www.elsolucionario.org THE HISTORY OF THE THEORY OF STRUCTURES 001-019_Titelei_Korr3_INDD-5_bp.indd 05.03.2008 13:44:32 Uhr KARL-EUGEN KURRER The History of the Theory of Structures From Arch Analysis to Computational Mechanics 001-019_Titelei_Korr3_INDD-5_bp.indd 12.03.2008 13:03:28 Uhr www.elsolucionario.org Author: Dr.-Ing Karl-Eugen Kurrer Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co KG Rotherstraße 21, D -10245 Berlin, Germany This book contains 667 illustrations Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at Cover: Computer-generated drawing of an FEM model for the Göltzsch Viaduct by Dr Roger Schlegel (Dynardo GmbH, Wiemar) plus historical illustrations (sources given in book) ISBN 978-3-433-01838-5 © 2008 Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH & Co KG, Berlin All rights reserved (including those of translation into other languages) No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers Registered names, trademarks, etc used in this book, even when not specifically marked as such, are not to be considered unprotected by law English translation: Philip Thrift, Hannover Typodesign: Sophie Bleifuß, Berlin Typesetting: Uta-Beate Mutz, Leipzig Drawings: Peter Palm, Berlin Production: HillerMedien, Berlin Printing: betz-druck, Darmstadt Printed in Germany 001-019_Titelei_Korr3_INDD-5_bp.indd 05.03.2008 13:44:32 Uhr FOREWORD The title of the book alone makes us curious: What is “theory of structures” anyway? Used cursorily, the term describes one of the most successful and most fascinating applied science disciplines But actually, you can’t use this term cursorily; for this is not just about theory, not just about methods of calculation, but rather those fields plus their application to real loadbearing structures, and in the first place to the constructions in civil engineering Languages sometimes find it difficult to define such a wide field rigorously and, above all, briefly; in the author’s country, the term Baustatik (literally “building statics”) has acquired a widely accepted meaning, even though that meaning is also too narrow And even the English expression “structural analysis” does not tell the whole story precisely because this is not just about analysis, but about synthesis, too, the overall picture in the creation of a loadbearing structure Right at the start we learn that the first conference on the history of theory of structures took place in Madrid in 2005 This theme, its parts dealt with many times, is simply crying out for a comprehensive treatment However, this book is not a history book in which the contributions of our predecessors to this theme are listed chronologically and described systematically No, this is “Kurrer’s History of Theory of Structures” with his interpretations and classifications; luckily – because that makes it an exciting treatise, with highly subjective impressions, more thematic than chronological, and with a liking for definitions and scientific theory; indeed, a description of the evolution of an important fundamental engineering science discipline with its many facets in teaching, research and, first and foremost, practice The history of theory of structures is in the first place the history of mechanics and mathematics, which in earlier centuries were most definitely understood to be applied sciences K.-E Kurrer calls this period up to 1825 the preparatory period – times in which structural design was still dominated very clearly by empirical methods Nevertheless, it is worth noting that the foundations of many structural theories were laid in this 001-019_Titelei_Korr3_INDD-5_bp.indd 05.03.2008 13:44:33 Uhr 001-019_Titelei_Korr3_INDD-5_bp.indd FOREWORD period It is generally accepted that the structural report for the retrofitting works to St Peter’s Dome in Rome (1742/43) by the tre mattematici represents the first structural calculations as we understand them today In other words, dealing with a constructional task by the application of scientific methods – accompanied, characteristically, by the eternal dispute between theory and practice (see section 11.2.5) These days, the centuries-old process of the theoretical abstraction of natural and technical processes in almost all scientific disciplines is called “modelling and simulation” – as though it had first been introduced with the invention of the computer and the world of IT, whereas in truth it has long since been the driving force behind mankind’s ideas and actions Mapping the loadbearing properties of building constructions in a theoretical model is a typical case One classic example is the development of masonry and elastic arch theories (see chapter 4) It has become customary to add the term “computational” to these computer-oriented fields in the individual sciences, in this case “computational mechanics” The year 1825 has been fittingly chosen as the starting point of the discipline-formation period in theory of structures (see chapter 6) Theory of structures is not just the solving of an equilibrium task, not just a computational process Navier, whose importance as a mechanics theorist we still acknowledge today in the names of numerous theories (Navier stress distribution, Navier-Lamé and Navier-Stokes equations, etc.), was very definitely a practitioner In his position as professor for applied mechanics at the École des Ponts et Chaussées, it was he who combined the subjects of applied mechanics and strength of materials in order to apply them to the practical tasks of building For example, in his Rộsumộ des Leỗons of 1826 he describes the work of engineers thus: “… after the works have been designed and drawn, [the engineers] investigate them to see if all conditions have been satisfied and improve their design until this is the case Economy is one of the most important conditions here; stability and durability are no less important …” (see section 2.1.2) Theory of structures as an independent scientific discipline had finally become established Important structural theories and methods of calculation would be devised in the following years, linked with names like Clapeyron, Lamé, Saint-Venant, Rankine, Maxwell, Cremona, Castigliano, Mohr and Winkler, to name but a few The graphical statics of Culmann and its gradual development into graphical analysis are milestones in the history of structural theory Already at this juncture it is worth pointing out that the development did not always proceed smoothly: controversies concerning the content of theories, or competition between disciplines, or priority disputes raised their heads along the way This exciting theme is explored in detail in Chapter 11 by way of 12 examples In the following years, the evolution of methods in theory of structures became strongly associated with specific structural systems and hence, quite naturally, with the building materials employed, such as iron (steel) and later reinforced concrete (see chapters 7, and 9) Independent materials-specific systems and methods were devised Expressed in simple 05.03.2008 13:44:33 Uhr www.elsolucionario.org terms, structural steelwork, owing to its modularity and the fabrication methods, concentrated on assemblies of linear members, whereas reinforced concrete preferred two-dimensional structures such as slabs, plates and shells The space frames dealt with in chapter represent a fulcrum to some extent This materials-based split was also reflected in the teaching of structural theory in the form of separate studies It was not until many years later that the parts were brought together in a homogeneous theory of structures, albeit frequently “neutralised”, i e no longer related to the specific properties of the particular building material – an approach that must be criticised in retrospect Of course, the methods of structural analysis can encompass any material in principle, but in a specific case they must take account of the particular characteristics of the material Kurrer places the transition from the discipline-formation period – with its great successes in the shape of graphical statics and the systematic approach to methods of calculation in member analysis – to the consolidation period around 1900 This latter period, which lasted until 1950, is characterised by refinements and extensions, e.g a growing interest in shell structures, and the consideration of non-linear effects Only after this does the “modern” age begin – designated the integration period in this instance and typified by the use of modern computers and powerful numerical methods Theory of structures is integrated into the structural planning process of conceptual design – analysis – detailing – construction – manufacturing Have we reached the end of the evolutionary road? Does this development mean that theory of structures, as an independent engineering science, is losing its profile and its justification? The developments of recent years indicate the opposite The history of yesterday and today is also the history of tomorrow In the world of data processing and information technology, theory of structures has undergone rapid progress in conjunction with numerous paradigm changes It is no longer the calculation process and method issues, but rather principles, modelling, realism, quality assurance and many other aspects that form the focal point The remit includes dynamics alongside statics; in terms of the role they play, thin-walled structures like plates and shells are almost equal to trusses and frames, and taking account of true material behaviour is obligatory these days During its history so far, theory of structures was always the trademark of structural engineering; it was never the discipline of “number crunchers”, even if this was and still is occasionally proclaimed as such upon launching relevant computing programs Theory of structures continues to play an important mediating role between mechanics on the one side and the conceptual and detailed design subjects on the other side in teaching, research and practice Statics and dynamics have in the meantime advanced to what is known internationally as “computational structural mechanics”, a modern application-related structural mechanics The author takes stock of this important development in chapter 10 He mentions the considerable rationalisation and formalisation, the foun7 001-019_Titelei_Korr3_INDD-5_bp.indd 05.03.2008 13:44:33 Uhr dations for the subsequent automation It was no surprise when, as early as the 1930s, the structural engineer Konrad Zuse began to develop the first computer However, the rapid development of numerical methods for structural calculations in