Design graphs for concrete shell roofs

B O O K REVIEWS Dynamic response of structures to wind and earthquake loading P. L. Gould and S. H. Abu-Sitta Pentech Press, London, 1980, 186 pp., £14.00 This is a well w r i t t e n i n t r o d u c t o r y t e x t which c o n c e r n s itself w i t h the d y n a mics of e n g i n e e r i n g structures. Some m e t h o d s for c o m p u t i n g t h e d y n a m i c r e s p o n s e of s t r u c t u r a l systems w h e n subjected to n a t u r a l forces, in particular wind and e a r t h q u a k e loadings are explained. T h e t e x t c o n c e n t r a t e s o n both deterministic and non-deterministic analysis t e c h n i q u e s . A p r e r e q u i s i t e of a n o n - d e t e r m i n i s t i c analysis is t h a t the n a t u r e of the n a t u r a l forces be described in a statistical m a n n e r and in this respect the t e x t gives a b r i e f b u t clear e x p o s i t i o n . T h e early stages of the b o o k are given over to a concise m a t h e m a t i c a l d e s c r i p t i o n of t h e d y n a m i c response analysis of linear S.D.O.F. and M.D.O.F. s t r u c t u r a l s y s t e m s w h e n s u b j e c t e d to e i t h e r d e t e r m i n i s t i c or n o n - d e t e r m i n i s t i c loadings. T h e l a t t e r stages of the t e x t c o n c e n t r a t e on the practical application of these t h e o r i e s to structural s y s t e m s with particular reference to wind and seismic loadings. As the a u t h o r s claim the b o o k provides an a p p r o p r i a t e a l t h o u g h n o t t o o detailed a b a c k g r o u n d to some c u r r e n t techniques of m o d e r n s t r u c t u r a l d y n a m i c analysis and design. T h e practising engineer with an interest in tire subject or the research s t u d e n t with a c o m p e t e n t k n o w l e d g e of s t r u c t u r a l mechanics will find this text useful. A feature of the book is that a c o m p r e h e n s i v e set of references are given w h e r e the reader might feel t h a t greater d e p t h or insight i n t o the subject is required. T h e t e x t is able to proceed from introd u c t o r y material to a t h o r o u g h p r e s e n t a t i o n of some state-of-the-art m e t h o d s for d y n a m i c analysis and design. In this respect a detailed s t u d y is p r e s e n t e d of four different types of s t r u c t u r e c o m p r i s i n g of, tapered c h i m n e y s , h y p e r b o l i c cooling towers, suspension roofs and nrultistorey buildings, all of which are particularly sensitive to f l u c t u a t i n g loadings. The coverage is b r o a d and c o n s e q u e n t l y there is the inevitable gap or two in material c o n t e n t . Perhaps some m e n t i o n of the i m p o r t a n t role of the discrete F o u r i e r t r a n s f o r m in b o t h d e t e r m i n i s t i c and n o n - d e t e r ministic analysis might have been made, however, p r e s u m a b l y such topics were sacrificed for the sake

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of conciseness. A l t h o u g h the main i n t e r e s t of t h e b o o k is directed t o w a r d s t w o particular t y p e s of d y n a m i c loading it is clear t h a t the t e c h n i q u e s exp o u n d e d u p o n have their a p p l i c a t i o n to o t h e r t y p e s of d y n a m i c e x c i t a t i o n . F o r e x a m p l e blast effects. In the case of wind and seismic loadings the t e x t explains t h e d i f f e r e n c e b e t w e e n these types of forces f r o m the perspective of a s u b s e q u e n t d y n a m i c analysis. A l t h o u g h t h e r e are o u t l i n e similarities b e t w e e n t h e m e t h o d o l o g i e s a d o p t e d for an analysis and design having e i t h e r o f these types of loadings the t e c h n i q u e s utilized are invariably q u i t e different. T h e t e x t is able to discuss these m a t t e r s in a clear fashion and by way of an i n t r o d u c t i o n there is a chart in the preface w h i c h gives an e x c e l l e n t overview to the p r o b l e m of design for b o t h types of loadings. T h e b o o k c o n t a i n s 175 clearly p r i n t e d pages and is well b o u n d . T h e s t a n d a r d of m a t h e m a t i c a l t y p o g r a p h y is high and the diagrams and figures are well laid o u t and presented. This reviewer would have n o h e s i t a t i o n in a d d i n g this t e x t to his reference collection.

