o s t i m p o r t a n t g r o u p . T h i s i n c l u d e s n o t o n l y c r a c k s i n t h e w a l l s ( I ) , b u t a l s o l a r g e g a p s i n t h e v i c i n i t y o f b a s e b o a r d s , a n d h o r i z o n t a l c r a c k s a t t h e j o i n t b e t w e e n w a l l a n d c e i l i n g ( 2 ) . I n a d d i t i o n , c o m p l a i n t s a b o u t jammed d o o r s ( 3 ) m u s t a l s o b e i n c l u d e d i n t h i s g r o u p ( s e e S e c t i o n 9 ) . The s e c o n d m o s t i m p o r t a n t damage g r o u p s t e m s f r o m e x c e s - s i v e s l a b d e f l e c t i o n s ( 6 ) , a n d i n c l u d e s t h e f o r m a t i o n o f t r o u g h s i n r o o f s ( 7 ) a n d c o m p l a i n t s a b o u t s l a n t i n g f u r n i t u r e ( 1 0 ) ( s e e S e c t i o n 1 0 ) . A f u r t h e r damage g r o u p c o n s i s t s o f p l a s t e r ( 8 ) a n d f i n i s h i n g damage ( 9 ) d u e t o e x c e s s i v e s l a b d e f l e c t i o n s ( s e e S e c t i o n 1 3 ) . A s a s e p a r a t e damage g r o u p may b e l i s t e d a l l c a s e s o f damage d u e t o e x c e s s i v e r o t a t i o n o f t h e r e i n f o r c e d c o n c r e t e e d g e b e a m s . T h i s i n c l u d e s h o r i z o n t a l c r a c k s a b o v e o r b e l o w c e i l i n g s u p p o r t s ( 1 6 ) , a s w e l l as e x c e s s i v e l a t e r a l b e n d i n g d e f l e c t i o n s o f s t e e l o r c o n c r e t e c o l u m n s ( 1 7 ) ( s e e S e c t i o n 1 2 ) . I n c l u d e d i n a f u r t h e r damage g r o u p w e r e t h e c r a c k s i n r e i n f o r c e d c o n c r e t e c o m p o n e n t s , f o r i n s t a n c e , c r a c k s w h i c h o c c u r o n t h e t o p s u r f a c e o f s l a b s a l o n g t h e l i n e s o f s u p p o r t , t h e c r a c k s a t t h e e n d o f t h e s o l i d e d g e s t r i p ( 1 8 ) , o r t h e c r a c k s o b s e r v e d n o r m a l t o t h e d i a g - o n a l i n t h e c o r n e r s o f two-way r e i n f o r c e d p l a t e s ( 1 9 ) ( s e e S e c t i o n 1 1 ) . F i n a l l y , a l l r e m a i n i n g d e f l e c t i o n damage w h i c h h a v e o c c u r r e d o n l y i n i s o l a t e d i n s t a n c e s w e r e c o l l e c t e d i n a s e p a r a t e damage g r o u p : c o l l a p s e o f p a r t i t i o n s ( 4 ) ; m o i s t u r e s e e p a g e ( 5 ) ; s h a t t e r i n g o f s h o p windows ( 1 1 ) ; f a c a d e c o n s t r i c t i o n ( 1 2 ) ; s e p a r a t i o n o f j o i n t s ( 1 3 ) ; l e a k s i n t i l e s t o v e s ( 1 4 ) ; v i b r a t i o n phenomena ( 1 5 ) ; a n d u n a c c e p t a b l e d e f o r m a t i o n s ( 2 0 ) ( s e e S e c t i o n 1 4 ) . The damage c a t e g o r i e s m e n t i o n e d a b o v e o c c u r r e d w i t h t h e f o l l o w i n g f r e q u e n c y : P a r t i t i o n w a l l damage 1 0 6 t i m e s E x c e s s i v e s l a b d e f l e c t i o n 6 0 f f C r a c k s i n r e i n f o r c e d c o n c r e t e c o m p o n e n t s 39
"
H o r i z o n t a l c r a c k s i n t h e v i c i n i t y o f s l a b s u p p o r t s 29 "Damage t o p l a s t e r aild f i n i s h e s 1 3 t i m e s 1 s o l . a t e d d e f l e c t z o n damage 1 2 t i m e s
The t o t a l number o f p o s s i b l e t y p e s of damage i s g r e a t e r t h a n t h e r e p o r t e d 1 8 1 c a s e s o f damage, s i n c e o f t e n niore t h a n o n e p o s s i b i l i t y c o u l d b e
o b s e r v e d i n a s i n g l e i n s t a n c e .