later years could not be envisaged at that time J H Argyris, one of the founding fathers of the modern finite element method, recognised this at an early stage in his visionary remark “the computer shapes the theory” (1965): besides theory and experimentation, there is a new pillar – numerical simulation (see section 10.4) By their very nature, computers and programs have revolutionised the work of the structural engineer Have we not finally reached the stage where we are liberated from the craftsman-like, recipe-based business so that we can concentrate on the essentials? The role of “modern theory of structures” is also discussed here, also in the context of the relationship between the structural engineer and the architect (see chapter 12) A new “graphical statics” has appeared, not in the sense of the automation and visual presentation of Culmann’s graphical statics, but rather in the form of graphic displays and animated simulations of mechanical relationships and processes This is a decisive step towards the evolution of constructions and to loadbearing structure synthesis, to a new type of structural doctrine This potential as a living interpretation and design tool has not yet been fully exploited It is also worth mentioning that the boundaries to the other construction engineering disciplines (mechanical engineering, automotive engineering, shipbuilding, the aerospace industry, biomechanics) are becoming more and more blurred in the field of computational mechanics; the relevant conferences no longer make any distinctions The concepts, methods and tools are likewise universal And we are witnessing similar developments in teaching, too This “history of theory of structures” could only have been written by an expert, an engineer who knows the discipline inside out Engineering scientists getting to grips with their own history is a rare thing But this is one such lucky instance This fully revised English edition, which explores international developments in greater depth, follows on from the highly successful German edition We should be very grateful to Dr Kurrer, and also “his” publisher, Ernst & Sohn, for this treatise 001-019_Titelei_Korr3_INDD-5_bp.indd FOREWORD Stuttgart, September 2007 Ekkehard Ramm Professor of Structural Mechanics, University of Stuttgart 05.03.2008 13:44:33 Uhr Encouraged by the engineering profession’s positive response to the first Preface edition of this book, which appeared in German only under the title of Geschichte der Baustatik in 2002, and the repeated requests for an English edition, two years ago I set myself the task of revising, expanding and updating the book Although this new version still contains much of the original edition unaltered, the content now goes much further, in terms of quantity and quality My aim was not only to take account of the research findings of the intervening years, but also to include the historical development of modern numerical methods of structural analysis and structural mechanics; further, I wanted to clarify more rigorously the relationship between the formation of structural analysis theories and progress in construction engineering The history of the theory of spatial frameworks, plus plate, shell and stability theory, to name just a few examples, have therefore been given special attention because these theories played an important role in the evolution of the design language of lightweight steel, reinforced concrete, aircraft and ship structures Without doubt, the finite element method (FEM) – a child of structural mechanics – is one of the most important intellectual technologies of the second half of the 20th century I have therefore presented the historico-logical sources of FEM, their development and establishment in this new edition Another addition is the chapter on scientific controversies in mechanics and theory of structures, which represents a “pocket guide” to the entire historical development from Galileo to the early 1960s and therefore allows an easy overview There are now 175 brief biographies of prominent figures in theory of structures and structural mechanics, over 60 more than in the first edition, and the bibliography has been considerably enlarged Certainly the greatest pleasure during the preparation of this book was experiencing the support of friends and colleagues I should like to thank Jennifer Beal (Chichester), Antonio Becchi (Berlin), Norbert Becker (Stuttgart), Alexandra R Brown (Hoboken), José Calavera (Madrid), Christopher R Calladine (Cambridge, UK), Kostas Chatzis (Paris), Mike Chrimes (London), Ilhan Citak (Lehigh), René de Borst (Delft), Giovanni Di Pasquale (Florence), Werner Dirschmid (Ingolstadt), Holger Eggemann (Aachen), Jorun Fahle (Gothenburg), Amy Flessert (Minneapolis), Hubert Flomenhoft (Palm Beach Gardens), Peter Groth (Pfullingen), Carl-Eric Hagentoft (Gothenburg), Torsten Hoffmeister (Berlin), Santiago Huerta (Madrid), Andreas Kahlow (Potsdam), Sándor Kaliszky (Budapest), Klaus Knothe (Berlin), Eike Lehmann (Lübeck), Werner Lorenz (Cottbus/ Berlin), Andreas Luetjen (Braunschweig), Stephan Luther (Chemnitz), William J Maher (Urbana), René Maquoi (Liège), Gleb Mikhailov (Moscow), Juliane Mikoletzky (Vienna), Klaus Nippert (Karlsruhe), John Ochsendorf (Cambridge, USA), Ines Prokop (Berlin), Patricia Radelet-de Grave (Louvain-la-Neuve), Ekkehard Ramm (Stuttgart), Anette Ruehlmann (London), Sabine Schroyen (Düsseldorf), Luigi Sorrentino (Rome), Valery T Troshchenko (Kiev), Stephanie Van de Voorde (Ghent), Volker Wetzk (Cottbus), Jutta Wiese (Dresden), Erwin Wodarczak (Vancouver) and Ine Wouters (Brussels) 001-019_Titelei_Korr3_INDD-5_bp.indd 05.03.2008 13:44:33 Uhr Dürer 190 Dürrenmatt 130 Dzhanelidze, G I 745 Eagleton 692, 694 Ebel 744 Eberlein 490, 493 Ebner 442, 630, 640, 713 Eddy 326 f., 329, 540, 727 Edwards, W 210 Efimow 318 Eggemann 396, 464 Eggenschwyler 437 f., 439, 634 Ehlers 527, 545 Eiffel 80 ff., 94 f., 227, 307, 325, 487 Einstein 621, 718, 744, 748 Eiselin 442 Eisenloffel 705 Emde, H 490, 494 f Emerson, W 214 Emperger, F v 463 f., 516, 524, 529, 727 f., 764 Emy, A R 47 Engelmeyer 144 Engesser 363, 447, 451, 530, 581, 587, 682, 726, 728, 738, 742 Ersch 187 Ernst, A 425, 427 Ernst, G 728 Etzel, K v 314 Euclid 769 Euler 32, 45, 90, 107, 137, 203, 270, 274, 277, 293, 296, 298, 335, 377, 443, 447, 453, 479, 733, 737, 756 Ewert 63 Eytelwein 33, 171, 250, 279, 281, 290, 294 ff., 302, 657, 696 f., 728 f., 733 Eyth 144 Faber, O 738 Fabri 31, 194, 206 f., 209, 358 Fairbairn 421, 712, 729, 762 Faiss, H 628 ff Falk, S 617 Falkenheiner 614 Falleni 190 Falter, H 186, 198 Faltus 729 ff Favaro 358 Favero 358 Federhofer 548 f Fedorov 57 Feldmann, E A 766 Feldtkeller, R 614 Felippa 25, 621, 640, 653 f., 672, 731 Ferradin-Gazan 310 Ferroni 191 Figari 358 Fillunger 451, 685 ff Finley 64 Finsterwalder, S 327, 547 Finsterwalder, U 547, 551, 555, 560, 726, 730, 758, 761, 772 Fischmann 446 Flachat, E 49, 95, 312 Flamant 533, 722, 762 Fleckner 255 Fleming, R 602 Flomenhoff 639 f., 717 Flügge, S 730 Flügge, W 327, 552, 726, 730 Flügge-Lotz 730 Foce 24, 186, 210, 212, 219, 240, 246, 396, 716 Föppl, A 157 f., 177 ff., 227, 254, 326 f., 329, 367 ff., 402, 411, 429, 433, 440, 474 ff., 478 ff., 485, 534, 548, 631, 685, 725, 730 f., 734, 742, 771 f Föppl, L 177, 441, 548, 736, 761, 772 Föppl, O 440 Förster, M 48, 503, 773 Föttinger 456 Fourcroy 53 Fourier 95, 756 Fraeijs de Veubeke 665 ff., 668, 731 Frank, P 727 Franz II 66, 280 Fränkel 36, 103, 180, 362, 731 Frazer, R A 615 f., 637 Freudenthal, G 250 Freudenthal, A M 731 f Freyssinet 487, 554 f., 746 Freytag, C 500, 513, 523, 526 Frézier 204 f., 719 Friedrich II 678 Friedrichs, K O 666 Friemann 117, 647 Fritsche, J 123, 451 Fritz, B 115, 467 Frobenius 611 Frocht, M M 605 Fröhlich, H 467 Fröhlich, O K 686 Froude 743 Fuchs, R 759 Fuchssteiner 567 Führer, F 692 Fuhrke, H 617 Fürst, A 538 Gaber 123 Gaddi 189 Galerkin 720, 732, 738 Galileo 31, 46, 90, 192 f., 211, 250 f., 253, 257, 260 ff., 301, 358, 675 ff., 708, 723, 737, 765, 774 Gallagher 463, 653, 671, 732 f Gargiani 26 Garibaldi 749 Gassendi 273 Gaudi 238 Gauß 534 Gauthey, E 291 f., 753 Gebbeken 125 ff., 129 Geckeler, J 550 f Gehler 453, 465, 530, 589 ff., 594, 731, 751 Gerhardt, R 27, 692 Germain, S 533 f Gerstner, F J v 33, 55, 59, 67, 157 f., 161 ff., 172, 177, 216 ff., 247, 250 f., 275 f., 278 ff., 282, 283 ff., 332, 570, 574, 694 f., 730, 733, 771 Gerstner, F A v 161, 282 f., 733 Ghezzi 680 Giencke 462 Gilly, D 295, 696 Gilly, F 295, 692, 695 Girard 276 f., 296, 733 Girkmann 124 ff., 131, 452, 722, 733 f Gispen, K 61 Giuffrè 716, 726, 734 Gizdulich 191 Goering 766 Goethe 31, 581, 662 Göring, H 478 Goffin 560 Gold 90 Goldsmith, M 740 Gorbunov, B N 608 Gordon, L 758 Gorki 768 Gorokhov 145 Gottl-Ottlilienfeld 148 Graf, O 457, 539 f., 564, 738 Graham, B 740 Grandi 31, 358 Grashof 332, 414, 425, 429, 460, 534 ff., 539 f., 548, 730, 734 Grasser, E 561 f Graubner 222, 239 Green, A E 24, 528, 553 f., 621 Green, G 176, 360, 534, 642, 654, 665 ff., 681 f., 721, 775 Gregory 90, 237 Greiner-Mai 306 Griffith 734 Griggs, F E 773 Grimm, J 139, 187 Grimm, W 139, 187 Grinter, L E 26, 603, 605 Groh 80 Gropius 474, 491 Groß 241 Groth, P 627 ff Grothe, J 555 Grubenmann, H U 70 Gruber 187 Grübler 354 Grüning, G 465 Grüning, M 38, 122 f., 372, 578 f Grunsky 68 Grunwald 151 Gruttmann, F 435 Guastavino Jr 326 Günther, W 771 Güntheroth 68 Guidi 358, 723, 734 f Guldan 720 Guntau 306 f Guralnick 539 Gvozdev 133, 607, 735, 770 833 778-848_Anhang_Korr2_INDD-5_bp.indd 833 05.03.2008 15:46:36 Uhr Heydenreich, K H 697 f Heyman 24, 121, 131, 186, 209 f., 214, 232 ff., 244, 246, 248, 311, 326, 568, 716, 723, 734 Higgins, T J 605 Hilbert 657 f Hinrich 181 Hitler 443, 450, 452, 664, 713 f., 757 Hodgkinson, E 76, 92, 729, 737 Hoening 115 Hoff, N 637 Hofmann, T J 41 Hofstetter, G 255 Hölderlin 29, 471, 692 f., 695, 698 Holl 195 Holle 527 Holzer, S M 48 Homberg, H 457, 618 Hooke 31, 90, 213 f., 271 f., 296, 737 f Horn, F 456 Horne 133 Housner, G W 767 Howe, W 64, 72 Hrennikoff 493, 562, 624, 627, 738 Hruban, K 540 Hu 665 Huber, M T 459 ff., 543, 736, 738 Hübsch 773 Huerta 1, 24, 87 f., 186, 212, 217, 246 Hughes 713 Hultin 714 Humboldt, A v 312 Hutton, C 214, 240 Huygens 32, 90, 272, 738, 775 Hyatt 499 Iguchi 738 Ingerslev 539 Isherwood 456 Ivanov 307 Jacobi, K G J 662 Jacobsthal, E 759 Jacquier 679 f., 708, 718, 752, 756 Jaeger, T 738 f Jäger, K 443 f., 451 Jäger, W 222, 239 Jagfeld 235, 239 Jagschitz 123 Jasiński 728, 739 Jenkin, F 218 Jenkins 738 Joffe, A F 768 Johanson 539 Johnson, B 754 Johnson, L 754 Jokisch 116, 597, 722 Jones, R E 670 Jones, R T 639 Jordan, P 611 Joseph II 279 Joule 