BOOK REVIEWS EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, VOL. 24, (1995)

Transcription

1 EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, VOL. 24, (1995) BOOK REVIEWS DYNAMICS OF STRUCTURES, by Ray w. Clough and Joseph Penzien, 2nd edition, McGraw-Hill, New York, No. of pages: 738. ISBN The first edition of Dynamics of Structures was published in I975 and was reviewed in the journal by George W. Housner [Earthquake eng. struct. dyn. 4, (1976)l. In a wide-ranging review Housner emphasized the many good points of the book and compared it with existing books on earthquake engineering. This comparison included the interesting comment that Clough and Penzien s book might have the title What Every Young Civil Engineer Should Know About Structural Dynamics, whereas the title What Every Young Research Worker Should Know About Earthquake Engineering might apply to Fundamentals of Earthquake Engineering by N. M. Newmark and E. Rosenblueth (Prentice-Hall, 1971), which today is the best known and most frequently cited of the books on earthquake engineering, which were mentioned by Housner in his review. Clough and Penzien s book has been cited more often than any other book in the lists of references in papers, which have been published in this journal since the date of the review, despite the appearance of many new books of relevance to authors. The organization of the material in the 2nd edition follows that in the 1st edition; thus, after an introductory chapter, the book is divided into five parts: I Single- Degree-of-Freedom Systems; I1 Multi-Degree-of- Freedom Systems; 111 Distributed-Parameter Systems; IV Random Vibration; V Earthquake Engineering. Probably it was the existence of the last part, and to a lesser extent the fourth part, in the 1st edition which prompted Housner to make comparisons with books on earthquake engineering in his review, although earthquake engineering does not appear in the title or even in some form of subtitle. This omission is understandable, as the material in Parts I-IV is applicable when determining the response of structures to all types of dynamic load. The overall length of the text has been increased from 634 to 738 pages in the 2nd edition. However, that gives only an approximate indication of the new material. The 2nd edition uses type which leads to slightly more words per page without any detriment to readability. In a book on this topic there are many equations, figures and tables; the information contained in the latter has often not been changed in the new edition, but the layout has been improved without necessarily requiring more space. Although the division into five parts exists in both editions, an important change of emphasis is indicated by comparing lengths of the parts in the two editions. The major increase in length is in the part on earthquake engineering with smaller increases in the material on single- and multi-degree-of-freedom systems and a significant reduction in length for distributed-parameter systems. Emphasis in this review is on new topics and those for which major changes have been made between the editions. Nevertheless, it should be noted that the authors have made minor changes throughout the text. It is not to be expected that the introductory first chapter, Overview of Structural Dynamics, will include major changes. Hamilton s principle, which formed a subsection in the 1st edition, containing the basic equations, is discussed more briefly under the subheading, Variational Approach, in the 2nd edition. However, while both editions contain a later chapter on variational formulations of the equations of motion, Hamilton s principle is established in some detail only in the 2nd edition. The headings of the chapters (no. 2-8) in Part I are: Analysis of Free Vibrations, Respodse to Harmonic Loading, Response to Periodic Loading, Response to Impulsive Loading, Response to General Dynamic Loading-Superposition Methods; also-step-by-step Methods, and Generalized Single-Degree-of-Freedom Systems, respectively. These are similar to those in the 1st edition, except that the original Chapters 2 and 3 have been amalgamated into Chapter 2 with the section on the application of Hamilton s principle omitted and three sections on generalized single-degree-of-freedom (SDOF) systems removed to Chapter 8 as a natural introduction to vibration analysis by Rayleigh s method. In the determination of the response to harmonic loading the alternative solution in terms of a complex exponential function has been added. In the section on the evaluation of the viscous damping ratio the free-vibration decay and the resonant amplification methods are given as before; the description of the half-power (bandwith) method is expanded in order to clarify its name; similarly the description of the resonant energy loss per cycle method is expanded. The last section of Chapter 3 introduces the important concept of complex-stiffness damping, for which the energy loss per cycle is independent of the excitation frequency. In the short chapter on response to periodic loading the material is rearranged so that the exponential form follows directly the trigonometric form and a preview of the frequency-domain method of analysis, which is discussed in detail in Chapter 6, is added. While the chapter on the response to impulsive loading is basically unaltered, that on superposition methods for the response to general dynamic loading has been rearranged and extended. Rearrangement applies to the analysis through the time domain with sections on the Duhamel integral and numerical summation. The analysis through the frequency domain, comprising the important topics of Fourier response integral, Discrete Fourier Transforms, and Fast Fourier Transforms, has been extended to show how dynamic response can be evaluated. The chapter concludes with a brief section which gives the relationships between the time- and