5 . THE TYPES OF FLEXURAL COMPONENT W H I C H PRODUCED THE MOST FREQUENT CASES OF DAMAGE
5 . 1 Number o f P a r t i c i p a t i n g Types o f B u i l d i n g Components
---
The m a j o r i t y o f i n s t a n c e s o f damage o c c u r r e d i n two-way r e i n y o r c e d s l a b s a n d r i b b e d s l a b s , a s shown i n F i g . 3. T h i s i s n o d o u b t b e c a u s e f o r m e r l y two-way r e i n f o r c e d c o m p o n e n t s w e r e allowecl. t o b e c o n s t r u c t e d w i t h a g r e a t e r s l e n d e r n e s s r a t i o % h a n one-way r e i n f o r c e d c o m p o n e n t s . U n t i l t h e i n t r o d u c t i o n o f t h e addendum t o D I N 1 0 4 5 two-way r e i n f o r c e d p l a t e s w i t l t f o u r s i d e s s i m p l y s u p p o r t e c l c o u l d h a v e s l e n d e r n e s s r a t l o s up t o 5 0 , w h e r e a s one-way r e i n f o r c e d s l a b s c o u l d b e b u l l t o n l y up t o R/h = 35. The a b o v e c o n j e c t u r e i s s u b s t a n t i a t e d by t h e s p e c i a . 1 a n a l y s i s shown i n F i g . 4 , i n w h i c h o n l y t h o s e b u i l d i n g c o m p o i ~ e n t s a r e i n c l u d e d whose t h e o r e t i c a l s l e n d e r n e s s r a t i o i s Ri/h ( 3 5 , o r t h o s e f o r w h i c h t h e s l e l ~ d e r r l e s s r a t i o i s n o t a p p a r e n t f r o m t h e aamage r e p o r t . H e r e R i i s t h e e q u i v a l e n t s p a n l e n g t h which i s f u r t h e r d e s c r i h e d i n S e c t i o n 6 , a n d w h i c h p e r m i t s a compar'.son o f e f f e c t i v e s l . e n d e r n e s s r a t i o u n d e r n r b i 1 , r a r y s u p p o r t conditions ( c o n t i n u o u s , c a n t i l e v e r , e t c . ) . Of t h e 1 5 6 damage c a s e s i n P i g . 3 , 8 8 a r e a l r e a d y e l i m i n a t e d by t h e a b o v e m e n t i o n e d l i m i t a t i o n o f s l e n d e r n e s s r a t i o . I t i s n o t e w o r t h y t h a t 6 3 clamage c a s e s o c c u r I n two-way r e i n f o r c e d c o m p o n e n t s a n d c n l y 1 5 i n t h o s e w i t h one-way r e i n ~ r o r c i n g . I t c a n n o t y e t be s t a t e d w i t h c e r t a i . n t y f r o m t h i s r ~ u r e l y s t a t i s t i c a l c o n s i d e - a t i o n w h e t h e r a l l 88 c a s e s c o u l d a c t u a l l y h a v e b e e n a v o i d e d by a s t r i c t e r l i m i t a t i o n o f t h e s l e n d e r n e s s r > a t i o . A s w i l l b e shown i n S e c t i o n
3 ,
t h e s l e n d e r n e s s r a t i o s h o u l d b e d e t e r m i n e d a s a f u n c t i o n of t h e s p a n l e n g t h R i . I n F i g .4
i t I s shown t h a t a l l t y p e s o f b u i l d i n g c o m p o n e n t s e x h i b j - t e d c a s e s o f damage. The empty c o l u m n s i n t h e p r e s e n t a t i o n s h o u l d n o t l e a d t o a f a i s e c o n c l ~ : s i o r i , f o r t h e y r e s u l t m e r e l y from a s y s t e m z t i c a p p l i c a t i o n o f t h e c h o s e n a l p h a b e t i c a l scheme a n d r e p r e s e n t b u i l d i n g c o m p o n e n t s which a r e o n l y r a r e l y o r n e v e r p r o d u c e d . M o r e o v e r , i n t h e c o n t e x t o f p r o b a b i l i t y t h e o r y t h i s c o n s t i t u t e s a c o m p a r a t i . v e l y s m a l l sarr.ple w h i c h c a n d e s c r i b e t h e b e h a v i o u r o f t h e w h o l e p o p u l a t i o n o n l y a p p r o x i m a t e l y . 5 . 2 C o m e a r i s o n o f t h e B e h a v i o u r o f One-Way S l a . b s w i t h Two-Way S l a b s -..- ---.---.--- C o m p a r i s o n o f F i g .3
a n d 4 showed t h a t t h e r e i s n o j u s t i f j c a t i o n f o r g i v i n g two-way s l a b s g r e a t e r s l e n d e r n e s s t h a n one-way s l a b s . F i g u r e7
o f t h e n e x t s e c t i o n p r o v i d e s a more t h e o r e t i c a l c o n f i r m - a t i o n o f t h i s . A s a. c a l c u l a t i o n shows, t h e d e f e c t i o n o f a s l a b w i t h f o u r - s i d e d s u p p o r t i s g r e a t e r t h a n t h a t o f a s l z b w i t h t w o - s i d e d s u p p o r t i f t h e c u r v a t u r e M/EI a t t h e c e n t r e i s t h e same f o r b o t h t y p e s o f s l a b s . The d i f f e r e n c e s are g r e a t e s t f o r a s q u a r e p l a t e . I n o r d e r t o g e t e q u a l d e f l e c t i o n b e h a v i o u r , i t s s l e n d e r n e s s r a t i o woul6. h a v e t o b e r e d u c e d by 6 p e r c e n t i n t h e c a s e o f s i m p l e s u p p o r t s on a l l s i d e s a n d 1 5 p e r c e n ti n t h e c a s e o f c o m p l e t e l y f i x e d s u p p o r t s , compared w i t h t h e s l a b s u p p o r t e d on two s i d e s . F o r t h e s a k e o f s i m p l i c i t y , h o w e v e r , i t i s recommended t h a t t h e two t y p e s b e t r e a t e d i d e n t i c a l l y a s f a r as t h e s l e n d e r n e s s r a t i o i s
c o n c e r n e d .
6 . THE EFFECTIVE SLENDERNESS RATIO OF REENFORCED CONCRETE FLEXURAL MEMBERS THAT HAVE CONTRIBUTED TO DAMAGE
The s l e n d e r n e s s r a t i o o f a b u i l d i n g component i s u s u a l l y u n d e r s t o o d t o b e t h e r a t i o o f s p a n l e n g t h t o h e i g h t . The h e i g h t i s t a k e n e i t h e r a s t h e e f f e c t i v e d e p t h h o r t h e t o t a l c r o s s - s e c t i o n a l t h i c k n e s s d o . I n t h e f o l l o w i n g , h w i l l be u s e d . The s l e n d e r n e s s r a t i o i s a r o u g h m e a s u r e o f d e f l e c t i o n b e h a v i o r . The g r e a t e r t h e s l e n d e r n e s s r a t i o t h e g r e a t e r i s t h e d e f l e c - t i o n u n d e r o t h e r w i s e i d e n t i c a l c o n d i t i o n s . T h e s e o t h e r c o n d i t i o n s a r e : i d e n t i c a l l o a d i n g , c o n s t a n t moment o f i n e r t i a a l o n g t h e s p a n , i d e n t i c a l c r e e p a n d s h r i n k a g e b e h a v i o u r o f t h e c o n c r e t e , a n d t h e same s t r u c t u r a l con- f i g u r a t i o n . The l a t t e r c o n d i t i o n c a n be a c c o u n t e d f o r by t h e i n t r o d u c t i o n o f a n e q u i v a l e n t member. The o t h e r c o n d i t i o n s w i l l b e n e g l e c t e d f o r t h e s a k e o f s i m p l i c i t y . The d e t e r m i n a t i o n o f t h e s p a n l e n g t h s R i o f t h e s u b s t i t - u t e beam c a n o c c u r i n v a r i o u s ways. Only o n e Q f t h e f o l l o w i n g two g r o u p s o f c o n d i t i o n s d e s c r i b i n g e q u a l i t y o f d e f o r m a t i o n a n d s t r e s s i n t h e a c t u a l a n d t h e s u b s t i t u t e beams h a s t o b e s a t i s f i e d a t any o n e t i m e .