313, 677 Jung 358 Jungbluth, O 469 834 778-848_Anhang_Korr2_INDD-5_bp.indd 834 Jünger, F G 446 Jürges, T 518 Jungwirth, D 568 Kączkowski, Z 754 Kafka 28 Kahlow 68 f., 186, 692 Kahn 718 Kaiser, C 195, 199, 241, 260 Kaliski, S 754 Kammüller 687 Kani 604 f., 739 f., 767 Kann, F 127 Kant 662, 677 f Kapp, E 143 Kappus 439 Kármán 447, 451, 639, 759 Karmarsch 56 Kaufmann, G 529 Kazinczy, F 740 Kazinczy, G v 121 f., 127, 129, 740 Kelsey, S 643 Kennard 73 Kepler 137 Kesselring 493 Khan, F R 740 f Khan, Y S 740 Kier 738 Kierdorf, A 538 Kinzlé 742 Kirchhoff 460, 533 f., 541, 543, 657, 664, 713, 722, 738 Kirkwood-Dodds 554 f Kirpichev 34, 36, 307, 374, 377 ff., 606, 695, 741 Kirsch, E G 493, 562, 622 f Kist, N C 122, 451 Klein, F 372, 414, 582, 600, 623, 654, 657 f., 745, 772 Klein, L 60 Kleinlogel 464, 530 f., 591 Klemm, F 53, 261 Klimke, H 470, 474, 490, 494 Klöppel 115, 117, 146, 390, 398, 451 ff., 455 f., 458, 462, 469, 618, 646 f., 737, 741, 742, 748 Knebel, K 470 Knothe 106, 392, 657 f., 666 ff., 757 Koechlin 81 f., 84, 94, 307, 703, 760 Koenen 362, 382, 465, 498 f., 501 ff., 507 ff., 512 ff., 522, 526 Kögler, F 444, 446 Koiter 741 f Kollbrunner 127, 689 Köller 635 f., 640, 713 Koloušek 742 Konietzky 242 König, J S 678 König, W 151 Kooharian 232 Köpcke, C 47, 224, 305, 352, 751 Kordina 561 f Körner 326 Kötter, F 409, 766 NAME INDEX Haase, H 227 Haberkalt 519 Hacker 478 Hadamard 534 Hagen 227, 281, 766 Hager, K 540 Hahn, H 727 Hahn, O 730 Hahn, V 646 Halfmann 717 Hambly 214 Hamel, G 655, 662 f., 766 Hamilton, R W 660 Hamilton, S B 23 Hamilton, W R 712 Hampe, E 528 Hänseroth 53, 261, 306 Häntzschel 106 Happel 534 Hargreaves 277 Hartmann, Friedel 373, 744 Hartmann, Friedrich 115, 443 f., 451, 530, 717, 722 Hauck 736 Haupt, H 60, 735 Havelock 743 Hayashi 107, 735 f Hebbel, F 751 Heck, O S 636 Hees 30 Hegel 695 Heinrich, B 188 Heinrich, E 188 Heinrich, G 687 Heinzerling 180 f Heisenberg 611 Hellinger 658 ff., 665 Helmholtz 313, 374, 677, 772 Henck, J B 766 Hencky 540, 736, 738, 750 Henneberg 476, 482 ff Hennebique 509, 513, 515 ff., 523 f., 536, 563, 591, 721 Henri, A 310 Heppel 305 Herbert, D 24 Hermann, J 678 Hermite 611 Heron 46, 256 Herrbruck 241 Herrmann, G 23, 607 Herrmann, L R 670 Herschel 712 Hertel, H 442 Hertwig, A 23, 115, 146, 255, 366 f., 371 f., 380, 387 ff., 397, 596, 601, 662, 685, 736 f., 775 Hertwig, R 391 Hertz, G 766 Hertz, H 534 Herzog, M 560 Hesse 722 Heun 726 05.03.2008 15:46:36 Uhr www.elsolucionario.org Koyré 727 Krabbe 115, 123 Krämer 570, 573, 580, 598, 620 f., 693, 700 Kranakis 293 Krätzig 554 Krauß, K 259, 260 Kretzschmar 720 Krohn, G 614 Krohn, R 98, 444, 741, 742 f Kromm, A 657 Krotov, Y V 608 Kruck 596 Krug, K 314 Krylov 720, 743, 768 Ktesibios 256 Kudriaffsky, J v 66 Kuhlmann, U 468 Kuhn 749 Kuhn, T S 136, 450, 674, 713 Kunert, K 467 Kulka 123 Kupfer 559, 567, 761 Kuppler, J G 68 Kurrer 25 Lacroix 756 Lafaille, B 552 La Fayette 746 LaFraugh 539 Lagrange 42, 45 f., 95, 253, 377, 533 f., 595, 681, 721, 737 La Hire 189, 201 f., 207 f., 215, 217, 259, 715, 743 Lahmeyer, J W 756 Laitko 306, 380 f Laissle 101 La Lande 280 Lamarle 305 Lamb, H 548 Lambin, A 591, 721 Lambot 499 Lamé 95, 301, 309 ff., 317, 399, 548, 583, 682, 722, 743 f., 753 Land 46, 101, 350, 353 f., 355 ff., 606, 706, 744 Landau, E 654 Landsberg 158, 180, 581 Lang, A N 641 Lang, G 22 Langefors 614, 641 Lansing, W 641 Laplace 401, 721 Lauenstein 326 Lavoinne 534 Lees 64 Lefèvre 250 Legendre 756 Leibniz 32, 90, 249, 272, 279, 283, 384, 598, 655, 677 f., 693, 695, 703 Leckie, A 643 Lehmann, C 27 Lehmann, D 108 Lehmann, E 743 Lemoine 94 Lenk, H 148 Lenk, K 554 Lentze, C 79 Leonhardt 442, 457, 555 ff., 560, 561 ff., 567, 646, 761 Leonardo da Vinci 46, 134, 186, 200, 202, 253, 256 ff., 265, 708, 747 Le Seur 679 f., 708, 718, 752, 756 Lévy, M 329, 534, 744 Levy, S 640 f Lewe, V 527 f., 540, 543, 548 Lewis, R W 671 Lie 115 Lieberwirth 240 Lienau 123 Lincoln 60 Lindenthal 114, 749, 764 Livesley, R K 240, 643, 644 ff Loitsyansky, L G 745 Loleit, A F 537 f Long, S H 64, 70, 744 f Lord Kelvin (Thomson, W.) 313, 434, 682, 743 Lorenz, G 725 Lorenz, W 72, 388, 496, 586 Louis Philippe 721 Love 532, 534, 548, 582 f., 713, 745 Ludwig, M 705 Lurie 745 f MacAdam 277 Mach 718 McHenry 624 McLean 663 MacNeill, J 758 Mader 462 Magnel 555, 746 Mahan 746 Maier, A 727 Maier-Leibnitz 122 f., 129, 131, 463, 465, 740 Maillart 238, 438 ff., 487, 532, 538, 548 f., 746 f Mainstone 255 Malinin 25 Maltzahn, C v 195 Manderla 108, 581, 587 ff Maney, G A 594 Mang, H 255 Mann, L 112, 410, 582, 595 f., 606, 735, 747 Maquoi 748 Marchetti 31, 358 Marcus 410, 527, 541 ff Mar 717 Marg 474 Marguerre 442, 654, 658, 687 ff Mariotte 90, 273 Mark, R 241 Marrey, B 555 Marti, P 538 Martin, H C 39, 249, 640 f., 649 ff., 652 f., 669 Marx 245, 246 f., 249, 313, 352, 413, 694 Mascheroni 213, 246, 747 Massonnet 135, 731, 747 f Matheson, J A L 594 Matschoß 146, 389, 432, 748 Mauersberger 53, 261, 306 Maupertuis 678 Maurer, B 25, 27 Mautner 554 f Maxwell 44, 307, 313 f., 319 ff., 342 ff., 345 f., 348 ff., 355 f., 359, 382, 397, 577, 579, 589, 683, 685, 695, 712, 716, 719, 724, 742, 744, 748, 750 ff., 758 Mayer, M 540 Mayer, R 313, 476, 677, 772 Mayor 476, 485 Medici, G 191 Mehrtens 64, 80, 93, 365 ff., 371 f., 389, 409, 588, 684, 717 f., 748, 751 Meinicke, K.-P 262, 314 Meissner, E 550, 759 Melan, E 543, 718, 748 f Melan, J 113 f., 116, 181, 183, 463, 488, 513 ff., 519, 718, 720, 722, 727, 748, 749, 764 Mellin 79 Melosh, R J 652, 670 Melzi 258 Menabrea 226, 247, 348, 360, 362, 370, 408, 567, 658, 665, 720, 731, 749 f Mengeringhausen 139 f., 474 f., 486, 490 ff Menzel 412 f Merriman 170, 750 Mersenne 272 f Méry 217, 227 Metzler 123 Meyer, A G 692, 699 Meyer, E 124 Michaux 244 Michelangelo 190, 192, 680 Michell 583, 623, 716, 743, 750 Michon 220 Mikhailov 306 Milankovitch 209 Mindlin 726, 750 f Minkowski 654 Mise 751 Mises 476, 485, 553, 608, 612 ff., 736, 738, 751, 768 Mitchell, D 568, 712 Mitis, I v 66 Möbius, A F 475 Modigliani 358 Mohr 34, 36, 44, 46, 83, 99, 103, 109, 122 f., 177, 305 ff., 327, 343, 344 ff., 347 f., 350 ff., 359, 362 ff., 371, 379, 382 f., 386, 389, 397, 475 f., 484, 541 f., 562, 581, 588 ff., 595, 606, 623, 683, 685, 687, 695, 706, 716 f., 728, 730 f., 744, 748, 751 f., 760 f Mohrmann 325 f Moiseiff 114 Molinos 305 Moller, G 773 Monasterio 212 Monge 51, 53, 95, 279, 281, 308, 721, 756 Monier 499 ff., 504 f Monzoni 73 Moody 727 Morison, G S 742 835 778-848_Anhang_Korr2_INDD-5_bp.indd 835 05.03.2008 15:46:37 Uhr Nachtigall 474 Nádai 441, 527, 543 Naghdi 752 f Nagel 331 Napoleon 58, 309, 733 Napoleon III 762 Napolitani 261 Navier 22, 34, 66, 88, 90, 95, 101, 113, 134, 161, 220 ff., 250, 270, 278, 290 ff., 296, 301 ff., 307, 348, 397, 402, 507, 534, 548, 583, 598, 657, 681, 695, 708, 715, 719, 730, 733, 746, 753 f., 756, 760 Neal, B G 130 f., 133, 135, 689, 738 Nebenius 57 Nemorarius 43, 46 Nervi 238 Neuber 755 Neufert 490 Neukirch 115 Neumann, C G 722 Neumann, F E 722 Neumann, P 513, 515, 519, 722 Neumeyer, F 692, 695 Néville 64, 72, 73 Newcomen 277 Newmark 605, 754 Newton 45, 143, 214, 251, 255, 265, 279, 384, 718 f., 725, 738, 748, 752, 758, 774 Niemann, G 771 Nietzsche 448 Nikolaus I 311, 312 Nikolaus von Oresme 727 Nouguier 84 Novozhilov 754 Nowacki 738, 754 Nowak, B 451 Ochsendorf 209, 236, 240, 692, 706 Ockleston 539 Oden 671, 713, 732 Olszak 738, 754 f Onat 232 Oravas 663 Ostenfeld 109, 514 f., 519, 581, 594 f., 596, 599, 606, 625, 647, 747, 755, 772 Ostwald, W 313, 452 Ott, K v 332 Otto, K 492 Padlog 732 Pahl 40, 152, 156 f Palladio 194 f., 745 Panetti 548 Panovko, Y G 745 Papadrakakis 713 Papin 677 Papkovich 755 Parent 90, 296 Parigi 191 Parkus 749 Parnell 278 Pascal 273 Pasternak 596 Pauli, F A v 75, 724 Pauli, W 759 Pauser 66, 239, 518 Peacock 86 Pearson 22, 277, 398, 400, 532 Pedemonte 24, 716 Peirce, B 611 Peirce, C S 611 Pellegrino, S 495 Perrodil 187, 225 Perronet 51, 191, 208, 755 Peters, T F 76 Petersen, C 398, 712 Petersen, J 462 Petersen, R 769 f Petit 209, 220 Petty 737 Petzold 617 Pflüger 462, 775 Pian 638, 664, 670, 717, 732 Pichler, G 692, 705 Pieper, K 241 Piobert 399 Pippard 230 f Pirlet 601 Pisarenko 756 Planat 325 Planck, M 759 Plato 46, 136 ff., 581 Podszus 195 Pohl, K 391 f., 608 Pohlmann 108, 393 Poincaré 718 Poinsot 95, 756 Poisson 95, 301, 533 f., 753, 756 Pole, W 77 f., 304 Poleni 215 f., 247, 680 f., 756 Polonceau, C 47 Polonceau, A.-R 95 Pólya 759 Poncelet 95, 161, 220, 223, 225, 318 f., 399, 574, 715, 746, 756 Porstmann 490 836 778-848_Anhang_Korr2_INDD-5_bp.indd 836 Pöschl, T 548, 687 Potterat 437 Prager 130 ff., 233, 476, 485, 757 Prandtl 177, 553, 750, 772 Prange 658 ff., 665, 757 Prato, C 670 Prechtl 55 Pronnier 305 Prony, G 95, 291 Proske 240 Pugsley 757 f Quade, W 614 Quast, U 561 f Rabich 758 Rabinovich 23, 758, 770 Radelet-de Grave 24, 396, 716 Ramm, E 25, 41, 186, 704, 745 Ramm, W 80, 586 Ramme 23 Ramsbottom, J 414 f., 419 Rankine 89, 157 f., 173 ff., 187, 223, 237, 307, 320 ff., 397, 575, 695, 714, 748, 758 f Raschdorff 385 Rathenau, E 99 Raucourt 310 Rautenstrauch 242 f Rayleigh 374 ff., 377, 534, 548, 745 Rebhann 305, 332 Redtenbacher 56, 155, 414, 427, 734 Reich, E 549 Reichenbach, G v 85 f., 90 Rein, W 447, 451 Reinhardt, R 736 Reinitzhuber 442 Reissner, E 543, 549 f., 663 f., 665, 740, 750, 759 Reissner, H 95 f., 380, 387 f., 456, 548, 634, 759 f., 766 Renn 194 Rennert, K 423 Résal 227 Reuleaux 317, 347, 350, 351 f., 356, 427, 699 Reuter, W 429 Ricardo, D 312 Richardson 620 Richardson, L F 540 Richart, F E 754 Richelot 722 Richter, J 680 Ricken, H 487 Rickert, H 145 Riedel, H.