2 458 BOOK REVIEWS frequency-domain transfer functions; these relationships will be proved and illustrated later. Step-by-step methods of determining the response to general dynamic loading (Chapter 7) are of great importance in earthquake engineering, as the superposition methods of Chapter 6 are not applicable to non-linear problems. However, even for linear problems the Duhamel integral method is rarely used in practice, as the input, usually the ground acceleration, is a complicated function of time, and thus numerical integration is essential. This has caused a change of emphasis in the presentation of this topic. In the 1st edition step-by-step methods formed a part of a chapter on the analysis of non-linear structural response, whereas they receive considerably more attention in the new edition and the extension to an incremental formulation for non-linear analysis appears towards the end of the chapter. As an introduction to general methods, the authors describe initially the piecewise exact method; this is an exact solution for a linear structure for which the excitation varies linearly with time during each discrete time interval. Thus, in practice it is an approximate method and might be more accurately called the piecewise linear method. Then the authors describe the central difference formulation, the Euler-Gauss procedure and the Newmark Beta methods. For the latter the constant average acceleration method (/3 = 1/4) and the linear acceleration method (/3 = 1/6) are described with inclusion of an explicit formulation. In this chapter structures are restricted to one degree of freedom. However, in Part I1 step-by-step methods for multi-degree-of-freedom (MDOF) systems, which occur in practice from a finite element idealization of a real structure, are described in matrix notation. As treated in the two chapters the vital step from SDOF to MDOF systems is made conceptually simple. Part I concludes with generalized singledegree-of-freedom systems (Chapter 8), where assemblages of rigid bodies and structures with distributed flexibility for which only the fundamental mode is of interest are treated. Analysis of the latter type of structure leads to a formulation of the Rayleigh method of determining natural frequencies. Part 11, Multi-Degree-of-Freedom Systems, contains eight chapters. Chapters 9-11 on the formation of the relevant equations of motion, the evaluation of structural property matrices and analysis of undamped free vibrations show only minor changes from the corresponding chapters in the 1st edition. The chapter on evaluation includes subsections on finite-element stiffness, lumpedmass and consistent-mass matrices; these are derived for conventional beam elements in flexure. This limited exposition illustrates very simply the basic ideas of the finite element method and demonstrates that, as symmetric stiffness and mass matrices are assumed throughout the book, all the analysis of structural dynamics is relevant to finite element models of structures. As in Part I, there are two chapters on the analyses of dynamic response, using superposition and step-by-step methods, in Part 11, but they are no longer consecutive. Although Chapter 12 on superposition methods is ap- proximately twice the length of the corresponding chapter in the 1st edition, the initial sections on normal coordinates, uncoupled equations of motion for structures with and without damping and response analysis by mode displacement superposition with its solution in terms of the Duhamel integral for each modal contribution are relatively unchanged. As in Part I, complexstiffness damping is added; when the response is the sum of modal contributions, use of complex-stiffness damping, for which energy loss per cycle is essentially independent of the frequency, is important. The 1st edition included a discussion of Rayleigh damping, where the damping matrix is a linear combination of the stiffness and mass matrices but damping can be prescribed for only two modes, and of extended Rayleigh damping, where additional terms, which are powers of the stiffness and mass matrices, are included in the expression for the damping matrix with the number of prescribed modal damping values equal to the total number of terms in the series. Information is given here about the important consequences of including an odd or an even number of terms in the derivation of the viscous damping matrix. The authors give also an alternative formulation for evaluating the damping matrix associated with a given set of modal damping ratios. These procedures lead to uncoupled modal equations for which there are computational advantages when evaluating response. In practice non-proportional damping matrices which yield coupled modal equations often occur, for example, in all soil-structure interaction problems and, using the authors