A. G. Collings

Design graphs for concrete shell roofs C. B. Wilby Applied Science Publishers Ltd, London, 1980, 170 pp., £15.00 T h e b o o k p r e s e n t s plots of stress result a n t s for a c e r t a i n t y p e of shell r o o f o b t a i n e d b y solving t h e relevant differential e q u a t i o n s b y m e a n s of an elect r o n i c a n a l o g u e c o m p u t e r . T h e basic u n d e r l y i n g principles of b o t h shell t h e o r y and t h e s i m u l a t i o n of the governing e q u a t i o n s b y t h e a p p r o p r i a t e a n a l o g u e circuit are concisely e x p l a i n e d in the first five c h a p t e r s of t h e text, while c h a p t e r 6 gives e x a m p l e s on the use of graphs; t h e actual p l o t s t h e n follow and t h e y o c c u p y a b o u t twot h i r d s of the b o o k . A l t h o u g h b o t h s y m m e t r i c a l circular cylindrical shells a n d n o r t h q i g h t shells are discussed, only results for the f o r m e r are p r e s e n t e d . F u r t h e r m o r e , these are restricted to two basic t y p e s of cylindrical shell u n d e r c o m b i n e d self-weight a n d u n i f o r m snow load ( t h e t e r m s ' i n t e r n a l ' and ' e x t e r n a l ' used to d e n o t e these two types refer to their a p p r o x i m a t i n g the c o n d i t i o n s of i n t e r n a l a n d e x t e r n a l u n i t s in a nmltibay shell r o o f ) . T h e n u m b e r of d i f f e r e n t shell g e o m e t r i e s (of fixed

d i m e n s i o n s ) c o n s i d e r e d is limited to 14, the t h i c k n e s s at the crown of the shell being fixed at 65 ram; each of t h e s e 14 cases is first analysed on the a s s u m p t i o n t h a t the t h i c k n e s s is cons t a n t t h r o u g h o u t t h e shell, and t h e n the analysis is r e p e a t e d for the case w h e n the t h i c k n e s s is gradually increased f r o m c r o w n to edge. In his a c c o u n t of the governing e q u a t i o n s , the a u t h o r presents b o t h S c h o r e r ' s m e t h o d as well as a t h e o r y o f his o w n in w h i c h a d d i t i o n a l t e r m s appear. It is n o t clear which of these t w o sets of e q u a t i o n s is the one used to o b t a i n the plots. The absence in these of t h e l o n g i t u d i n a l b e n d i n g m o m e n t s w h i c h the a u t h o r ' s t h e o r y allows for and S c h o r e r ' s m e t h o d neglects, would imply t h a t the latter techn i q u e has been a d o p t e d ; nevertheless, m e n t i o n is m a d e in c h a p t e r 3 of a s t u d y of the relative effects of individual t e r m s in b o t h sets of e q u a t i o n s . Irrespective of t h e m e t h o d a d o p t e d , h o w e v e r , the accuracy of the results it to be q u e s t i o n e d . T h e use of the a u t h o r ' s t h e o r y is likely to lead to s p u r i o u s results since his set of equat i o n s does n o t a p p e a r to c o n f o r m to the w e l l - k n o w n s y m m e t r y of the s t a t i c - g e o m e t r i c analogy for thin shells. This is a q u e s t i o n of c o n s i s t e n c y in the f o r m u l a t i o n of the governing equations, and, f r o m this p o i n t o f view, S c h o r e r ' s a p p r o x i m a t i o n is indeed a c o n s i s t e n t one ; the r e c o g n i t i o n of this fact has led to o t h e r a p p r o x i m a t e equations, which contained additional t e r m s (such as, for example, the one in F i n s t e r w a l d e r ' s t h e o r y ) , being neglected. U n f o r t u n a t e l y , even if S c h o r e r ' s e q u a t i o n s have p r o v i d e d the basis for the design graphs, the range o f shell g e o m e t r i e s covered is such t h a t t h e i r spans fall s o m e w h a t b e l o w the m i n i n m m lengths required for Schorer's a p p r o x i m a t i o n to be of a c c e p t a b l e accuracy. A n o t h e r surprising feature in the analytical part of the book is the specification of five b o u n d a r y conditions at the apex of the n o r t h - l i g h t shell, even t h o u g h the governing partial d i f f e r e n t i a l e q u a t i o n is still of the e i g h t h order! However, this has no bearing on the plots since, as already m e n t i o n e d , no results for this type of r o o f are p r e s e n t e d . In view of the q u e s t i o n of a c c u r a c y of results and the fact t h a t half of the plots simply c o m p l e m e n t i n f o r m a t i o n already available for s y m m e t r i c a l cylindrical shells of c o n s t a n t t h i c k n e s s (see, for e x a m p l e , ' C o m p u t e r analyses of cylindrical shells' by J. E. Gibson, F. N. Spon Ltd, L o n d o n , 1961), the b o o k , in its present form, is of limited value to the designer. This is u n f o r t u nate, since the o t h e r half of the plots, in w h i c h the results of the effect of gradual t h i c k e n i n g from apex to edge are p r e s e n t e d , is, to ttlc reviewer's

knowledge, the first attempt to tabulate a practical factor seldom allowed for in the analysis (at least in the preliminary stages of design). Although the variation in thickness is made to follow a fixed analytical expression designed to simplify the corresponding analogue circuit, the author shows how such a thickening may be approximated in practice by simple construction methods; and, even though problems of interpretation might arise in the edge zone where it is difficult to distinguish between 'edge beam' and 'shell thickening', Professor Wilby is to be congratulated for departing, in his analysis, from the standard case of uniform thickness. To summarize, one cannot help feeling that the value of the book would be greatly enhanced if the inconsistencies in the governing equations were removed, the range of geometries presented increased, and a short discussion, based on a comparison between the case of uniform thickness and that of gradual thickening of the shell, included. The latter might enable conclusions of a more general type to be reached and would constitute a real contribution to our knowledge of the structural response of cylindrical shell roofs. Incidentally, the contents of the book would, in any case, be described more accurately by the title 'Design graphs for circular cylindrical shell roofs'. M. N. Pavlovic<