-K 295 Riedel, W 623 f Riedler 61, 144, 386, 427 Rieger 194 Rippenbein, Y M 608 Ritter, A 751, 760 Ritter, H 760 Ritter, W 113, 324 f., 439, 480, 509, 513 ff., 519, 531, 563, 581, 588, 601, 704, 744, 760 Ritter, W E 459 NAME INDEX Mörsch 228, 229 f., 467, 498, 509, 513, 515, 522 ff., 562, 564, 566, 735, 751 f Moseley, H 77, 217, 218 f., 297, 304, 746 Moser, S 146 f Müllenhoff, A 434 Müller, C H 659 Müller, J 150 Muller, J 555 Müller, O 773 Müller, S 61, 391, 601, 736 Müller-Breslau 34, 36, 46, 62, 183, 227, 306 f., 328 ff., 343, 348 ff., 353 ff., 362 ff., 371, 377, 379, 381 ff., 389, 397, 408 f., 431, 445 ff., 476, 481 ff., 500, 531, 548, 570, 577 ff., 581, 589, 592, 599 ff., 608, 683, 687, 695, 703, 706, 712, 728, 736 f., 744, 747 f., 751, 752, 759 Muskhelishvili 752 Musschenbroek 203, 274 f., 296, 752 05.03.2008 15:46:37 Uhr Rittershaus 353 Ritz, W 375 f., 658 Roberval 45 f., 743 Robinson, J 215 Röbling, J A 68 ff Roebling, E W 69 Roebling, W A 69 Rohn, A 440 Roik 468 Ropohl 148 f., 151 Rŏs, M G 127, 451, 747 Rothert 125 ff., 129 Röting 170 Rottenhan 280 Rousseau 52 Rueb, B 530 Ruh, M 494 Rühlmann 34, 261, 310, 752, 756, 760 f Rumjancev 57, 58 Rumpf 147 f Runge, C 548 f., 654, 768 Rüsch 327, 547, 551, 555, 559, 561, 567, 726, 730, 761 Ruta 440 Rvachev 761 f Saavedra 187, 223, 762 Saint-Guilhem 227 Saint-Simon 309 f., 312 Saint-Venant 22, 335, 398 ff., 406 ff., 410, 428 f., 437, 443, 533, 695, 722, 762 f Samuelsson 25, 604, 614, 714, 722 Sanders, A 514 f., 519 Sanders, G 731 Sandkühler 157, 693 Sanchez, J 494 Sattler 467 f Sauer, R 435, 476 Savart 400 Savin 763 Saviotti 358 Sawczuk 739 Sayno 358 Schade, H H 456 Schadek 362 Schädlich 48 Schaechterle, K 441, 456 f., 530 Schäfer, K 496, 568 f Schäffer 158, 180 Schaim 124 Schairer, S 639 Schaper, G 390, 397, 447, 448 f., 457 Schardt 462 Scheer, J 480, 493, 618 Scheffler, H 219, 223, 227, 297, 305, 575 f., 746 Schellbach 655, 722 Schelling 695 Schifkorn 64 Schindler, R 749 Schinkel 278, 729 Schinz 80, 93 Schlaich, J 470, 496, 561, 568 f Schlegel, R 242 f Schleicher 391 f., 737 f., 775 Schleusner 608, 663, 687 f Schlink 476, 485 Schmidt, H 496 Schnabel 51, 55, 146, 309 Schneider, C C 96, 742 Schneider, R 425 Schnirch 67 Schober, H 470 Schưnert 148 Schưnfli 389 Scholz, E 24, 324 Schopenhauer 136, 662 Schröder, H 647 Schubert, J A 74 f., 331, 731, 774 Schübler 101 Schüle, F 524 Schulz, F J E 204, 206, 208 Schuster, R 513 Schwartz, H A 759 Schwartzkopff 105 Schwedler 47, 50, 80, 91, 93, 98, 101, 106, 223, 224, 341, 382, 474, 475 ff., 483 f., 550, 585 f., 588, 695, 709, 719, 748, 763 Schwerin, E 550 Sedlmayr, H 472 Seger, H 511 Seguin 66, 95 Seifert, L 445 Séjourné 228, 230 Selberg 115 Senefelder 574 Serensen 763 f Serlio 190 Seyrig 82, 227 Sganzin 208 S’Gravesande 274, 752 Shapiro 762 Shaw, S E 605 Shukhov 474 f., 486, 487 f., 548 Silberschlag 206, 295 Sinopoli 210, 240, 246 Slaby 386 Slater, W A 538, 772 Smith, A 312 Sobek 474, 740 Sobolev 373 Šolín 715, 764 Sommerfeld 725, 759 Sonne 158, 180 Sonnemann 306 Sontag, H J 467 Sor, S 535 Southwell 604 f., 750, 764 Spangenberg 717, 761, 765 Späth, J L 220 Spierig, S 624 f., 627 Spitzer, J A 513, 515 Stamm 469 Standfuß, F 560 Staudt, K G C v 318 Stein, E 644 Stein, P 469 Steiner, F 180, 182 ff., 727 Steinman 114, 749, 764 f Stelling, E G 440 f Stephan, S 470 Stephenson, R 76 ff., 315 f., 712, 729 Steppling 279 Sternberg, H 223, 728 Steuermann 539 Steup 720 Stevin 32, 44 f., 46, 193, 259, 725, 765 Stickforth 440 Stiglat 496, 543, 560 Stirling 215 Stodola, A 550 Stokes 682 Strassner, A 530 f Stratton, S 736 Straub, H 253, 261, 765 Strecker, F 614 Striebing 150 Stuckenholz, G 414 Stuckenholz, L 414, 417 ff Study, E 611 f Stüssi 127 ff., 134 f., 294, 689, 765 f Sutherland, H B 758 Swain 26, 99, 232, 237, 766 Swift, J 744 Sylvester, J J 610 Symonds 130 f., 135, 689 Szabó 177, 253, 532, 766 f Szilard, R 543 Tacola 194 Tait, P G 434 Takabeya 767 Tanabashi 767 Tartaglia 46 Taton 52 Taut, B 695 Taylor, C H 726 Teichmann 116 f., 135, 380, 392 ff., 597, 645 Telford 65, 87, 89, 164, 278, 714 Tempelhof 295, 728 Terzaghi 548, 685 ff Tessanek 279, 289 Tetmajer, L 325, 447 f., 767 f Teßmann 150 Thabit ibn Qurra 46 Thalau 116 Theimer 115 Thompson, F 729 Thomson, W 313, 434, 682, 743 Thul, H 560 Thullie 513 ff., 519 Thürlimann 134 f., 568, 689 Timoshenko 63, 106, 177 f., 261, 336, 399, 532, 672, 730, 738, 745, 750, 768 Timpe, A 582 Todhunter 22, 277, 397, 400, 532 Todt 392, 451 Tölke, F 766 837 778-848_Anhang_Korr2_INDD-5_bp.indd 837 05.03.2008 15:46:38 Uhr www.elsolucionario.org Udet, E 491 Ungewitter 325 Unold 115 Vainberg, D V 608 VanGelde 240 Vauban 50, 746 Varignon 41, 43, 45 f., 202, 319, 769 Vasari 190 Vène 296, 297 Vèrges 292 Vermeulen 414 Vianello 409 f., 769 f Vicat 95 Vierendeel 529, 591, 721, 770 Vieta 573, 700 Villarceau 227 Vitruvius 46, 138 f Vlaslov 770 Vogel, U 135, 464 Vogeler 504 f Voigt, W 426, 682 Völker, P 507, 515 Voltaire 52, 678, 718 Wadell, J A L 603 Wagner, H 439, 617, 630, 634 Wagner, W 435 Wall, W A 745 Wallis 737 Walther, A 616 f., 646 Walthelm 567 Wanke 720 Wapenhans 241, 466, 680 Ward 737 Warren 64, 73, 341 Washizu 665 ff., 770 f Wasiutynski 105 Watt 154, 277 Wayss, G A 498, 500, 503 ff., 509, 512 f., 548 f Weber, C H 177, 439 ff., 730, 771 Weber, M 413, 428, 456 Weber, M M v 105 Weber, W 188, 238 ff Wedekind 773 Wedler, B 560 f Wehle, L B 641 Weierstraß 381 Weikel, R C 652 Weingarten 366, 367 ff., 371 ff., 658, 685 Weisbach 157 f., 166 ff., 402 ff., 407 f., 572, 575, 734, 771 Wellmann 421 Wendt, H 151 Werner, E 261 Werner, G 69 Westergaard 23, 538, 750, 754, 772 Westphal, G 305, 760 Weyrauch 103, 224, 305, 307, 366, 372 f., 658, 685, 706, 772 Whewell 167 Whipple 92, 98, 709, 773 Victor Emmanuel II 749 Wiebeking 57 f Wiedemann, G 730 Wieghardt, K 623, 734 Wiegmann 47, 773 Wierzbicki 773 f Wiley, W H 170 Wilhelm II 379, 386 Wilke, R 74 Wilkins 737 Williot 329 Willis 737 Wilson, E L 732 Windelband 145 Winkler 22, 34, 89, 102 ff., 182, 187, 217, 223 ff., 232, 244, 275, 307, 330, 331 ff., 344, 350, 379, 397, 414, 426, 481, 500, 548, 581, 586, 588, 706, 731, 748 f., 751 f., 774 Wippel 543 Witte, H 469 Wittfoth 555, 560 Wittmann 325 f Wöhler 424, 774 Wöhlert, F 414 Wölfel, P L 96 Wolff, C 284 Wolff, F 505 Wolff, J 195 f Wolff, M 250 Woltmann 281 Wood 539 Worch 647, 712 Wren 214, 255, 737, 774 f Wuczkowski 530 Wußing 51 Wydra 279 Wyss, T 566 Yamamoto, Y 670 Yang, J 750 Young 86 ff., 221 ff., 247, 775 838 778-848_Anhang_Korr2_INDD-5_bp.indd 838 Zerna, W 24, 528, 553 f., 561, 621, 775 Zesch 728 Zeuner 170, 414, 427, 751 Zhuravsky 92, 709, 775 f Zienkiewicz 25, 40, 462, 604, 620, 653 f., 668, 671 f., 722, 732 Zimmer, A 625 Zimmermann, H 105 f., 439, 443 ff., 447 f., 474, 476 ff., 481, 484, 597, 742, 776 Zimmermann, P 376, 765 f Zipkes 529 Zöllner 170 Zott, R 380 Zschetzsche 484, 717 Zschimmer 145, 147 Zurmühl 615, 617 Zuse 39, 393, 486, 570, 580, 597, 599, 606 ff., 617, 647, 703 Zweiling 687 ff., 776 f NAME INDEX Tong, P 670 Topp, L J 39, 249, 640 f., 649 ff., 669 Torroja, E 238, 529, 552, 555 Town, I 64, 70 f Traitteur, W v 66 Tranter 230 Trautwine 169 f Trautz 80 Tredgold 768 Trefftz 654, 768 f Tresca 95, 736 Trost 463, 468 Trostel 250 Trudaine 51, 295, 755 Truesdell 716, 769 Tschauner 115 Turner, C A P 532, 536 ff., 727 Turner, M J 39, 249, 640 f., 648 ff., 652 ff., 658, 669 Turley, E 522 Twain 766 12.03.2008 12:38:42 Uhr SUBJECT INDEX Abutment thickness 206, 208, 212, 220 Accumulation phase 37, 106, 109, 121, 526, 531 f., 543, 547, 550, 562, 571 f Acoustics 374 Active earth pressure 211 Additional boundary condition 668 Addition principle 463 Administration and science 511 Aerodynamics 394, 611 Ageing theory 467, 558 Aircraft design 442 Aircraft construction 596, 664 Aircraft fuselage 635, 638 Aircraft industry 469 Aircraft spar 392 Aircraft structure 630 Aircraft wings 635, 637 f Airship and aircraft construction 384 Airship hanger 432 Airy stress function 623 Algebraic scholastics 572 Ammonite shell 491 Analytical mechanics 659 Analytical theory of science 148 Anchor 522 Anchorages for splices in prestressing tendons 556 Angle of rotation 407 Angle of rupture 208 f Angle of twist 400 Angle lever 265 f Anisotropic shell 462 Annular plate 628 Antenna systems 491 Anti-mathematics movement 62 Application phase 32, 54 Applied thermodynamics 277, 414 Approximation method 587 Approximation function 249, 376, 669 Aqueduct 180 Arch profile 89 Arch thickness 205, 207, 575 Aristotelian motion theorem 46 Aristotelian natural philosophy 675, 677 Aristotelian tradition 45 Arithmetical operation 607 Assembly language 625 Asymmetric cross-section 441 Asymmetric load 550 Asymmetric masonry arch 575 Automatic System for Kinematics Analysis (ASKA) 630 Automation 156, 161, 248 Automation of engineering calculation 646 Automatic calculating machine 607 Automation of structural calculations 608 Automotive engineer 628 Automotive industry 625 ff Average compressive stress 221 Average stress 88 Axial force 169 Axial force diagram 120 Axial stress 88, 108 Axially loaded elastic extensible bar 655 Axially symmetric shell 476 Balanced cantilever 420, 573 Band matrix 316 Band structure 632 Bar end moments 109 f., 120 Bar cell 624 Bar element 639 f Base coordinates 595 Based rule 139 Basic Bessemer steel 97 Basic symbol 600 Basket arch 189, 199 Beam grid 455, 457, 539, 573, 624, 705 Beam grid model 539 Beam models 76 Beam on elastic supports 103, 335 Beam on two supports 269 Beam oscillation 617 Beam trussed from above 49 Beam trussed from below 49 Beauty and law 137 ff Beauty and utility 692, 695 ff Beltrami-Michell stress differential equation 583 Bending about two axes 336 Bending deflection 257 Bending elasticity 334 Bending failure 276 Bending failure problem 46, 251, 264, 273 Bending line 300, 303 Bending moment 171, 301, 303, 521 Bending moment diagram 80, 112, 126, 171 f., 368, 385, 580 Bending stiffness 109, 115, 298, 300, 316, 335, 337, 375, 460, 587 Bending strength 171 Bending stress 113 Bending stress equation 520 Bending test 123, 275 f., 438 Bending theory for cylindrical shells 549 Bending theory for rotational shells 549, 551 Bending theory for shells 548 Bending theory of straight beams 179 Bendixsen’s method 594 Bent-up reinforcing bars 564 ff Berlin school of structural theory 379 ff., 572, 579, 592, 685, 703 Bernoulli hypothesis 438, 519 f., 548 Bessel function 534 Bessemer method 35 Bessemer steel 397 Betti’s theorem 607 Beyer bible 552 Biharmonic equation 534, 623 Bleich’s theorem of four moments 596 Bodywork calculation 627 Bodywork optimisation procedure 627 Boiler formula 549 Bologna process 63 Bolted pinned joint 98 Boolean algebra 574 839 778-848_Anhang_Korr2_INDD-5_bp.indd 839 05.03.2008 15:46:38 Uhr 840 778-848_Anhang_Korr2_INDD-5_bp.indd 840 Conservative system 377 Conservative vibration problem 615 Consolidation of deformable porous soils 685 Consolidation period 22, 24, 37, 115, 144, 158, 173, 180, 230, 307, 318, 323, 358, 373, 379, 387, 433, 476, 485, 570 f., 573, 578 ff., 596, 600, 605 f., 615, 623, 642 Consolidation problem 686 Consolidation theory 690 Constitution phase 22, 34, 75, 90, 305, 307 f., 533, 548, 574 Constitutive relationship 682 Construction language 72, 545, 560 Constructional discipline 708 Construction engineer 560, 597 Continuous arch 573 Continuous stiffening girder 115 Continuous beam 50, 76, 77, 80, 103, 122 f., 127, 129, 179, 296 ff., 316, 327, 335, 362, 369, 385, 452, 540, 542, 557, 573, 580, 617, 632, 698 Continuous beam theory 317, 587 Continuous frame 38 Continuous multi-storey frame 531 Continuous longitudinal stiffener 457 Continuous polygonal arch 701 Continuous two-span beam 48 Continuous theory 462 Continuum analysis 455, 459 Continuum hypothesis 270, 690 Continuum mathematical model 621 Continuum mechanics 440, 458, 554, 612, 642 