example, in a frame which consists of two substructures, one of steel and the other of concrete. After describing the construction of the matrices, methods of determining response from coupled equations of motion are outlined with full discussion reserved for later sections or chapters. This chapter concludes with three new sections. Firstly, the relationship between the unit impulse response transfer function and the corresponding complex frequency-response transfer function is derived; these functions form the Fourier transform pair, which was mentioned in Chapter 6. (This derivation was given in the 1st edition, but in Part IV on Random Vibration). The last two sections develop a practical procedure for solving coupled equations of motion. This is achieved most easily in the frequency domain, where in principle the inversion of the complex impedance or dynamic stiffness matrix is required. Irrespective of whether a complex stiffness (representing hysteretic damping) or viscous damping is assumed, the terms in this matrix are frequency dependent and inversion is required at the closely spaced frequencies, which are associated with the generation of a Fast Fourier Transform (FFT). For a structure with many degrees of freedom this would not be a practical procedure. However, the complex frequency-response transfer functions can be obtained at widely spaced values of frequency. Then an efficient interpolation procedure, which yields the transfer functions at the intermediate closely spaced discrete frequencies, which are required for use of the FFT procedure, is described. Perhaps surprisingly these transfer functions are smooth functions of

3 BOOK REVIEWS 459 frequency, even although they have peaks at the natural frequencies of the structure, and thus interpolation is feasible. Vibration analysis by Matrix Iteration and Selection of Dynamic Degrees of Freedom, Chapters 13 and 14, replace a chapter on practical vibration analysis in the 1st edition. In addition to major reordering of the material, there have been some important additions and deletions. While conventional direct iteration for the determination of lowest, highest and intermediate modes is presented in both editions, there is more emphasis on the preferred method of inverse iteration in the new edition. This takes advantage of the narrow banding of the stiffness matrix, instead of being based on the fully populated flexibility matrix; also as it is applied inversely, it converges towards the fundamental mode shape. The Holzer and Holzer-Myklestad methods of determining natural frequencies approximately, which were simple in concept and useful in pre-computer and pre-finite element eras, have been deleted. Perhaps it was surprising that these methods were included in the 1st edition, but they were easily understood by students. Chapter 14 commences with a discussion of finite element degrees of freedom for 1-, 2- and 3-dimensional elements. After illustrating the very large number of degrees of freedom, which are associated with a finite element idealization of a relatively simple mutli-storey building frame, reduction of this number by acceptable assumptions about dynamic behaviour and by the process of static condensation has added importance. The following sections, which are similar to material in the 1st edition, demonstrate that the Rayleigh-Ritz method is an excellent procedure for reducing a model from the large set of finite element degrees of freedom to the smaller set which is required to evaluate dynamic properties. Also subspace iteration is an efficient method of solving eigenvalue problems and dynamic response can be defined efficiently in terms of the resulting mode shapes with acceptable accuracy achieved through a truncated set of co-ordinates. Then the book contains an important new section on the reduction of modal truncation errors; its purpose is to advise readers on the question of how many modal co-ordinates are required in order to avoid significant truncation errors. The chapter concludes with a long section on derived Ritz vectors; this provides important information on how to choose the trial vectors which are required to initiate the efficient subspace iteration procedure. In Chapter 15 step-by-step methods for determining the response of MDOF structures are described. Analysis is in terms of the incremental equations of motion in matrix form, which are essential for treating non-linear problems, and progresses through the constant average acceleration method (a surprising omission in the 1st edition), the linear acceleration method and its unconditionally stable extension, the Wilson 0 method. However, material on the performance of the Wilson 0 method, which was given for initial displacement problems in the 1st edition, is now omitted. In the concluding section strategies for the analysis of coupled MDOF systems are described. In many practical problems localized non- linearity may occur in known locations, for example, uplift problems. They may be treated advantageously by using substructures, where one non-linear substructure contains all the degrees of freedom associated with nonlinear effects and the degrees of freedom representing interconnections with the linear substructure. Then static condensation is applied to the linear substructure. Alternatively, coupling effects, which may arise from changes from the original