(1) D e f o r m a t i o n C o n d i t i o n s
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Same maximum s l o p e o f t h e d e f l e c t i o n c u r v e , max. t a n a Same maximum e n d r o t a t i o n , max.
@ A ( 2 ) S t r e s s C o n d i t i o n s
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Same s t r e s s a t t h e c e n t r e s e c t i o n a m
Same c u r v a t u r e a t t h e c e n t r e s e c t i o n (M/EI),, o r Same maximum s t r e s s , max, a
An e x t e n s i v e d i s c u s s i o n o f t h e a r g u m e n t s which e n t e r i n t o t h e c h o i c e o f t h e most s u i t a b l e m e a s u r e s o f c o m p a r i s o n c a n b e f o u n d i n t h e p u b l i c a t i o n by A . Mehmel ( R e f . 2 ) . I n t h e a n a l y s i s c a r r i e d o u t h e r e t h e f o l l o w i n g d e f i n i t i o n o f t h e e q u i v a l e n t s p a n l e n g t h s was a d o p t e d , i n a g r e e m e n t w i t h Mehmel a n d t h e p r o p o s a l s f o r t h e new e d i t i o n o f t h e German R e i n f o r c e d C o n c r e t e Code: F o r t h e e q u i v a l e n t s p a n l e n g t h t i , t h e s p a n o f a s i m p l y s u p p o r t e d beam w i t h c o n s t a n t moment o f i n e r t i a s h o u l d b e c h o s e n i n s u c h a manner t h a t u n d e r u n i f o r m l y d i s t r i b u t e d l o a d i n g t h e same r a t i o o f c e n t r e - l i n e d e f l e c - t i o n t o s p a n l e n g t h a n d t h e same c u r v a t u r e a t t h e c e n t r e - l i n e s e c t i o n e x i s t a s i n t h e a r b i t r a r i l y s u p p o r t e d beam u n d e r c o n s i d e r a t i o n . F o r a c a n t i l e v e r , t h e d e f l e c t i o n a t t h e f r e e e n d and t h e c u r v a t u r e a t t h e r e s t r a i n e d s e c t i o n a r e t o b e compared. E x p r e s s e d i n f o r m u l a e , t h e s e d e f i n i t i o n s a r e as f o l l o w s ( F i g . 5 ) :
lli = k - l l C o n d i t i o n ( 1 ) (same r e l a t i v e d e f l e c t i o n ) C o n d i t i o n ( 2 ) (same c u r v a t u r e ) When c o n c e n t r a t e d a n d l i n e l o a d s w e r e p r e s e n t i n a d d i t - i o n t o t h e u n i f o r m l o a d , t h e d e f l e c t i o n o f t h e a r b i t r a r i l y s u p p o r t e d beam was c a l c u l a t e d a c c o r d i n g t o t h e well-known d e f o r m a t i o n l a w s o f s t a t i c s a n d compared w i t h t h e v a l u e s o f a s i m p l y s u p p o r t e d beam u n d e r u n i f o r m l o a d i n g . F o r v a r i a b l e moments o f i n e r t i a o f t h e a r b i t r a r i l y s u p p o r t e d beam t h e same p r o c e d u r e was f o l l o w e d .
With t h e a i d o f t h e t h e o r e t i c a l r e l a t i o n s h i p f = c . ( M / E I ) m - l 1 2 a n d t h e two c o n d i t i o n s d e s c r i b e d a b o v e , t h e d e s i r e d f a c t o r k f o r t h e d e t e r m i n a t i o n o f t h e s u b s t i t u t e s p a n l e n g t h c a n be f o r m u l a t e d a s f o l l o w s : From C o n d i t i o n ( 1 ) : C . ( M / E I ) ~ ' ~ = ( 5 / 4 8 ) ( M / E 1 ) m ' e ' k By i n t r o d u c i n g C o n d i t i o n (2) we o b t a i n c = ( 5 / 4 8 ) k F o r t h e s p e c i a l c a s e o f a u n i f o r m l o a d a n d c o n s t a n t moment o f i n e r t i a , t h e f a c t o r k f o r a beam e l a s t i c a l l y r e s t r a i n e d a t b o t h e n d s i s o b t a i n e d a c c o r d i n g t o F i g .
6
f r o m t h e f o r m u l a f o r t h e e l a s t i c a l l y r e s t r a i n e d c a n t i l e v e r F o r two-way r e i n f o r c e d s l a b s t h e f a c t o r k was d e t e r - mined i n a s i m i l a r manner a n d i s shown i n F i g .7 .