Continuum model 426 Continuum physics 648 Control system 672 Cooling tower 432 Copernican planetary system 675 Copperplate engravings 571 Corbelled arch 188 Corps of military engineers 33 Corpuscular model 426 Counterweight 420 Crane-building 411, 562 Crane column 421, 424, 426 Crane hook 425 Crane engineer 432 Crane manufacture 432 Crane rail 431 Crane rail beam 431 Cranked lever 43, 208 Creep and shrinkage 556 f Creep and shrinkage of concrete 467 Cremona diagram 50, 317, 321 f Crystallography 493 Critical factor 132 Critical load 121, 376 f Critical load increase factor 121 Critical loading case 223 Critical rationalism 146 Cross-girder 456 ff Cross method 603 f., 605 Cubic grids 493 Curved arched beam 337 SUBJECT INDEX Civil engineering laboratory 390 f Civil engineering school 51 Clapeyron’s theorem 342 f., 346, 607 Clapeyron’s theorem of three moments 314 ff., 632 Classical civil engineering theory 161 Classical engineering 156 Classical engineering form 153 Classical fundamental engineering science disciplines 322 f., 572, 647 Classical phase 36, 46, 84, 105 f., 108, 143, 182, 225, 307, 317 f., 324 f., 327, 329 f., 475 f., 531, 571, 576 f., 623, 703 Close-mesh lattice girder 85 Coefficient matrix 632 Cold-formed hollow section 109 Collapse 444 ff., 479, 524 Collapse mechanism 238, 262, 266 Collapse mechanism analysis 245 Complementary energy formulation 668 Complementary energy principle 668 Complementary work 642 Cable-stayed bridge 95 Composite beam 465 Cableways 431 Composite column 463 CAD program 705 Composite floor slab 465 Calcomp plotter 628 Composite frame 465 Calculus of variations 375, 608, 621, 655, 657, Composite strength 169, 170 f 659, 661 f., 669, 678 f., 688 Composite system 49, 72, 585 f Canal bridge 180 Composition law 136, 478, 481, 485, 491 Canonic transformation 659 ff Compression test 219, 525 Canonic variational theorem 662 Compression zone 507 Canonic variational theorem of Hellinger and Compressive strength 173, 209, 233 f., 301 Prange 658 ff Compressive strength test 302 Cantilever 171, 276 Compressive stress 220 f., 224 Cantilever beam 48, 117, 265, 267 ff., 335, 337, Compressive stress curve 525 573 Compressive stress diagram 221 Cantilever method 602 ff Compressive stress distribution 221 f Carry-over factor 604 Computational engineering 40, 570 Carry-over method 617 ff., 621 Computer Aided Design (CAD) 470, 472, 627 Cartesianism 52 Computer Aided Engineering (CAE) 627 Castigliano’s energy theorem 640 Computer-aided framework topology 494 Castigliano’s first theorem 360, 378, 607, 642 Castigliano’s second theorem 113, 348, 360, 378, Computer-aided graphical analysis 694, 704 f., 707 606 f., 642, 658 Computer-aided structural analyses 625 ff Castigliano’s theorems 355, 358, 366 f., 373 f., Computer Aided Testing (CAT) 627 379, 661 Computational Fluid Dynamics (CFD) 672 Castigliano’s third theorem 360 Computational Solid Mechanics (CSM) 672 Cast-iron arch 85 Computer-assisted graphical analysis 692 Cast-iron arch bridge 87 f., 90 Computer network 41 Cast-iron bridge 64 f., 72, 76 Computer statics 570 Cast-iron tube 85 Computing plan 580, 608 f., 703 Catenary 192 Computing sheet 608 Catenary arch 214, 221, 290 Concentric joint 588 Catenary model 235 Concept of the truss model 568 Cause-effect relationship 163, 261, 290, 579 Concrete arch 85 Cell tube 630 ff., 635, 637 Concrete arch bridge 562 Cellular hollow section 433 Concrete dome 551 Cement 522 Concrete stress 521 Cement research 511 Concrete compressive stress 509, 520 f Centre-of gravity axis 88 Conical shell 550 Chain suspension bridge 66 Conjugated potential function 666 Chaos and fraction 671 Conservation laws in dynamics 690 Characteristic compressive strength 222 Conservation of energy law 314, 677, 683 Chemical energy 154 Boolean localisation matrix 653 Boundary element method (BEM) 619 Boundary value problem 658 Box beam 638, 664 Braced sway frame 581, 593 Brachistochrone 655, 679 Bredt’s theorem 443 Breaking length 264 Bubnov-Galerkin method 642 Buckling coefficient 126 Buckling of columns 294 Buckling load 274, 376, 446 Buckling matrix 619 Buckling problem 93 Buckling strength 179, 253 Buckling strength test 302 Buckling theory 171, 277, 443 ff., 618 Buckling test 274 f., 443 Building industry 511 Burr’s system 70 05.03.2008 15:46:39 Uhr www.elsolucionario.org Curved bar 334 f., 426 Curved body 331 Curved cantilever beam 705 Curved elastic arched beam 337 Curved elastic trussed girder 81 Curved plate 335 Curvilinear coordinate 553 Curvilinear integral 534 Cylindrical shell 179, 546, 549, 551, 624 Cylindrical water tank 508, 549 D’Alembert principle 374 Deck plate 458 Deflection curve 327, 579 f Deflection measurement 220, 538 Deflection theory 114 Deformation complementary energy 364, 378, 642 Deformation energy 247, 257, 358, 364, 367, 375, 378, 408, 410, 642, 683 Deformation equation 401 Deformation figure 112 Deformation measurement 93, 220, 224 Deformation parameter 592, 594 Deformation work 179, 348 Deformed system 117 f Degree of freedom 624, 626 Degree of prestress 556 Delta wing 640, 648 Denominator 120 Desktop computer 41 Descriptive geometry 51, 53 f., 308, 352, 354, 475, 572 Design equation 502 Design language 586 Design method 514, 518 Design model 525 Design office 97, 600 Design theory 503, 514, 529 Determinant theory 37, 389, 601 Deterministic safety concept 472 Diagram analysis 575 Differential calculus 32, 39, 54, 164, 179, 213 f., 216, 247, 270, 289, 383, 681, 695 Differential equation for the elastic membrane 541 Differential equation for plates 533 Differential geometry 43, 188 Diffusion phase 41, 117, 398, 528, 654, 662 Dirichlet’s energy criterion 657 Dirichlet’s stability theorem 655 Direct stiffness method 621, 647, 652 ff., 654, 658, 669 Discipline-formation period 22 f., 34 ff., 45 f., 84, 91, 94, 113 f., 158, 166, 168, 220, 251, 260, 290, 297, 306 ff., 577, 585, 589, 596, 642, 684 Disk memory 628 Discontinuous element 624 Discontinuum mechanics 243 Discrete mathematical model 621 Displacement equations 593 Displacement jump 594, 599 Displacement method 37 f., 107, 108 ff., 116, 358, 570 f., 581 ff., 602, 606 f., 621, 625, 641 f., 645, 652, 656 Displacement parameter 595 Displacement variable 581, 599, 606 Displacement vector 625, 664 f Dissipation work 126 Disturbed region 568 Double-layer frame grid 493, 495 Double strut system 564 Dockyard crane 431 Dodecahedron 137 Domain decomposition 671 Dome 325 Dome theory 475 Domical rib vault 244 Double Fourier series 540 Double trigonometric series 533 f Drawing office 517 Dresden school of applied mechanics 383, 592, 594, 684 Dresden school of kinematics 351 ff., 382 Dual diagrams 321 f Dual nature of structural theory 596 Dual nature of theory of structures 606, 644 Dual polygons of forces 322 Dynamic boundary conditions 376, 583 Elasto-Statics Element Method (ESEM) 628 Electrical engineering 179, 386, 411, 605 Electrical engineering theory 614 Electrical networks 602, 605, 614, 646 Electrical vibrations 374 Elementary frame 632 Elementary mathematics 179 Element axial force 548 Element bending moment 548 Element shear force 548 Element stiffness matrix 625, 649, 651 f., 653 f., 669 Element stress matrix 654 Element torsion moment 548 Element trust force 548 Elementwise linear approximation 655 Elliptical arch 190 Emperger column 464 Empirical rule 210 Encyclopaedia of applied mechanics 166 ff Encyclopaedia of bridge-building 332 f Energy conservation law 375 f Energy conservation principle 247 Energy dissipation 314 Energy doctrine 354 ff., 367, 373, 379, 382 f., 589 Energy method 607, 618 Energy principle 42, 172, 176, 294, 348, 359, 460 Earth pressure 251, 294 Energy theorems of Castigliano 684 Earth pressure theory 33, 182 Engesser’s complementary work 661 Eccentric plastic hinge 126 Engineering aesthetics 388 Eclecticism 385, 389 Engineering education 26 Effect-cause relationship 579 Engineering hydromechanics 163 Effective torsional stiffness 461 Engineering manual 168 Effective width 456 Engineering model 534 Eigenvalue analysis 615 f Engineering office 523 Eigenvalue problem 637 Engineering philosophy 143, 146, 148 f., 151 Einstein’s summation convention 594 Engineering science history 146 Elastic arch beam 294 Elastic arch theory 82, 102, 115, 185, 187, 220 ff Engineering science theory 149 Engineering sociology 151 Elastic continuum 661, 681 Enlightenment 52, 174, 181, 204, 272, 277, Elastic frame theory 531 284, 693, 694 Elastic/inelastic zone 449 Entropy 154 Elastic in-plane-loaded plate 540, 566 Epistēmē 40, 158, 351 f., 576 f., 580, 611, 695 Elastic limit state 125, 127, 276 Epistemology 142, 145 Elastic line 293, 296 f Equilibrium conditions 45, 120, 337, 401, 478, Elastic membrane 294, 542 509, 567, 583 f., 574, 593, 596, 606, 622, 633, Elastic modulus 173, 198, 220, 226, 228, 257, 659, 661 301 f., 347, 403, 519, 583, 622, 681 Equilibrium equations 520 Elastic plate 528, 623 Equilibrium principle 45 Elastic pole 601 Equivalent trussed framework system 623 Elastic-plastic torsion of bars 441 Erection procedure 77, 84 Elastic slab 294, 528 Eccentric joint 588 Elastic theory for masonry arches 246 Establishment phase 22, 35 f., 46, 50, 72, 79, Elastic ultimate load 266 89, 91, 105, 168, 176, 305, 307 f., 324, 398, Elastic weight 540, 542 531, 574 f., 593, 622, 694 Elasticity conditions 226, 558 Euler buckling cases 335 Elasticity equations 234, 349, 365, 558 Euler buckling theory 425, 443 Elasticity equations of the second order 112 Euler cases 377 Electricity pylon 487 Euler curve 447 Electronic computation 644 Euler differential equation 656, 658 Electro magnetism 672 Euler safety factor for buckling 453 f Elasto-plastic deformation 123 841 778-848_Anhang_Korr2_INDD-5_bp.indd 841 05.03.2008 15:46:39 Uhr 842 778-848_Anhang_Korr2_INDD-5_bp.indd 842 General theory of trusses 347, 498 General law of work 43 f General work 688 General work theorem 355, 367, 539, 579, 606, 679 f., 683 f Generalised coordinates 374, 377 Generalised displacement 377 f., 643 f Generalised flexibility 642 Generalised force 374, 377 f., 643 f Generalised stiffness 644 Geodesic dome 489 f General variational theorem 665 f., 668 Geometrical imperfections 447 Geometrical mechanics 46 Geometrical mechanics of rigid bodies 611 Geometrical theory of proportion 251 Geometrically determinate 109, 111, 120 Geometrically determinate system 119 Geometrical factor of safety 236 Geometrically indeterminate 109, 120 Geometric boundary conditions 583, 656 Geometric composition theory 139 Geometric proportioning rule 139 Geometric series 491 ff Geometric similarity 262, 268 Geometric view of statics 46, 135, 218, 681, 685, 707 