linear stiffness or from modal coupling associated with non-proportional damping, can be treated as pseudo-forces. The final chapter of Part I1 on the variational formulation of the equations of motion includes few major changes. Modern methods of determining the response of structures with their distributed characteristics of stiffness and mass reduce to the solution of MDOF systems, where the number of degrees of freedom is large. Earlier methods, such as Rayleigh-Ritz, had similarities, although until the development of modern computers the number of unknowns was severely limited. Thus the importance of chapters on distributed-parameter systems (the subject of Part 111) may be questioned. This reviewer believes, and considers that authors of most books on structural dynamics would agree, that some knowledge of the dynamic behaviour of distributed-parameter systems is essential before a practitioner attempts to determine dynamic response for a practical structure from a sophisticated computer program. However, different authors adopt different definitions of some in their books. In the 1st edition Clough and Penzien considered only flexural and axial vibration of beams. Thus vibrations problems, where the displacement is a function of more than one coordinate, as in plates and shells, were not included. In support it can be stated that in any book on dynamics some possible topics have to be excluded, more specialist books on the dynamics of plates and shells exist, and the problems that can be solved directly from the equations of these distributed-parameter systems are limited in scope. Considering these comments, it is not surprising that Part I11 is now significantly shorter. Topics omitted include the chapter on the dynamic direct stiffness method, the effects of shear deformation and rotatory inertia on flexural vibrations, stress waves during pile driving and shear wave propagation in buildings. Modest additions include new material on flexural vibration due to support excitation and the free vibrations of beams on elastic foundations; in both cases there is relevance to more complex problems in earthquake engineering. The general arrangement of material in Part IV, Random Vibrations, in the two editions is similar. There are four chapters (20-23) on probability theory, random processes, and stochastic response of linear SDOF systems and of linear MDOF systems. The first two chapters contain considerable introductory material. In a long section on one-dimensional random walks the probability density function for a random variable, which is defined as the product of several random variables, is derived; the corresponding case where the main variable is the sum of several random variables is considered in both editions. There are brief sections on the principal

4 460 BOOK REVIEWS axes ofjoint probability density functions which will look familiar to those who are acquainted with Mohr s circle for principal stresses, and the special case of the Rayleigh probability density function. These were included previously, but with less emphasis, in a much longer section on two-dimensional random walks. Chapter 21 on Random Processes contains basic definitions of essential concepts, such as stationary and ergodic processes, autocorrelation and power spectral density functions, etc; the chapter has only some small changes compared to the earlier version. Considering the response of linear SDOF systems, relationships between the input and output autocorrelation functions and between the input and output power spectral density functions (this latter relationship being of prime importance) are derived and the response characteristics of narrow-band systems, the non-stationary mean square response, which results from zero initial conditions, and fatigue predictions for narrow-band systems are described. For MDOF systems the material on time-domain and also frequency-domain response for linear systems and on the forcing functions due to discrete and distributed loadings, all evaluated in terms of normal modes, follows the pattern of the 1st edition. The autocorrelation function for total response is given in its approximate form as a simple summation in terms of autocorrelation functions associated with each modal process, but in the new edition a cautionary note is added; when the system has closely spaced pairs of frequencies, the corresponding cross-correlation terms in the double summation for the autocorrelation function for the total response cannot be neglected. This is akin to determining maximum response from the Complete- Quadratic-Combination (CQC) method of weighting maximum modal contributions, instead of from the Square-Root-of-the-Sum-of-the-Squares (SRSS) method, which has been the subject of some papers in this journal and is discussed later in the book. This chapter concludes with a new section on the determination of frequencydomain response for linear systems, which have frequency-dependent parameters and/or normal modes, which are coupled through the non-orthogonal nature of the damping matrix. Response is determined by using the relation between the spectral density matrices for response and excitation; this is the matrix equivalent of the important relation between input and output spectral densities, which was derived in the previous chapter for SDOF systems., Analogously the matrix relationship is