T h i s f i g u r e was u s e d f r e q u e n t l y d u r i n g t h e damage a n a l y s i s . B u t , a s h a s a l r e a d y b e e n m e n t i o n - e d i n S e c t i o n 5 , o n e s h o u l d n o t d i f f e r e n t i a t e i n p r a c t i c e b e t w e e n two-way a n d one-way s l a b s i n t h e d e t e r m i n a t i o n o f t h e e q u i v a l e n t s p a n l e n g t h . I t s h o u l d be n o t e d , h o w e v e r , t h a t i n t h e d e t e r m i n a t i o n o f t h e a p p r o p r i a t e d e f l e c t i o n s l e n d e r n e s s o f a two-way s l a b , t h e e q u i v a l e n t s p a n l e n g t h a n d n o t t h e l a r g e s t g e o m e t r i c a l s p a n l e n g t h s h o u l d a l w a y s b e u s e d . A s c a n b e s e e n f r o m t h e e x a m p l e shown i n F i g . 8 , t h e g r e a t e s t s p a n l e n g t h c a n y i e l d t h e s m a l l e s t d e f l e c t i o n s l e n d e r n e s s r a t i o u n d e r c e r t a i n s u p p o r t c o n d i t i o n s a n d s p a n l e n g t h r a t i o s . T h i s i s t h e c a s e f o r a l l t h e t y p e s o f s l a b s i n d i c a t e d by d o t t e d l i n e s i n F i g . 7 .F o r s l a b s s u p p o r t e d o n t h r e e s i d e s , t h e e q u i v a l e n t s p a n l e n g t h c a n no l o n g e r b e d e t e r m i n e d l o g i c a l l y a c c o r d i n g t o t h e a b o v e - m e n t i o n e d d e f i n i t i o n , s i n c e t h e s l a b n o r m a l t o t h e f r e e e d g e c a n n o t b e c o n s i - d e r e d a s a c a n t i l e v e r p l a t e n o r a s a s l a b s u p p o r t e d o n two s i d e s . I t s u p p o r t s i t s e l f e l a s t i c a l l y i n t h e o t h e r d i r e c t i o n . I t i s recommended t h a t i n t h i s c a s e t h e s p a n l e n g t h p a r a l l e l t o t h e f r e e e d g e b e c o n s i d e r e d a s t h e g o v e r n i n g o n e .
7 . THEORETICAL DETERMINATION OF THE PROBABLE DEFLECTION OF THE REINFORCED
CONCRETE SUPPORT MEMBERS INVOLVED I N A CASE OF DAMAGE
Only i n a few c a s e s h a s t h e m a g n i t u d e o f t h e d e f l e c t i o n t h a t c a u s e s t h e damage b e e n m e a s u r e d . U s u a l l y , a s p e c i a l i s t was con- s u l t e d o n l y a f t e r a c o n s i d e r a b l e l a p s e o f t i m e f o l l o w i n g t h e o c c u r r e n c e o f d i s t u r b i n g phenomena, a n d d u r i n g t h e e x a m i n a t i o n a n i n i t i a l d e f l e c t i o n v a l u e was e s t a b l i s h e d . T h i s v a l u e , h o w e v e r , i n c l u d e s t h e form-work camber a n d i s c o n s e q u e n t l y u n r e l i a b l e . I n c o n n e c t i o n w i t h t h e d e f l e c t i o n damage a n a l y s i s c a r r i e d o u t h e r e i t was t h e r e f o r e n e c e s s a r y t o c a l c u l a t e t h e d e f l e c t i o n s t o b e e x p e c t e d f o r e v e r y s i n g l e c a s e o f damage on t h e b a s i s o f t h e m o s t r e a l i s t i c a s s u m p t i o n s . However, t h e c a l c u l a t i o n s w e r e a l s o n e c e s s a r y f o r a s e c o n d r e a s o n . They p e r m i t t e d a s y s t e m a t i c r e v i e w o f t h e c o n s e q u e n c e s o f a l l c a u s e s o f damage. T h u s , t h e r e l a t i v e i m p o r t a n c e o f i n d i v i d u a l c a u s e s c o u l d b e w e i g h e d a g a i n s t e a c h o t h e r a n d a d d i t i o n a l c a u s e s c o u l d b e d i s c o v e r e d w h i c h m i g h t n o t y e t h a v e b e e n r e c o g n i z e d by t h e l o c a l e x p e r t . The b a s i s f o r t h e s e d e f l e c t i o n c a l c u l a t i o n s w i l l s u b - s e q u e n t l y b e d e s c r i b e d b r i e f l y . F u r t h e r d e t a i l s , p a r t i c u l a r l y t h e co- e f f i c i e n t s u s e d , c a n b e o b t a i n e d f r o m t h e d i s s e r t a t i o n by t h e f i r s t a u t h o r ( R e f . 3 ) . 7 . 1 C h a r a c t e r i s t i c V a l u e s , L o a d s , I n t e r n a l F o r c e s a n d D e f o r m a t i o n
...