German idealism 695 German Standards Committee (DIN) 527 Glider model 486 Global displacement state 625 Global system of coordinates 626, 653 Golden rule of mechanics 412 Graph theory 152, 156 Graphic editor 704 f Graphic interface 707 Graphic monitor 628 f Graphic software 706 Graphical analysis 50, 182, 317 ff., 355, 484, 531, 572, 576 f., 682, 703, 705 Graphical integration machine 317, 322 Graphical method of fixed points 601 Graphical statics 35 f., 48, 50, 84, 94, 144, 179, 307, 311, 317 ff., 347, 355, 484, 572, 576, 682, 703, 705 Grashof ’s grillage method 535, 538, 540 Gridwork method 624 f Gridwork model 628 Grillage method 534, 539 Groin vault 244 Group theory 156 Guyed cantilever 84 Hamilton-Jacobi theory 659, 662 ff Hammerhead crane 430 Hanging chain 192 f Harmony 701 Heavy-duty crane 432 Hemispherical shell 488 Hemispherical spatial framework 488 Hennebique’s system 515 ff., 523 Hennebique’s T-beam system 514 Hennebique’s trussed framework model 563 SUBJECT INDEX Flexibility of complete structure 644 Flexibility of element 644 Flexural buckling 392 Floating crane 431 Flutter Bible 615 Flutter calculation 393, 645 Folded plate 460, 528, 544, 545 ff Folded shell 528, 544 Force-deformation behaviour 220 Force-deformation diagram 172 Force diagram 36, 703 Force method 37 f., 107, 116 f., 340 ff., 349 f., 383, 467, 483, 558, 570, 581 ff., 592 ff., 602, Factory organisation 422 604, 606 f., 614, 621, 632, 635 ff., 641 ff., 654 Failure load 539 Form-active loadbearing structure 706 Failure mechanism 217, 239 Forging shop 97 Failure mode 121, 217 Formalisation idea 598 Failure moment 86 Formalisation of structural calculations 571 Fairbairn foundation 421 Formalised theory 620, 641, 645, 662 Falk scheme 619 Formal language 599 False arch 188 Formal operation 574, 700 Fatigue 418 Formalised language 574, 579 FE main program 654 Formation law 136 ff., 141, 478, 481, 485, 490 f., FEM textbook 654 493, 495, 695 Fictitious forces 117 ff Form-finding 191, 194 Field problem 619 FORTRAN 628 Finite bar segment 647 FORTRAN IV 654 Finite difference method (FDM) 493, 540 ff., Foundation anchor 425 619 f., 631 Foundation dynamics 390 Finite elements 249 Four-bar linkage 352 f Finite element analysis 248 f Fourier’s heat conduction equation 686 Finite element mapping (FEMAP) 628 Finite element method (FEM) 40, 241, 249, 435, Four-span continuous beam 78 Frame 544 462, 493, 562, 570 f., 619 ff., 648 Frame analysis 591 Finite procedure 646 Frame equation 531 f Fire resistance 505 Frame table 602 Fire test 509 Frame theory 595 First boundary value problem 583 Framework 71 First Bredt equation 412, 429 Framework cell 631 f First formation law of trussed framework Framework cell discretisation 630 theory 47, 487 First fundamental law of thermodynamics 682 Framework theory 37 Frictionless wedges 202 First-order tensor 612 Full-size test 539 First-order theory 119, 588 First prime task of thrust line theory 214 f., 217 Fully plastic cross-section 123, 125, 266 Functional 664 First stage of formal operations 574, 577 Functional analysis 655 Fixed arch 223, 335, 338 Fundamental engineering science disciplines Fixed bar 595 28, 37, 84, 142 ff., 277, 313, 348, 359, 498, 548, Fixed-based frame 573 585, 600, 612, 614, 617, 621, 641 Fixed-end arch 115, 528, 573 Fundamental theory 33, 571 Fixed-end arch system 210 Funicular force 164 Fixed-end beam 122 f., 253, 263 Funicular curve 165, 540 Fixed-end column 258 Funicular polygon 179, 193, 201 f., 206, 311, Fixed-end curved elastic bar 705 318 ff., 325, 329, 577, 704 Fixed-end elastic arch 241 Fuselage 630 Fixed-end moment 267, 269, 301 Fixed three-pin arch 230 Fixed two-pin arch 230 Gantry crane 491 Flat plate 335 Gas tank 549 Flat steel plate 469 Gaussian curvature 533 Fluid mechanics 612, 671 General bending theory of shells 553 Flexibility 643 General dynamics 612 Flexibility matrix 613, 642 f General technology 148, 151 Flexibility method 641 General theory of linear elastic trusses 36 Euler’s polyhedron theorem 137, 479 Experimental mathematics 646 Experimental physics 177 External memory 627 External pressure 548 External torsion moment 402 External virtual work 342, 683 External work 187, 247, 353, 376 Extra-symbolic meaning 574 f Extremum of deformation work 659 Eye-bar shop 98 12.03.2008 12:41:10 Uhr Inclined pin-jointed bar 286 Inclined principal tensile stress 563 Incremental launching method 560 Industrial Revolution 21, 57, 64, 93, 101, 153, 155, 160, 163, 168, 180, 246, 251, 272, 277 f., 283, 289, 291, 296, 308, 313, 317, 330, 397, 414, 418, 421, 586, 597 Industrial standard 525 Infinitely convergent series 602 Infinitesimal calculus 40, 598, 648, 655 Influence coefficient 640 Influence line 74, 99 ff., 185, 229, 305, 329, 335, 338 ff., 348, 354 f., 379, 579 f., 580, 684 f Influence line theory 230, 431, 578, 706 Influence line concept 102 Initial phase 23, 33, 90, 213, 277 Innovation phase 40, 107, 117, 121, 231, 398, 456, 469, 471, 475, 528, 539, 558, 567, 571, 619 ff., 641, 643, 647, 653, 662 In-plane-loaded plates 545 ff Integral calculus 32, 39, 54, 164, 179, 213 f., 216, 247, 270, 289, 383, 681, 695 Integral equation method 534 Integral plate 469 Integral tables 362 Integration machine 320, 322 Integration period 39, 121, 230, 553 f., 605, 608 Interactive THRUST 706 Internal bending work 187 Internal pressure 548 Internal secondary conditions 668 Internal virtual work 119, 131, 342, 355, 683 Intra-symbolic meaning 574, 620 Invention phase 38, 107, 121, 327, 398, 448, 527, 534, 543 f., 547, 551, 553 f., 596 f., 621, 624, 637, 687 Inverted catenary 67, 90, 189, 287, 289, 335, 681 Inverted funicular polygon 286 f Iron arch bridge 181, 183 Iron beam bridge 180 Irregularly formed roof 471 Isherwood system 456 Isochromatic lines 188 Isothermic deformation 372 Iteration method 394 Heterogeneous manufacture 245 Hexahedron 137 Higher dynamics 180 Higher engineering education 50 ff Higher technical education 55, 58 High-rise buildings 560, 592 High-speed aerodynamic 637 High-strength concrete 555 Historical disciplines 708 Historical engineering science 25, 186, 248 Historical epistemology 243 f Historical theory of structures 25, 186, 248 Historicity of structures 25 Historico-genetic teaching 27, 692, 707 f Historico-logical comparison 709 Historico-logical longitudinal section analysis 708 Historico-logical transverse section analysis 708 History of art 700 History of elastic theory 335 History of engineering 145 f., 151 History of engineering science 248, 389 History of engineering science knowledge 248 Holistic design 568 f Hollow box 76, 316 Hollow-rib plate 462 Hollow section 442 Homogeneous quadratic function 681 Hookean body 313, 576 Hookean relationship 650 Hooke’s law 32, 104, 121, 173, 271 ff., 390, 519, 607, 682 Hoop force 326 f Hoop tension 679 Horizontal frame 593 Howe truss 72 Huber differential equation 460 Huber’s plate theory 459 f Hybrid displacement model 670 Hybrid finite elements 664 Hybrid model 670 Hybrid stress model 670 Hybrid variational theorem 663 f Hydrostatic pressure 549, 681 Hydraulic crane 417, 420 Hydraulic cylinder 421 Hydraulic jack 78 Hyperbolic paraboloid 553 Hyperbolic paraboloid shells 552 Hyperboloid 487 Jacobian determinant 480, 482 Jacobi-Gauss iteration method 605 Joint angles of rotation 589, 593 f Joint displacement 593 Joint of rupture 311 Icosahedron 137, 488 f Idea of formalisation 573, 580, 620 Ideal buckling load 447 Ideal compressive stress 449 Ideal-elastic and ideal-plastic material law 122 f., 452 Ideal elastic material behaviour 252, 275, 277, 294 Ideal elastic modulus 467 Ideal plastic material behaviour 252, 275, 494 Imposed load 72, 82, 101, 165, 199, 223 Kern 88, 237, 335 ff Kern point moment 229 Keystone 224 kh-method 508 Kinematic chain 126 f Kinematic doctrine 354 ff., 379, 382, 589 Kinematic machine 46, 350 Kinematic machine model 683 Kinematic method 131 f., 328, 607, 706 Kinematic model 680 Kinematic pin-jointed system 591 Kinematic pin system 593 Kinematic relationship 583, 682 Kinematic theorem 103 Kinematic theory 103, 483, 706 Kinematic theory of beams 355 f Kinematic theory of trusses 353, 684 f Kinematic series 353 f Kinematic spatial framework theory 484 Kinematic trussed framework theory 327, 484 Kinematic ultimate load theorem 237 Kinematic view of statics 42, 46, 135, 206, 218, 347, 685, 707 Kinematically determinate 47 Kinematically determinate system 119 Kinematically indeterminate system 286 Kinematically permissible hinge mechanism 235, 237 Kinetic energy 257, 374 f Kirchhoff differential equation for plates 540, 657 Kirchhoff ’s plate theory 460, 533 Lagrange equation 377 ff Lagrange formalism 606 Lagrange’s generalised coordinates 595 Lamé elastic constants 622 Lamé-Navier displacement differential equation 583 Land’s theorem 99, 355 Language of matrix algebra 645 Language of matrix theory 644, 653 Laplace differential equation 401 Laplace operator 461 Large deflections 664 Large deformations 629 Large displacements 688 Lateral buckling 177, 437, 453, 455, 504 Lattice dome 462, 478 f., 481, 485 Lattice girder 70 f., 113, 630 Lattice girder bridge 79 Lattice shell 487 Lattice structure 344 Law of friction 295 Law of materials 583 Legendre transformation 666 Leibnizians 677 Lever arm 274 Lever arm of the internal forces 507 Lever principle 42, 45, 265 Lifting bridge 431 Lifting gear 418 Lifting procedure 78 Light pen 628 f Lightweight steel construction 469 ff Lightweight steel road deck 457 Limitation principle 668 Linear algebra 183, 323, 577, 579, 645 Linear buckling analysis 624 Linear combination 601 Linear compressive stress distribution 525 Linear distribution of compressive stress 509 Linear elastic analysis 241 Linear elastic body 622 843 778-848_Anhang_Korr2_INDD-5_bp.indd 843 12.03.2008 12:41:22 Uhr www.elsolucionario.org Machine dynamics 175 Machine kinematics 175, 317, 414 Machine shop 97 Machine tool 352, 354, 413, 415 Macroelement 632, 635 f Main bridge shop 97 Mainframe computer 628 Main girder 456 ff Main routine 645 Manipulation of symbols 692 Manipulator of symbols 580 Marxism 149 ff., 312 Masonry arch theory 74, 87 Masonry arch collapse mechanisms 204 Mass-active loadbearing structure 706 Mass inertia tensor 612 Materials tests 519 Materials research 539 Materials testing 255, 512 Materials testing science 514 Materials laboratory 62 Mathematical elastic theory 179, 336, 532 ff., 543, 548, 582 f Mathematical physics 659 Mathematical shell theory 548 Mathematicisation of the science 698 Matrix algebra 574, 611, 620, 640 ff Matrix calculation 652 Matrix formulation 610 Matrix iteration 637 Matrix iteration procedure 615 Matrix