in terms of the complex frequency-response matrix, where each element is the complex response in one displacement co-ordinate due to a unit harmonic loading in another coordinate. The method of generating these complex frequency-response functions at closely spaced frequencies was described in Chapter 12 and has been summarized earlier in this review. Part V, Earthquake Engineering, is considerably longer than the last part in the 1st edition, where the title is the more restrictive, Analysis of Structural Response to Earthquakes. Nevertheless, three of the five chapters in the present version are concerned with the determination of structural response to earthquakes. The first two chapters introduce the information about earthquakes, which is essential for a structural dynamist who wishes to determine the probable seismic response of a structure. Thus there are descriptive sections on seismicity, earthquake faults and waves, the structure of the earth, plate tectonics. the elastic rebound theory of earthquake generation, and measures of earthquake magnitudes; these sections contain new material, particularly on plate tectonics. The pseudo-velocity spectral response occurs frequently in the literature on earthquake engineering. Thus the reviewer welcomes the extended presentation of this concept, its relation to relative displacement and absolute acceleration spectral responses and the underlying assumptions in generating these expressions. The several factors, which influence response spectra, are discussed, although the effects of some factors cannot be quantified. However, the numerical effects of local soil conditions on the shapes of response spectrum curves have been studied recently; relevant interesting results are presented here. The dual criteria of seismic design consist of: a moderate or design earthquake, which may reasonably be expected to occur once at the site during the structure s lifetime, and for which there should not be significant damage; and the most severe, or maximum probable, earthquake, which can be expected at the site. The deterministic procedure for establishing the peak free-field surface ground acceleration (PGA) for the design and maximum probable earthquakes is described. While the latter has often been used, Probabilistic Risk Assessment (PRA) methodologies have been developed recently; they provide a consistent probabilistic approach, which generates a seismic hazard curve that shows the annual mean frequency exceedance as a function of PGA for the site under consideration. The analytical procedure is summarized, and appropriate references are given. Response spectrum shapes are described, including piecewise linear, the ATC-3 (Applied Technology Council) spectra for use in building codes, the USNRC (United States Nuclear Regulatory Commission) design spectra for application to nuclear power plants, and uniform-hazard site-specific response spectra. Often time-history dynamic analyses must be performed in order to predict the maximum response to earthquakes; this will occur for the maximum probable earthquake, where non-linear behaviour, will preclude the use of linear modal analysis, and can occur for complex structures under moderate earthquakes. As the design and maximum probable earthquake free-field ground motions are specified usually in terms of smooth response spectra, the procedure for generating compatible accelerograms for use in time-history dynamic analysis is important and is described in detail. Chapter 25 concludes with presentations for the generation of (a) multiple components of spectrum compatible accelerograms, which represent motion at a fixed point, and (b) multiple components of earthquake motions which represent free-field surface motions at a number of points; the latter will be required in order to determine the response of a very large structure. The three chapters (26-28) on response consider deterministic response to earthquakes for systems on rigid foundations and then with soil-structure interaction included and lastly stochastic response. In the first of

5 BOOK REVIEWS 46 1 these chapters, topics which were in the 1st edition, include: discussion of when soil-structure interaction is important (i.e. the cases which should be deferred to the next chapter) and when multiple support excitation should be considered; the response to translational excitation of lumped SDOF elastic systems, of generalizedco-ordinate SDOF elastic systems (discussed in Chapter 8), of lumped MDOF elastic systems, for which the maximum response is determined from the simple SRSS method of combining maximum modal responses, and distributed parameter elastic systems, where the modification of the matrix equation for response of structures, which have been idealized through the finite element method with a consistent mass matrix, is given. A comparison is made between the expressions for seismically induced forces in a multi-storey building, which are obtained from the analysis and data in the book, and the seismic design forces, which are specified in the ATC-3 recommended code provisions. Topics, which are new or have been extensively altered in presentation, include: the response to multi-support excitation of MDOF elastic systems; the response of SDOF elastic-plastic systems, where a comparison in terms of natural frequency and displacement ductility factor is made for the