C o n s t a n t s---
The s t r u c t u r a l s y s t e m o f t h e l o a d - b e a r i n g r e i n f o r c e d c o n c r e t e members i n v o l v e d , a s w e l l a s t h e i r d i m e n s 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 , h a v e b e e n o b t a i n e d f r o m t h e formwork a n d r e i n f o r c i n g p l a n s . The most s i g n i f i c a n t d a t a a r e c o n t a i n e d i n t h e t a b l e s o f t h e A p p e n d i x . The i n d i v i d u a l damage c a s e s h a v e b e e n p r e s e n t e d t h e r e i n a s y s t e m a t i c s e q u e n c e , F i r s t come t h e t y p e s o f p a r t i t i o n w a l l damage a r r a n g e d a c c o r d i n g t o t h e m a g n i t u d e o f t h e e q u i v a l e n t s p a n l e n g t h , min. R i . Then, s t a r t i n g f r o m c a s e 9 2 , we h a v e t h e c o m p l a i n t s o f e x c e s s i v e s l a b d e f l e c t i o n , p r o v i d e d t h a t s i m u l t a n e o u s l y p a r t i t i o n w a l l damage h a s n o t o c c u r r e d . T h e s e h a v e a l s o b e e n a r r a n p e d a c c o r d i n g t o t h e e q u i v a l e n t s p a n l e n g t h . S i m i l a r l y , s t a r t i n g f r o m c a s e 1 3 3 , h o r i z o n t a l c r a c k s i n t h e v i c i n i t y o f s l a b s u p p o r t s ; f r o m c a s e 1 4 4 , c r a c k s i n t h e r e i n f o r c e d c o n c r e t e c o m p o n e n t ; a n d f r o m damage c a s e 1 5 4 , i s o l a t e d c a s e s o f d e f l e c - t i o n damage w h e r e t h e r e i s a d e f i n i t e c a u s e f o r c o m p l a i n t . C o n c e r n i n g t h e i n s t a n c e s o f damage s t a r t i n g a t 1 6 3 , i t i s known o n l y t h a t a d e f l e c - t i o n damage h a d o c c u r r e d . The l o a d i n g o f t h e b u i l d i n g c o m p o n e n t s was d e t e r m i n e d anew by o u r own r e - c a l c u l a t i o n . I n a d d i t i o n t o t h e d e a d w e i g h t , o n l y t h e p r o b a b l e p e r m a n e n t l y - a c t i n g l i v e l o a d was a p p l i e d . F o r l i v i n g a r e a s ,t h i s l i v e l o a d was assumed a t
50
k I ? h 2 , and f o r c o m m e r c i a l p r e m i s e s , d e p e n d i n g on t h e t y p e oT u s a g e , a t approximately 1 0 0 t o 200 kp/m2.S j m i l ; . r l y , t h e i n t e r ' n a l f o r > c e s wei7e newly d e t e r r ~ i n e d artd, a s f a r a s p o s s i b l e , compared w i t h t h e T ~ a l u t ? s o f t h e o r i g i n a l s t a t i c s c a l c u l a t i o n s . I n d o i n g s o , 2.n att;ernpt was rrlade t o c o n s i d e r , a s f a r as
p o s s i b l e , a l l e f f e c t s : f o r e x a r r p l e c h a n g e s i r ~ s t r e s s e s d u e t o r e i n f o r c e - ment b e i n g p l a c e d t o o l o w , o r p a r t i a l r e s t r a i n t s i n t h e e d g e s u p p o r t s which a r e nor.mally n e g l e c t e d i n s t a t i c s c a l c u l a t i o n s . The d e g r e e s o f r e s t r a i n t t h u s o b t a i n e d were r e c o r d e d i n t h e c o r r e s p o n d i r ~ g s k e t c h e s o f t h e s t r u c t u r a l . s y s t e m i r ~ t h e Appendix.
I n d e t e r m i n i n g t h e modulus o f e l ~ . s t i c i t y o f t h e c o n c r e t e t h e i n f l u e n c e o f t h e stlless l e v e l was a l s o c o n s i d e r e d . The f l e x u r a l t e n s i l e s t r e n g t h o f t h e c o n c r e + , e was o b t a i n e d fr20rn t h e b a s i c v a l u e o f a permanently w e t t e d c o n c r e t e as w e l l a.s
a
number o f i n f l u e n c e c o e f f i c i e n t s( d i f f e r e n t i a l . d r y j n g o f t h e c r o s s s e c t i o n , i n f l u e n c e o f t h e s i z e e f f e c t s , d e t e r l o r a t i o n o f s t l - e n g t h due t o p e r n ~ a r ~ e n t a n d c y c l i c l o a d s , e t c . ) .
The c r e e p c o e f f i c i e n t 4 . a n d t h e s h r i n k a g e c o e f f i c i e n t E~
were t a k e n f r o m t h e v a l u e s o b t a i n e d a t t h e MPA* MunLch o f t h e Comit6 E u r o p g e n du E6ton ( C E B ) ( R e f . 4 ) . Both t h e s e v a l u e s d e p e n d n o t o n l y on t h e t e m p e r a t u r e a n d h u m i d i t y o f t h e a i r s u r r o u n d i n g t h e b u i l d i n g
component, b u t a l s o on t h e c o m y , o s i t i o n o f t h e c o n c r e t e ( c e m e n t c o n t e n t a n d w a t e r / c e m e n t r a t i o ) a n d on t h e t i m e o f i n i t i a l . l o a d i n g . A l s o i m p o r t a n t a r e t h e p o s s i b i l i t i e s o f d i l y i n g of' t h e b u i l d i n g component, d u r i n g l o a . d i n g a n d tile time a t which t h e damage h a d o c c u r r e d .
F'or c a s e s where d u r i n g i n s p e c t i o n 01. i n t h e d e s c r i p t i o n
o f t h e damage no f u r t h e r d i r e c t i v e s cou1.d b e o b t a i n e d f o r t h e d e t e r - m i n a t , i c n o f t h e r e q u i r e d c o e f f i c i e n t s , e x p e r i e n c e f r o m o t h e r s m a l l e r b u i l d i n g corctponents was c a l l e d u p o n . F o r e x a m p l e , t h e d u r a t i o n o f s h o r i n g o f a n apartnierlt s l a b vras assumed t o be two weeks as a n a v e r a g e . U s u a l l y , t h e w a t e r / ' c e m e n t r a t i o o f t h e c o n c r e t e was r e c o n s t i t u t e d f r o m t h e a t t a i n e d c o n c r e t e s t r e n g t h by a s s u m i n g 300 kp/m3 cement c o n t e n t . 7 . 2 C a l c u l a t i o n o f t h e T e r m i n a l D e f l e c t i o n V a l u e s
---