multiplication 613, 619 Maximum bending moment 127, 508 Maximum line of thrust 219 Maximum principal stress 566 Maximum span moment 101 Maxwell-Betti reciprocal equation 658 Maxwell’s theorem 343 f., 348 f., 607, 661 Means-purpose relationship 579 Mechanics of rigid bodies 484 Mechanical calculator 598, 599 Mechanical engineering 154, 167, 173, 180, 337, 352, 386, 405, 411, 459, 586, 596, 686 Mechanical networks 614 Melan arch bridge 464 Melan system 488, 537 Member end moments 589, 594 f Member angles of rotation 589, 593 f Member chord rotation 117 f., 120 Member stiffness 604 Membrane 374 Membrane stress condition 326 f., 548 Membrane theory 476, 479, 550 Membrane theory for rotational shells 550 Menabrea’s principle of minimum deformation energy 222, 607, 658 Meridian force 327 MERO system 491 ff Mesh geometry 542 Method of fluxions 216, 383 Method of base coordinates 596 Method of successive approximation 39, 603 f Microprocessor 571 Middle-third rule 88, 223, 237 Military engineering corps 309 Military schools 51 ff Minimal area problem 655 Minimal line of thrust 219 Minimum arch thickness 208 f Minimum load increase factor 116 Minimum of total energy 661 Minimum thickness 224, 236 f Mobile shed structure 491 Modern structural mechanics 641 Mohr’s analogy 83, 329, 349, 540, 542 Mohr’s general work theorem 607 Molecular hypothesis 681 Möller’s T-beam 514 Moment equilibrium 588 f Moment of resistance 410, 426 Monier-Broschüre 500 ff Monier slab 502 Monier system 498 ff Monier’s patent 499 ff Monolithic reinforced concrete frame 516 Motor dyad 612 Motor matrix 612 Motor symbolism 612 Motor tensor 612 844 778-848_Anhang_Korr2_INDD-5_bp.indd 844 Movable counterweight 420 Moving bridge 180 Moving load 101 Multi-bay frame 573, 592 Multi-constant theory 623, 682 Multi-dimensional continua 647 Multi-storey frame 592 f., 602 Mushroom flat slab 536 ff., 540, 543 Napoleonic Wars 55 NASA Structural Analysis System (NASTRAN) 629 f Natural causality 153 Natural frequency 375 Natural philosophy of Aristotle 676 Navier’s beam theory 598 Navier-type boundary conditions 534 NC machine 472 Neutral axis 88, 125, 507, 557, 603 Neutral fibre 521 Néville truss 73 Newton’s law of force 143 Newton’s law of inertia 143 Newton’s law of reaction 143 Newton’s second law 45 n-method 509 Nodal load 626 Node displacement 342 Node equilibrium 111 Node rotation 109 Non-central system of forces 321 Non-classical engineering mathematics 157 Non-classical engineering sciences 154 f., 156, 580 Non-elastic buckling theory 450 Non-Euclidean geometry 490 Non-interpretive operation 693 Non-isothermic deformation 372 Non-linear algebra 646 Non-linear analysis 627 Non-linear elastic analysis 241 Non-linear-elastic material behaviour 427 Non-linear elastic truss 363 Non-linear FEM 243 Non-linear procedure 571 Non-linear sets of equations 135 Non-linear stress-strain diagram 224 Non-linear stress-strain relationship 642 Non-n cross-section design process 561 Non-rigid foundation 104 Non-sway frame 593 Non-sway system 603 Non-Uniform Rational B-Splines (NURBS) 470 Normal stress diagram 439 Number juggler 702, 707 Numerical engineering methods 602 Octahedron 137 Octagonal dome 551 One-dimensional elastic continua 335, 666 One-sided uniformly distributed load 508 f Online interactive graphical analysis 706 Open-hearth furnace 97 SUBJECT INDEX Linear elastic continuum 230, 362, 623 f Linear elastic FEM 243 Linear-elastic spring 296 Linear-elastic theory of truss 690 Linear-elastic trussed framework theory 364, 382 Linear electrical networks 614 Linearisation of perception 700 Linear programming 646 Linear theory of structures 607 Linear transformation 610, 612 Line diagram analysis 573, 575 ff., 600 Line of pressure 218 Line of resistance 218 Line of thrust 89 f., 192, 194 f., 201, 206, 209, 218 ff., 225 f., 234 f., 236 f., 287, 326, 335, 337, 567, 681, 705 Line of thrust method 223 Line of thrust theory 89, 213 ff., 246 Line of fracture 539 Lithography 574, 576 Load-carrying capacity 122, 124, 127, 129, 222, 239, 258, 454, 466, 506, 565 Load increase factor 131 Loading tests 509 f., 529 Load vector 120 Local approximation function 670 Local buckling 453, 455 Local system of coordinates 626 Localised Ritz approache 654 Locomotive crane 421 Longitudinal rib 456 Longitudinal stiffener 456, 458, 635 Long’s system 71 Lower kern line 336 Lower kern point moments 601 05.03.2008 15:46:41 Uhr Plate bending stiffness 461 Plate buckling 456 Plate deflection 533 Plate stiffness 540 Plate theory 179, 460, 493, 532 Plates with in-plane loading 528, 544 Platonic bodies 136 f., 479, 491 Plotter 629 Poisson’s ratio 440, 533, 583, 622 Polar moment of inertia 408 Pole diagram 353, 356 Pole distance 320 Pole plan 354 Polygonal dome 551 Pair of elements 354 ff Parabolic distribution of compressive stress 509 Polygon of forces 202, 311, 318 ff., 325, 577 Polyhedron 319, 492 Parabolic two-pin arch 220 Political economics 52 Paradigm change 451 Portal frame 431 Paradox of elastic theory 134 Portal method 602 ff Paradox of the plastic hinge method 127 ff Portland cement 497, 511, 524 Paradox of the plastic hinge theory 133 Potential energy 374, 377, 655 Paradox of ultimate load theory 689 Potential equation 666 Parallelogram of forces 32, 42, 44 f., 575 Powerful Efficient Reliable Mechanical Analysis Partial differential equation of Terzaghi 686 System (PERMS) 630 Partially plastic cross-section 125 Practical elastic theory 414 Particle physics 672 Practical beam theory 220 Passive earth pressure 211 Practical bending theory 32, 34 f., 37, 90, 253, Pauli truss 294 293, 301 f., 307, 331, 364, 382, 433 f., 437 ff., Perforate plate 624 676 Perforated quadratic plate 628 Practical torsion theory 433 Permanent way theory 105 Prange’s variational theorem 663 Permissible concrete compressive stress 508 Precambered leaf spring 628 Permissible tensile stress of concrete 549 Prefabrication 77 Permissible tensile stress of steel 521, 549 Prefabrication industry 555 Permissible steel tensile stress 508 Preparatory period 23, 31 ff Permissible stress 334, 509 Pressure cylinder 424, 426 Perpetuum mobile 193 Pressure-volume diagram 313 Philosophy of technology 143 Prestressed carriageway 557 Photoelastic experiment 188 Prestressed concrete 554 ff Photoelastic measurement 567 Prestressed concrete beam 467, 555 Photoelastic test 566 Prestressed concrete bridge 560 Photogrammetric method 191 Prestressed concrete construction 496 Piecewise linear approximation 655 Prestressed concrete engineer 556 Pinned beam 122 Pinned trussed framework model 48, 50, 91, 98, Prestressed concrete research 555 Prestressed force 558 108, 113 Prestressed ground anchors 557 Pin-jointed bar 289 Prestressed masts 557 Pin-jointed framework 342, 529, 623 Prestressed piles 557 Pin-jointed truss 49 Prestressed pipes 557 Pin-jointed trussed framework 585 Pin-jointed trussed framework model 529, 584 Prestressed ring flanges 108 Prestressed shells 557 Pithead gear 431 f Prestressed tanks 557 Plane of rupture 207 f Primary boundary conditions 668 Plane shell structure 566 Primary stress 587 Planetarium dome 488, 551 Prime mover 352 f., 413 Planning disciplines 708 Principal compressive stress 566 Plastic deformation 199, 260 Principle of deformation minimum 614 Plastic design method 127 Principle of Dirichlet 607 Plasticity condition 126, 131 Principle of Engesser 607 Plastic hinge 121, 125 ff., 129, 210 Principle of extremum of potential energy 659 Plastic hinge method 127, 134 Principle of induction 167 Plastic hinge theory 122, 135, 266, 276 Principle of least action 678 f Plastic limit state 127 Principle of Maxwell and Betti 579 Plate 374 Organic manufacture 245, 698 Organ projection 144 Orientation phase 31 f Orthogonal frames 593 Orthogonalisation methods 601 Orthogonally anisotropic plate 458 Orthotropic bridge deck 456 ff., 469 Orthotropic plate 455 ff., 469, 543 Out-of-plane-loaded structure 532 ff Overhead moving crane 99 Overhead travelling crane 414 ff., 419, 422, 431 Overall stiffness matrix 651 ff Principle of Menabrea 230, 362 f., 368, 370, 379, 408, 567, 660 f., 683 Principle of minimum complementary potential energy 642 Principle of minimum deformation energy 183, 226, 640 Principle of minimum potential energy 654 Principle of minimum total potential 642 Principle of minimum loading 219 Principle of the stability of the elastic equilibrium 655 Principle of virtual displacements 37 f., 42, 43, 45, 99, 119 f., 131, 133, 135, 236, 239, 294, 347 ff., 355 ff., 377, 413, 484, 533, 595 f., 606 ff., 642, 656, 659 f., 661, 681, 687 f Principle of virtual forces 36 ff., 42, 44, 294, 342, 348 f., 355 ff., 362 f., 378, 383, 577, 589, 596, 606 ff., 642, 658 f., 666, 683 f., 687 f Principle of virtual work 214 Principle of virtual velocities 43, 45, 345, 383 Principal tensile stress 566 Principal stress 566 Principal stress line 566 Principal stress trajectories 565 f Programmability 394 Program systems 609 Projective geometry 34, 318 ff., 322, 324 f., 329, 354, 576, 611, 682 Proportion 701 Propped cantilever 131 f Ptolemaic planetary system 675 Puddling furnace 35, 278 Pulley 251 Pure bending 436, 509, 520 Pure mathematics 582 Pure mechanics 175 Purpose-means relationship 158, 163, 261, 290 Quadratic approximation function 669 Quadratic element 668 Quadratic trussed element 623 Quadripole theory 614 Quantum mechanics 611 Quantum theory 621 Radial stress 550 Radio mast 487 Rari-constant concept 426 Rari-constant theory 622, 682 Rationalisation of structural calculations 600 f Rationalisation movement 318, 324, 486, 571 Rational mechanics 596 Rayleigh-Ritz coefficient 375 ff Rayleigh-Ritz method 375 ff., 642 Real-time analysis 692 Reciprocal diagram 320 ff Reciprocal figure 319 Reciprocal force polygon 319 Reciprocal funicular polygon 319 Reciprocal theorem 343, 374, 379, 612 Rectangular bar cell 625 f Rectangular element 649, 670 Rectangular plate 649 845 778-848_Anhang_Korr2_INDD-5_bp.indd 845 05.03.2008 15:46:41 Uhr Safety factor for load-carrying capacity 454 Safety theorem 236 Sail vault 244 Saint-Venant torsion theory 177, 398, 405, 412, 433, 443 Sandwich construction 469 Schism of architecture 694 f Schlink dome 485 Schwedler dome 475 ff., 481, 484 f., 550 Schwedler truss 294 Scientific revolution 143, 154, 251, 259, 674 Scientific revolution in structural mechanics 647 Scientific school 380 f Scientific-technical revolution 155 Screw 251 Secondary condition 670 Secondary stresses 98, 108, 529 f., 566, 581, 587, 603 Second boundary value problem 584 Second Bredt equation 412, 429 Second fundamental law of thermodynamics 682 Second industrial revolution 512, 513, 522 f Second-order