maximum values of response of the elastic-plastic system with those for an equivalent elastic system; and methods of combining maximum modal responses. Here the CQC method, which has been mentioned earlier is presented in detail with an illustrative example, where the predictions for maximum response from the SRSS and CQC methods for a three-dimensional structure are compared. Finally methods for combining the two maximum responses, which are produced by two horizontal components of excitation, are described; the 30 per cent rule, which is commonly used in building design, is included. In Chapter 27 the subject of deterministic earthquake response is continued with the inclusion of soil-structure interaction (SSI). Although there are sections on this topic in the 1st edition, the approach here looks different. After a brief explanation of the concepts, the kinematic interaction effect for a rigid massless foundation-the socalled Tau effect -is derived. The ratio of the amplitude of a harmonic in the translational motion of the rigid base to the corresponding free-field amplitude is determined in terms of the ratio of the relevant base dimension to the wavelength. This averaging effect, which is negligible when the wavelength is very long compared to the base length, leads to very large reductions in the amplitudes of harmonics when the wavelength and base length are approximately equal. A brief description follows of the direct analysis concept for a soil-structure system, in which the underlying soil is represented as a bounded finite element model. This approach has a major deficiency, as there is no radiation damping. Also the input is specified at the rigid base, whereas in practice it is specified in the free-field. The analysis, which relates baserock and free-field accelerations and is in terms of Fourier transforms, was given in the 1st edition (pp ), but is not included here. The attention of the reader is drawn specifically to this unexpected deletion through a footnote. The main subject of this chapter is the substructure analysis of response with SSI included. However, before presenting this important topic the authors refer readers to the more comprehensive treatment in the excellent books by John P. Wolf [Dynamic Soil-Structure Interaction, 1985, and Soil-Structure Interaction in the Time Domain, 1988, both published by Prentice-Hall, Englewood Cliffs, N. J. These books were reviewed in this Journal by the late Milos Novak, Earthquake eng. struct. dyn. 14,951 (1986) and 21, 363 (1992), respectively]. As a first example of substructuring, a lumped SDOF system on a rigid mat foundation forms substructure no. 1 and the soil foundation, represented by an elastic half-space, forms substructure no. 2. On the surface of the latter there is a rigid massless plate in order to ensure compatibility of displacements with the lower surface of the rigid base mat. Impedances in the frequency domain of substructure no. 2 can be found in the literature for the various modes of vibration of the base mat. Then the authors show how to use these impedances, together with the equations of motion of substructure no. 1 in the frequency domain, to determine the response of the simple structure. This analysis is then extended to consider a structure, which can be represented by a multi-degree-of-freedom system using the finite element method and has multiple-support excitation. Embedment of the structure can be introduced by making the second substructure have a cavity of appropriate geometry. As analysis is in the frequency domain, material damping of hysteretic form, which can be introduced through a complex modulus, is advisable. The section ends with descriptions of methods for generating the required impedance matrices so that they represent actual conditions rather than bounded soil layer models, which possess infinite impedances at certain frequencies due to the invalid assumption of rigid boundaries. The last section of this chapter considers the response of underground structures, for which soil-structure interaction can be treated in a quasi-static fashion as the mass of displaced soil is very large compared to the mass of the structure. Consequently, the approach differs from that for above ground structures. This quasi-static approach is illustrated by determining approximately the axial and flexural deformations of a tunnel which are caused by a harmonic shear wave. In the last chapter on Stochastic Structural Response the response of linear systems is described first with appropriate expressions quoted from Part IV. Then the extreme-value response of non-linear SDOF and MDOF systems is given in detail. Most of the latter material is a rearrangement of sections in the 1st edition, but here the discussion of stiffness-degrading models of SDOF structures, previously limited to bilinear behaviour, is extended to trilinear behaviour. Finally, the implications of the generally accepted philosophy of seismic design for the specification of ductility demands, for which the design criteria have been defined in Chapter 25, are illustrated by further consideration of the trilinear SDOF model; numerical results for the latter provide also insight into the inelastic behaviour of MDOF structures. The book has been written to serve as a reference book for practising engineers as well as serving as a textbook for university students, where the material is expected to