The d e f l e c t i o n c o m p r i s e s a n e l a s t l c a n d a p l a s t i c component. P a r t o f t h e s e d e f o r m a t i o n s o c c u r i m m e d i a t e l y upon a p p l i c a t i o n o f t h e l o a d ; t h e r e m a i n d e r i s t i m e - d e p e n d e n t . The c a l c u l a t i o n o f t h e t h e o r e t i c a l d e i ' l e c t i o n was c a r r i e d o u t f o r b o t h t h e u r ~ c r a c k e d ( S t a t e I ) a n d t h e c r a c k e d ( S t a t e 1 1 ) s e c t i o n . The d e p l e c t i o n w h i c h would p r ~ o b a b l y o c c u r i n a n a r b i t r a r y s t a t e o f c r a c k f o r r n a t i c n was t h e n d e t e r m i n e d by i n t e r p o l a t i o n . E l a s t i c D e f l e c t i o n : S t a t e I:r:
= e n - !I.a 2
I I E p-
En I I S t a t e 11: l1 = c , 0 ha 2
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T r a n s l a t o r ' s N o t e : M a t e r i a l T e s t i n g L a b o r a t o r y* *
kp = k i l o pond = k i l o gram f o r c eThe c o e f f i c i e n t c d e p e n d s o n t h e s t r u c t u r a l s y s t e m , t h e l o a d d i s t r i b u t i o n , a n d t h e v a r i a t i o n o f t h e moments o f i n e r t i a . The v a l u e
f o r c was d e t e r m i n e d f r o m t a b l e s o f well-known b o o k s on s t a t i c s . The
moment o f i n e r t i a ( I ) was d e t e r m i n e d t a k i n g i n t o a c c o u n t t h e f a c t o r n f o r s t e e l i n s e r t s . I n S t a t e I1 t h e d e f o r m a t i o n o f t h e s t e e l was d e t e r m i n e d by c o n s i d e r i n g t h e p a r t i c i p a t i o n o f t h e c o n c r e t e b e t w e e n t h e c r a c k s ( s e e Ref . l 7 ) . I n c r e a s e i n D e f l e c t i o n d u e t o C r e e p f k a n d S h r i n k a g e f s o f t h e c o n c r e t e : S t a t e I : f k 1 - -
n~
' @ ' f o I I I S t a t e 11: f i l - - ~ I I @ ' f o The v a l u e sn
a n d s r e p r e s e n t c u r v a t u r e c o e f f i c i e n t s w h i c h e n c o m p a s s t h e r e s i s t a n c e t o d e f l e c t i o n d u e t o t h e s t e e l i n s e r t s a n d t h e r e s u l t i n g s t r e s s r e d i s t r i b u t i o n . They w e r e d e r i v e d i n R e f . 3 . 7 . 3 M a g n i t u d e o f D e f l e c t i o n s Which I n i t i a t e d Damage--
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P a r t i c u l a r c a r e was t a k e n i n d e t e r m i n i n g t h e m a g n i t u d e s o f t h e d e f l e c t i o n s a t w h i c h damage o c c u r r e d . I n a d d i t i o n t o t h e g e n e r a l c o e f f i c i e n t s l i s t e d i n S e c t i o n 7 . 1 , f u r t h e r d a t a c o n c e r n i n g t h e c h r o n o l o g y o f t h e b u i l d i n g c o n s t r u c t i o n , t h e t y p e o f damage, a n d t h e t i m e o f f i r s t o b s e r v a t i o n o f damage h a d t o b e c o l l e c t e d . The c a l c u l a t i o n p r o c e d u r e w i l l b e shown b r i e f l y i n t h e f o l l o w i n g two e x a m p l e s . ( a ) The c r a c k s o f a s u p p o r t e d p a r t i t i o n w a l l a r i s e o n l y f r o m t h o s e d e f l e c t i o n c o m p o n e n t s w h i c h o c c u r r e d a f t e r t h e e r e c t i o n o f t h e w a l l a n d a f t e r t h e a p p l i c a t i o n o f t h e i n t e r i o r p l a s t e r f i n i s h . T h e s e d e f l e c t i o n c o m p o n e n t s d e p e n d o n t h e i n c r e a s e o f c r e e p a n d s h r i n k a g e d e f o r m a t i o n o f t h e c o n c r e t e , o n t h e a d d i t i o n a l l o a d i n g w h i c h became e f f e c t i v e s u b s e q u e n t l y ( e . g . a p p l i c a t i o n o f t h e f l o o r c o v e r i n g , t h e c e i l i n g f i n i s h , o r t h e l i v e l o a d ) , a n d on t h e e x t e n t o f e x i s t e n c e o f S t a t e 11. F o r c a s e s w h e r e no more a c c u r a t e i n f o r m a t i o n c o u l d b e g a t h e r e d f r o m d o c u m e n t s , i t was a s s u m e d t h a t t h e p e r m a n e n t l y a c t i n g l i v e - l o a d component became e f f e c t - i v e o n l y a p p r o x i m a t e l y f i v e m o n t h s a f t e r t h e p a r t i t i o n w a l l p l a s t e r i n g h a d b e e n c o m p l e t e d . I n S e c t i o n 9 a s a m p l e c a l c u l a t i o n i s p e r f o r m e d f o r d e t e r m i n a t i o n o f t h e d e f l e c t i o n w h i c h i n i t i a t e d t h e damage. ( b ) I n t h e c a s e o f a s a g g i n g s l a b , t h e a c t u a l l y m e a s u r e d d e f l e c t i o n i s i t s e l f t h e s o u g h t - a f t e r d e f l e c t i o n w h i c h i n i t i a t e s t h e damage, s i n c e o n l y t h i s v a l u e seemed d i s t u r b i n g t o t h e o b s e r v e r . N e v e r t h e l e s s , e v e n i n t h e s ec a s e s t h e t h e o r e t i c a l d e f l e c t i o n was c a l c u l a t e d i n o r d e r t o c h e c k w h e t h e r t h e d e f l e c t i o n of t h e s l a b was r e a l l y t h e s o l e c a u s e . 7 . 4 C o e f f i c i e n t s o f D e f o r m a t i o n Which Were C a l c u l a t e d S i m u l t ~ a n e o u s l ~
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With t h e 2 e f l e c t i o n---
I n o ~ d e r t o f i n d t h e r e 1 e t i o : l s h i p s w h i c h g o v e r n t h e o c c u r r e n c e o f a p a r t i c u l - a r i n s t a r c e o f damage, t h e r e l a t i v e d e f l e c t i o n f / E , t h e maximum c u r v a t u r e max. l / ' p , t h e l a r g e s t e n d r o t a t i o n o f t h e s u p p o r t s , max.