Non-linear design of concrete structures Ed. 114.Z. Cohn

Study No. 14: University of Waterloo, Canada, 1980, 670 pp., $23.00 This volume contains most of the papers presented at the C S C E - A S C E - A C I CEB International Symposium held at the University of Waterloo in August. 1979. It is now published as the fourteenth of the SM Studies Series of the Solid Mechanics Division of that University. The contents are divided into four groups under the headings of (i) Fundamentals of nonlinear analysis and design, (ii) Framed structures, (iii) Bridges and other structures and (iv) Wall and panel structures. The volume contains 24 papers and it is not possible to comment on every paper but collectively they represent an excellent overview of the current state of knowledge regarding the nonlinear design of concrete structures. The potential benefits which would result from the systematic introduction of such concepts in design codes are indicated and the corresponding com-

putational complexities are also discussed. The first section consists of five papers starting with a compact but extremely instructive summary (written by M. Z. Cohn) of the problems and prospects of the subject considered with particular emphasis placed on elastoplastic constitutive relations. This paper can be strongly recommended to any engineer seeking an authoritative introduction to this field. Another paper in this section which is particularly important is the discussion by N. C. Lind of structural safety. Professor Lind gives a comprehensive format for the mathematical structure of the reliability problem and concludes that nonlinearity in structural behaviour is not a serious obstacle. However, the author of this paper points out two forms of difficulty which he considers to be more serious. The first is the influence of human factors usually ignored in conventional reliability analyses but considered to be responsible for most failures. Professor Lind indicates that this influence may be represented by random variables of human error but it is this reviewer's opinion that such considerations are essentially nonstatistical and could be treated more appropriately by fuzzy (rather than stochastic) concepts. The second section contains seven papers and three of these were particularly interesting to this reviewer. The paper entitled 'Optimal inelastic design of seismic-resistant reinforced concrete framed structures' by V. V. Bertero and S. W. Zagajeski presents an automated optimal design procedure which can be considered in three stages The first stage consists of a preliminary design of subassemblages and is performed by nonlinear programming. The second stage consists of elastic and inelastic dynamic analyses and the third stage produces an optimal design from the results obtained in the previous stages. The lengthy paper (54 pages) gives full details of the various suggested procedures and illustrations are presented for a ten-storey, threebay frame. The paper by O. De Donato e t al. draws our attention to the significant progress made with regard to mathematical programming methods of optimal design but also points out that these developments have had little influence (so far) on design practice. The authors make a contribution towards the closing of this gap by developing an optimal design method for prestressed concrete beams using a mini-computer. Another paper in this section is concerned with .the nonlinear analysis and design recommendations contained in the CEB model code and is authored by G. Macchi.

The CEB provide rules for verifying the integrity of a given structure in accordance with certain limit-state principles but gives little guidance as to how a structure may be designed directly. Professor Macchi considers the practical procedures which may be applied within the spirit of the CEB model code and his paper is an important addendum to that code. The third section contains four papers including one outlining a comprehensive methodology for the optimal limit design of r.c. bridges by M. Adin e t al. and another presenting a nonlinear finite element method for the full range analysis of concrete bridge decks by R. J. Cope e t al. A further paper by P. G. Bergan e t al. discusses the requirements of design codes for concrete off-shore structures and emphasizes some special problems for which nonlinear studies are particularly important. The fourth (and final) part of the book contains eight papers on various aspects of the design of wall and panel structures for various types of static and dynamic loadings. The book is well produced and represents extremely good value. It is a much more integrated volume than normally results from the proceedings of a conference. This is presumably due to a careful selection of papers by the organizers and to good editorial work in the preparation of the final publication. It is strongly recommended to all those interested in the practical implementation of recent research into the nonlinear behaviour of concrete structures. J. M u n r o

Analysis of structures by the forcedisplacement methods 114. Smo/ira

Applied Science Publishers Ltd, London, 1980, 389 pp., £25.00 The author states that his main object in writing this book was 'to develop a method by which forces and displacements could be obtained directly from a given diagram of a structure by setting out matrices with a minimum of intermediate work'. He goes on to tell us that one can analyse elastic structures by selecting suitable static variables as in the flexibility method, or by selecting kinematic variables as in the stiffness method. The third procedure according to the author is to consider the static and kinematic quantities to be 'simultaneously indeterminate' and it is this approach which is developed in the book into a technique which the author dubs the 'force-displacement method'. The first chapter tackles the analysis of beams

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