6 462 BOOK REVIEWS provide the basis for a series of graduate level courses. Thus, as in the 1st edition, many example problems are solved in the text in order to help the understanding of readers. Also at the end of most chapters there are further exercises for students to solve. The authors advise teachers that the solution of response problems in structural dynamics is notoriously time-consuming, so that few exercises should be prescribed for coursework. In general, the worked examples follow those in the 1st edition with a few worked examples on new topics and some others, particularly on earthquake engineering, where the data has been updated. In the 1st edition all numerical examples used data with units of pounds, feet (or inches), seconds etc. In the new edition SI metric units are introduced through tables of conversion factors and definitions, which are given on the inside of the front and back covers, and the addition of metric equivalents in brackets in worked examples. However, these equivalents are given only in the earlier chapters of the book and are not stated for those worked examples, where data are given on the figures, and for the problems at the ends of the chapters. The reviewer appreciates that provision of metric equivalent values is a time-consuming and also tedious task. When metric equivalents of force, or stiffness, are given in brackets, they are quoted in kilograms, instead of Newtons, although the latter are included in the conversion table on the cover pages. This reviewer considers that the use of metric units, which do not conform with SI units, is unfortunate. Apart from the above minor criticism this is an excellent and authoritative book on structural dynamics. In addition, it gives a wide-ranging and important introduction to earthquake engineering. G. B. WARBURTON Nottingham EARTHQUAKE RESISTANT CONSTRUCTION AND DESIGN, SECOND CONFERENCE, edited by S. A. Savidis, A. A. Balkema, Rotterdam, Volumes 1 and 2; no. of pages: Price: Dfl /f102. For the set of two volumes, ISBN ; for volume 1, ISBN ; for volume 2, ISBN These two volumes form the Proceedings of the Second International Conference on Earthquake Resistant Construction and Design (ERCAD), which was held at the Technical University of Berlin on June The first conference was also held in Berlin in 1989, and the single volume proceedings were published in The contents of the latter were described very briefly in this journal (vol. 20, p. 892). It is of interest to compare briefly the two conferences, as represented by the published proceedings. Whereas the first conference proceedings included 57 papers with 47 of these from Europe with 17 originating in Germany, the second conference proceedings contain 144 papers with less emphasis on European contributions. The latter comprise approximately two-thirds, while about one-quarter emanate from Asia. Approximately 20 per cent of the papers are from Italy, while each of Japan, Germany, Greece and Iran contributes between 10 and 15 papers. Thus, there has been a large increase in the number of papers and a wider and more even representation of authors countries. Some increase would be expected, as contributions to earthquake engineering have been growing throughout the five-year period between the two conferences. Possibly, the success of the first conference has also contributed to the growth in size of the conference. However, it is surprising to note that the second one occupied three days while the first was one day longer. As the volumes contain 144 papers, this review must be highly selective and cannot describe any paper in detail. Indeed, if a future conference includes substantially more papers, a review will probably be impossible. This will not surprise readers, who are familiar with recent major English language conferences on earthquake engineering (World, US. National and European), which, with from several hundred to over a thousand papers, are well beyond the maximum size for an overall review. Of course, a review would be feasible if attention is confined to opening addresses and keynote lectures. However, the present volumes, like the proceedings of the first ERCAD conference, regrettably contain no opening address, keynote lectures or state-of-the-art reviews. The books are divided into eight broad subject areas: (1) Seismology, ground motion, source and site effects; Microzonation (20 papers); (2) Dynamic properties and response of soils, liquefaction (16 papers); (3) Soilstructure interaction, foundations, pile-groups, tunnels (18 papers); (4) Dams, bridges, tanks and historical buildings in seismic regions (11 papers); (5) Seismic isolation (13 papers); (6) Analysis and design of structures and structural components; Eurocode (33 papers); (7) Experimental methods for structures; System identification (12 papers); (8) Seismic risk and hazard, damage in earthquakes (15 papers). In addition, there is a ninth section, Supplement, which contains 6 papers. EURO-SEISTEST is described in the first paper (Pitilakis et d.); this is a European research and development project with the objective of establishing a European test site for engineering seismology and earthquake engineering in a seismically active area near Thessaloniki, Greece. Three papers consider specific earthquakes and their effects: the long predominant periods of