t h e l a r g e s t a n g l e of t h e t a n g e n t s t o t h e n e u t r a l ax:;s, max. tan!tii9alrd t h e f i n a l c r a c k o p e n i n g d w e r e c a l c u l ~ t e d , i n a d d i t i o n t o t h e d e f l e c t i o n f S c h ( s e e T a b l e s j n t h e A p p e n d i x , c o l u m n s 2 1-
2 5 ) .8 . FACTORS RESPONSlBLE FOR TdE OCCURRENCE OF DEFLECTION DAMAGE 8 . 1 T h e o r e t i c a l l y P o s z i b l e S o u r c e s o f Dan,age ---..---.----...---
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A s h a s b e e n r e p e a t e d l y i n d i c a t e d , t h e German R e l n f o y c e d C o n c r e t e Code C I N 1 0 4 5 c o n t a i n e d v a r i o u s deficiencies which e x p l z i n some o f t h e n l e n t l o n e d t y p e s of d e f l e c t i o n damage. Such d e f i c i e n c i e s ( N o s . I
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V i n column 1 7 o f t h e t a b l e s i n t h e A p p e n d i x ) i n c l u d e e s p e c i a l l y t h e f a c t t h a t e x c e s s i v e d e f l e c t i o n s l e n d e r n e s s r a t i o s w e r e p e r m i t t e d f o r two-way r e i n f o r c e d p l a t e s . A n o t h e r l a y i n t h e f a u l t y b a s j s u s e d f o r c a l c u i a t i o n o f d e f l e c t i o n s . ? ' h i s y i e l d e d e x c e s s i v e l y s m a l l . v a l u e s aild t h e r e b y g a v e t h e d e s i g n e r t h e i . l l u s i o n o f t o o f a v o u r a b l e a d e f o r n a t i o n b e h a v i o u r o f r e i n f o r c e d c o n c r e t e b u l l d i n g c o m p o n e n t s . The d e f l e c t i o n was c a l c u l a t e d f o r a n u n c r a c k e d s e c t i o n w i t h t h e same modulus o f e l a s t i c i t y c f c o n c r e t e f o ? a l l c o n c r e t e s t r e n g t h s . l ' h e t h i r d d e f i c i e n c y l a y i r i t h e f a i l u r e t o r e q u i r e a d e q u a t e c o n s i d e r a t i o n o f t h e c r e e p a n d s h r i n k a g e d e f o r n a t i o n s o r t h e c o n c r e t e . T h i s may c e l l b e b e c a u s e s u f f i c i e n t i r ) f o r r o a t i o n on t h e e f f e c t s o f c r e e p a n d s h r i n k a g e of' c v n c r e t e h a s o n l y b e e n a c c u m u l a t e d g r a d u a l l y d u r i n g t h e l e s t few d e c a d e s . A l s o , a s e r i e s o f e r r o r s weye c o m m i t t e d i n t h e s t a t i c a l c a l c u l a t i o n s . T h e s e e r r o r s (Plos. lrI t o X i n column 17 o f t h e t a b l e s i n t h e A p p e n d i x ) r e s u l t e d p a r t : c u l e r l y f r o m ' I n c o r r e c t . assumpt!.ons c o n c e r n i n g t h e s t a + , i c s y s t e m , a n d o n l y s e c o n d a r i l y rrom l i u m e r i c a l e r r o r s . F o re x a m p l e , i t i s u s u a l l y i n a p p r o p r i a t e t o assume f u l l e n d r e s t r a i n t s f o r a s l a b c o n n e c t i r ~ g t o a
38
crn b r i c k w a l l o f a o n e - s t o r e y r e s i d e n t i a lb u l i l d i n g . S j m i l a r l y , t h e f a v 0 u r a b J . e e f f e c t u f t o - s i o n a l s t i f f n e s s o f s i m p l y upp ported two-way r e i n 3 o r c e d p l a t e s :;hould b e t a k e n i n t o a c c o u n t o n l y \:hen a r a i s i n g o f t h e c o r r l e r s i s p r e v e n t e d e i t h e r by d e s i g n o r by s t a f 2 i c c o n d i t . i o n s
.
A l s o , i n s u f l n i c i e : n t c o n s i ~ l e r a t i o n o f f ' o u n d a t i o n s e t t l e m e n t c a n l e a d t o b1lild:ng damage, s i r ~ c e s t r e s s r e d i s t r i b u t i o n w i l l r e s u l t i n a d i f f e r e n t l o a d i n g e f f e c t o f t h e r e i n f o r c e d c o n c r e t e b u i l - d i n g c o m p o n e n t s t h a n h a d b e e n assumed i n t11e s t a t i c c a l c u l a t ' o n s . F i n a l l y , t h e d a n g e r o f o v e r l y f a v o u r a b l e 1oad:ng a s s u m p t i o n s must a l w a y s b e b o r n e i n m i n d . A wide v a r i e ' ; y o f c a u s t l s o f damage a p p e a r s p o s s i . b l e d u r i n g c o n s t r u c t i o n o f t h e b u i l d i n g ( N o s . X I-
XV i n column 1 7 o f t h e t a b l e s i n t h e A p p e n d i x ) . A s o n e o f t,he p r i n c i p a l . :;ourc:es, l n s u f f i c l e n t compressive s t r e n g t h o f c o n c r e t e may b e m e i ~ t i o n e d . T h e r e a r e v a r i o u s p o s s i b l e rclasorls f'o? t h i s : u n s a t i s f a c t o r y g r a i n - s i z e d i s t r i b u t i o n , i n : j ~ f f f . c I e n t cerrient,