displacement theory 135 Second-order tensor 612 Second-order theory 38, 113 ff., 121, 126, 171, 184, 335, 380, 393, 581, 587, 596, 645 f Second prime task of thrust line theory 201 f., 214 f., 217, 287, 320 Second principle of thermodynamics 154 Second stage of formal operations 574 ff., 579 f., 606 Second theorem of Castigliano 408, 683 Segmental arch 203, 206 Semicircular arch 202, 205 f., 209, 236 f Semi-graphical fixed-point method 531 Semi-inverse method 400, 404 Semi-octahedron 493 Semi-probabilistic safety concept 472 Semi-regular Archimedean bodies 492 Sensitivity to errors 601 f Shallow foundation 534 Shear centre 435 ff Shear connector 467 Shear crack 565 f Shear design 524, 565 Shear elasticity 334 Shear field 633 ff., 638, 640 Shear field layout 630 ff., 636 f Shear field theory 635 Shear-flexible beam 672 Shear-flexible elastic plate 664 Shear-flexible orthotropic plate 462 Shear flow 429 Shear force 563 f., 633 Shear lag 664 Shear link 564 Shear measurement 568 Shear modulus 402 f Shear reinforcement 563, 565 Shear stiffness 335 Shear stress diagram 335 Shear stress vector 401 Shear strength 567 Shear studs 465, 467 Shear test 564, 567 Shell analysis 670 Shell construction 560 Shell roof 494 Shell plate 460 Shell structure 489 Shell theory 327, 527, 547 ff., 621 Shell-type spatial framework 476 Shell-type trussed framework 476 Shell wing model 637 846 778-848_Anhang_Korr2_INDD-5_bp.indd 846 Shift lift project 390 Shipbuilding 596 Shipbuilding engineering 456 Shipbuilding industry 469 Shipbuilding science 456 Shot-fired fixings 465 Shrinkage 519 Similarity theory 262 Siemens-Martin steel 97 Simple machines 46, 162, 200, 251, 295 Simply supported beam 47 f., 78, 116, 127, 129, 171, 253, 298, 528, 753 Simply supported beam with cantilever 573 Simply supported >-beam 123 Single-pin arch 573 Single-pin frame 573 Single strut system 564 Six-node triangle 668 Skew bridges 431 Slab bending moment 536 Slab strip 658 Slab test 540 Slab theory 179 Slab thickness 507 ff Slenderness 447 Slenderness ratio 448 Slewing jib crane 416 f., 431 Slipway frame 431 f Slope deflection method 594 Soap-bubble allegory 434 Sobolev’s embedding theorem 373 Software company 646 Soil mechanics 685 f Solid-web box beam 634 Solution vector 112 Space frame 631 Space truss model 622 Spatial bridge system 481 Spatial elastic continuum 493 Spatial elastic theory 553 Spatial framework theory 481 ff Spatial trussed framework 562 Spatial truss system 596 Specific symbolic machine 643 Spherical shell 550 Spring constant 272 Square slab 535 Stable equilibrium condition 209 Stabilised pin-jointed system 590 f Stabilised pinned system 118 f., 593 Stability case 453 Stability of the elastic line 657 Stability problem 117, 120, 645 Stability theory 455, 605, 688 Standardisation theory 490 Statically determinate 47 Statically determinate trussed framework 91 Static law 136 ff., 139, 140 f., 478, 481, 485, 491, 495 Static method 131 f., 707 Statics of stone constructions 333 Static ultimate load 238 Statically equivalent node loads 650 SUBJECT INDEX Rectangular reinforced concrete slabs 534 f Rectangular slab 533 f., 624 Rectangular triangular bar cell 624 Reduction method 618 Regula falsi 34 Regular polyhedra 136 Regularity 701 Reinforced concrete arch 509, 528 Reinforced concrete beam 520, 525, 528, 564 Reinforced concrete column 536 Reinforced concrete construction 498 Reinforced concrete plate 528 Reinforced concrete shell 488, 528, 547 Reinforced concrete shell structure 496 Reinforced concrete slabs 223, 499, 502, 515, 528 Reinforced concrete standard 521, 524 Reinforced concrete theory 499, 592 Reinforcing steel 555 Relaxation method 604 f Resolved strut 445 Rheological model concept 468 Restraint forces 111 ff., 119, 593, 595, 599, 606 Residual stresses 180 Reversible electric motor 419 Ribbed slab 628 Rib vault 244, 325 f., 705 Rigid body mechanics 612, 672 Rigid foundation 104 Rigid frames 528 ff., 573, 589 Rigid frame system 578 Rigid framework 578 Rigid joint 530 Rigid-jointed frame 585 Rigid-jointed framework 581, 590 Rigid-plastic material behaviour 222 Rigid-plastic material law 233 Rise/span ratio 196 Ritter’s method of sections 50 Riveted construction 450 Riveted gusset plate 108 Riveted joint 49, 98, 342, 485, 529, 586 Riveted solid-web beams 85 Riveted steel truss 566 Riveting machine 97 Rolling shop 97 Rotationally symmetrical domes 326 Rotational restraints 109 Rotational shell 548 05.03.2008 15:46:41 Uhr www.elsolucionario.org Statically indeterminate 47 Statically indeterminate parameters 592 Stationary value of canonic functional 659 Steam boiler 414 Steam engine 173, 277, 313, 315, 415 Steel core 465 Steel plate crane 704 f Steel tensile stress 509 Steelwork industry 92 ff Stiffened cylindrical shell 635 Stiffened rectangular plates 618 Stiffened shell structure 635 Stiffening beam 114 Stiffness 643 Stiffness coefficient 119 Stiffness matrix 112, 120, 642 f., 649, 651 f., 672 Stiffness method 641 Stirrups 563 Stochastic 156 Stochastic computation 671 Stone bridge 180 Storage yard 97 Storey frame 604 Storey-height frame 628 Strain-displacement relationship 649 Strain distribution 258, 336 Strain stiffness 109, 115, 335, 337 Strain tensor 665 Strength test 35, 65 Stress analysis 113, 220, 304 Stress diagram 125 Stress distribution 266, 276, 515 Stress equation 507 Stress field 568 Stress pattern 566 Stress problem 117, 120 Stress proof 449 Stress-strain diagram 252, 313, 682 Stress-strain relationship 468, 525 Stress tensor 583, 612, 664, 665 Stress trajectory 144, 565 Stringer 635, 637 Strip method 324 Strip of slab 508, 536 Structural Analysis Program (SAP) 494 Structural engineering disciplines 498 Structural imperfections 447 Structural iteration methods 602 ff Structural law 136 ff., 139, 140, 478, 485, 487 490 f., 493, 495 Structural machine 478 Structural matrix analysis 380, 394, 570, 610 f Structural matrix method 617 Structural models 35 Structural shell theory 327 Structure of the computer 645 f Stüssi beam 129, 134 Subroutine 645 Substitute member method 366, 482 ff., 685 Supercritical buckling 658 Superposition equation 343 Superposition principle 588 Superposition theorem 112 ff., 120 Support moment 269 Suspension bridge 64 ff., 79, 181, 183, 292 Suspension bridge theory 65, 90, 115 Suspended platform 431 Sway frame 593 Sweptback wings 639 Swing bridge 431 Symbolic machine 573, 580, 598 f., 610, 620 f., 703, 706 Symmetry 701 System of classic engineering sciences 143, 153, 155, 157, 278, 598 Symbolic operations 642 System matrix 349 f., 362 System theory 142, 148 f., 151 Theory of elastic plates 77 Theory of elastic trussed frameworks 621, 684 Theory of folded plates 545 ff Theory of friction resistances 162 Theory of influence lines 366 Theory of linear-elastic truss systems 562 Theory of orthotropic plates 459 ff Theory of out-of-plane loaded structures 532 Theory of plates 527 Theory of plate and shell structures 543 f Theory of porous media 686 Theory of prestressed concrete 528 Theory of proportion 261 Theory of reinforced concrete 518 Theory of resistance 162 Theory of rigid frames 611 Theory of sandwich construction 469 Tabular calculation 394 Theory of secondary stresses 37, 109, 366, 581, Tangential stress 550 587 ff., 591, 685 Teaching of engineering 427 Theory of sets of equations 600 f T-Beam 521, 544, 565 f Theory of sets of linear equations 599, 610, 612 T-Beam section 562 Theory of shell structures 37 f., 381 Technical finality 153 Theory of spatial frameworks 475 ff Technical revolution 498, 512, 514, 522, 555 Theory of stability 596 Tectonic 699 Tekhnē 40, 158, 351, 576 f., 579 f., 695, 698, 703 Theory of statically indeterminate trussed framework 341 ff Template shop 97 Theory of statically indeterminate systems 318 Temporary bridge 491 Theory of steam engine 168 Temperature stress 661 Theory of suspension bridges 164 ff Tensile resistance 265, 267 Theory of the arch plate 567 Tensile strength 165, 172 f., 188, 261, 263, 275, Theory of the beam on elastic supports 107 f 301 Theory of the elastic line 32, 35, 298 Tensile strength test 86, 225, 233 f., 302 Theory of thin elastic plates 533 Tensile stress 199, 209, 241 Theory of trussed frameworks 294, 612 Tensile test 166, 219, 251, 252 f., 263, 265, 268, Theory of viscoelastic bodies 463, 468 270, 274 Theory of warping torsion 433, 435, 439 f Tension field theory 634 Thermal effect 82, 372 Tensor algebra 609, 611 Thermal energy 373 Tensor analysis 156, 553 f., 574, 608, 611 Thermal expansion coefficient 501 f Tensor calculation 381 Thermal load case 363 Tensor calculus 528 Thermal stress 179 Test and model 115 Thermodynamics 154, 168, 173, 308, 313 f., 672 Test beam 466, 565 Thin skin 637 Test model 638 f Thin reinforced concrete shell 326 Testing facility 97 Thin shell 327 Testing machine 423, 445 Thin-wall box beam 634 Tetmajer straight line 448 Thin-wall hollow-box beam 560 Tetrahedron 137, 493 Thin-wall hollow section 412, 428, 442 Tetrahedron framework 140 f., 480 Thin-wall open section 434 Theorem of Castigliano 382 Thin-wall structure 470 Theorem of Clapeyron 314, 682, 684 f Third boundary value problem 584 Theorem of Maxwell 382 Theorem of minimum deformation energy 360 Third prime task of thrust line theory 214, 217 Third stage of formal operations 574 Theorem of three moments 308, 313 Thought experiment 265 Theorem of ultimate load design 133 Three-cell hollow cross-section 442 Theoretical kinematics 351 Three-centred arch 189 f., 196, 238 Theoretical mechanics 662 Three-dimensional continua 659 Theory of beam grids 457 Three-dimensional displacement method 608 Theory of continuous suspension bridges 114 Three-dimensional elastic continua 666 Theory of curved elastic bars 425 f Three-dimensional lattice girder 631 f Theory of earth pressures 331, 333 Theory of engineering sciences 144 f., 148, 151 ff Three-dimensional trussed framework 614 Three-hinge system 188 Theory of elastica 272 Three-moment equation 316 Theory of elastic arches 337, 366 847 778-848_Anhang_Korr2_INDD-5_bp.indd 847 05.03.2008 15:46:42 Uhr ... in- F I G U R E - Cover of the book published to mark cluded in this The history of science, too, treated the history of theory of structures the first conference on the history of theory of structures. . .THE HISTORY OF THE THEORY OF STRUCTURES 00 1-0 19_Titelei_Korr3_INDD-5_bp.indd 05.03.2008 13:44:32 Uhr KARL-EUGEN KURRER The History of the Theory of Structures From Arch Analysis... to the origins of the discipline of theory of structures provide reasons for the history of theory of structures in a narrower sense The famous book by Timoshenko on the history of strength of