t o o l a r g e a wat,er/cement r a t i o , f r o s t e f f e c t s , e t c .O c c a s i o n a l l y , t o o few r e i n f o r c e m e n t s were i n s t a l l e d , c o n t r a r y t o t h e r e i n f o r c i n g s c h e d u l e s , o r t h e wrong s t e e l q u a l i t y was u s e d . Q u i t e f r e q u e n t l y t h e r e i n f o r c e m e n t was n o t l o c a t e d a t t h e s p e c i f i e d d e p t h . D e f i c i e n t form-work o r e x c e s s i v e s p a n l e n g t h s b e t w e e n b a r s u p p o r t s c a n a l s o c a u s e d e t r i m e n t a l d e f l e c t i o n s . W e may a l s o m e n t i o n i n s u f f i c i e n t s l a b t h i c k n e s s , o r a t o o n a r r o w l y f o r m e d s o l i d c o n c r e t e e d g e s t r i p o f a r i b b e d s l a b . F i n a l l y , e r r o r s h a d b e e n c o m m i t t e d a l s o i n t h e d e s i g n p h a s e o f t h e b u i l d i n g c o m p o n e n t s . Such a n e r r o r ( N o s . X V I - X X i n column 1 7 o f t h e t a b l e s i n t h e A p p e n d i x ) o c c u r s , f o r i n s t a n c e , when n o r e i n f o r c e - ment h a s b e e n p r o v i d e d f o r t h e r e s i s t a n c e o f p o s s i b l e r e s t r a i n t moments. T h i s r e s u l t s i n l a r g e c r a c k s i n t h e c o n c r e t e t e n s i o n z o n e . Very f r e - q u e n t l y t h e d e f o r m a t i o n s f o r t h e a s s u m e d s t r u c t u r a l a c t i o n o f t h e re- i n f o r c e d c o n c r e t e b u i l d i n g c o m p o n e n t s c o u l d n o t t a k e p l a c e w i t h o u t s t r e s s i n g a d j o i n i n g b u i l d i n g c o m p o n e n t s f a r beyond t h e i r l o a d c a p a c i t y . I n t h i s c o n n e c t i o n we may m e n t i o n t h e h o r i z o n t a l c r a c k s i n t h e e x t e r i o r p l a s t e r w h i c h h a v e come a b o u t f r o m t h e r o t a t i o n o f t h e e d g e s u p p o r t s o f r e i n f o r c e d c o n c r e t e s l a b s . The s u p p o r t i n g o f r e i n f o r c e d c o n c r e t e c o m p o n e n t s o n p l a t e g l a s s windows must a l s o b e v i e w e d a s a d e s i g n e r r o r a n d s i m i l a r l y , t h e u n i n t e n t i o n a l s u p p o r t i n g o f s l a b s o n p a r t i t i o n w a l l s o r aluminum c u r t a i n w a l l s . A s p e c i a l damage c a u s e i s t h a t o f a p a r t i t i o n w a l l r e s t i n g o n t h e f l e x i b l e s u p p o r t p r o v i d e d by a r e i n f o r c e d c o n c r e t e s l a b . P a r t - i t i o n w a l l s were a l s o s u p p o r t e d on t h e s l a b s i n f o r m e r d a y s when t h e s l a b s were m a i n l y s u p p o r t e d by wood a n d s t e e l g i r d e r s . However, t h e w a l l s d i d n o t c r a c k t o t h e same e x t e n t a s t h e y do t o d a y . . The w a l l s m e r e l y had t o r e s i s t c h a n g e s i n t h e e l a s t i c d e f o r m a t i o n s c a u s e d by t h e v a r i a b l e l i v e l o a d . B u t t h e c o n c r e t e s l a b s commonly u s e d t o d a y a r e s u b j e c t t o s u b s t a n t i a l t i m e - d e p e n d e n t c r e e p a n d s h r i n k a g e d e f o r m a t i o n s . F u r t h e r m o r e , g r e a t e r s p a n l e n g t h s a r e c h o s e n . The p a r t i t i o n w a l l c a n n o t accommodate s u c h l a r g e d e f o r m a t i o n s a n d c o n s e q u e n t l y i t c r a c k s . T h i s s p e c i a l c a u s e o f damage was i n c l u d e d among t h e d e s i g n e r r o r s , a l t h o u g h s t r i c t l y s p e a k i n g , g i v e n t h e s t a t e o f k n o w l e d g e a t t h e t i m e i t c a n n o t p r o p e r l y b e c a l l e d a n e r r o r .
8 . 2 ACTUAL CAUZES OF DAMAGE
F i ~ u r e
9
g i v e s a s u r v e y o f t h e a c t u a l c a u s e s o f damage, a r r i v e d a t t h r o u i h t h e u n i f o r m a n a l y s i s o f t h e r e p o r t s r e c e i v e d . The a b o v e - m e n t i o n e d t h e o r e t i c a l l y p l a u s i b l e c a u s e s a r e p l o t t e d on t h e a b s c i s s a , w i t h a r e f i n e d g r i d i n t h e o r d e r o f t h e n u m b e r i n g s c h e m e , w h i l e t h e f r e q u e n c y o f t h e i r o c c u r r e n c e i s p l o t t e d a l o n g t h e o r d i n a t e . I t became a p p a r e n t t h a t m o s t c a s e s o f d e f l e c t i o n damage c o u l d b e t r a c e d t o e x c e s s i v e l y f l e x i b l e p a r t i t i o n w a l l s u p p o r t (XIX). Very f r e q u e n t l y t h e damage o c c u r r e d a s a c o n s e q u e n c e o f e x c e e d i n g t h e p e r m i s s i b l e d e f l e c t i o n s l e n d e r n e s s r a t i o o f t h e r e i n f o r c e d c o n c r e t e s u p p o r t member ( I ) . The s o l i d p a r t o f column I i n t h e h i s t o g r a mr e p r e s e n t s a l l t h e c a s e s w h i c h w e r e d u e t o a v i o l a t i o n o f t h e p r o v i s i o n s i n e f f e c t a t t h a t t i m e ; t h e d a s h e d p o r t i o n r e f e r s o n l y t o c a s e s w h e r e t h e d e f l e c t i o n s l e n d e r n e s s r a t i o was g r e a t e r t h a n 35. Thus t h e d a s h e d p a r t a g a i n p o i n t s t o t h e p a r t i c u l a r s u s c e p t i b i l i t y t o damage o f two-way r e i n f o r c e d s l a b p a t t e r n s .
The o t h e r c a u s e s o f damage a r e much l e s s p r o m i n e n t i n c o m p a r i s o n t o t h e s e two s o u r c e s o f e r r o r s . The n e x t i m p o r t a n t
