THE HISTORY OF THE THEORY OF STRUCTURES -- Foreword -- Preface -- Preface to the first, German edition -- CONTENTS -- 1 The tasks and aims of a historical study of theory of structures -- 1.1 Internal scientific tasks -- 1.2 Practical engineering tasks -- 1.3 Didactic tasks -- 1.4 Cultural tasks -- 1.5 Aims -- 1.6 An invitation to a journey through the history of theory of structures -- 2 Learning from the history of structural analysis: 11 introductory essays -- 2.1 What is structural analysis? -- 2.1.1 Preparatory period (1575 - 1825) -- 2.1.2 Discipline-formation period (1825 - 1900) -- 2.1.3 Consolidation period (1900 - 1950) -- 2.1.4 Integration period (1950 to date) -- 2.2 From the lever to the truss -- 2.2.1 Lever principle according to Archimedes -- 2.2.2 The principle of virtual displacements -- 2.2.3 The general law of work -- 2.2.4 The principle of virtual forces -- 2.2.5 The parallelogram of forces -- 2.2.6 From Newton to Lagrange -- 2.2.7 Kinematic or geometric view of statics? -- 2.2.8 Stable or unstable, determinate or indeterminate? -- 2.2.9 Syntheses in statics -- 2.3 The development of higher engineering education -- 2.3.1 The specialist and military schools of the ancien régime -- 2.3.2 Science and enlightenment -- 2.3.3 Science and education during the French Revolution (1789 - 1794) -- 2.3.4 Monge's teaching plan for the École Polytechnique -- 2.3.5 Austria, Germany and Russia in the wake of the École Polytechnique -- 2.3.6 The education of engineers in the United States -- 2.4 Insights into bridge-building and theory of structures in the 19th century -- 2.4.1 Suspension bridges -- 2.4.2 Timber bridges -- 2.4.3 Composite systems -- 2.4.4 The Göltzsch and Elster viaducts (1845 - 1851) -- 2.4.5 The Britannia Bridge (1846 - 1850) -- 2.4.6 The first Dirschau Bridge over the River Weichsel (1850 - 1857).

2.4.7 The Garabit Viaduct (1880 - 1884) -- 2.4.8 Bridge engineering theories -- 2.5 The industrialisation of steel bridge-building between 1850 and 1900 -- 2.5.1 Germany and Great Britain -- 2.5.2 France -- 2.5.3 United States of America -- 2.6 Influence lines -- 2.6.1 Railway trains and bridge-building -- 2.6.2 Evolution of the influence line concept -- 2.7 The beam on elastic supports -- 2.7.1 The Winkler bedding -- 2.7.2 The theory of the permanent way -- 2.7.3 From permanent way theory to the theory of the beam on elastic supports -- 2.8 Displacement method -- 2.8.1 Analysis of a triangular frame -- 2.8.2 Comparing the displacement method and trussed framework theory for frame-type systems -- 2.9 Second-order theory -- 2.9.1 Josef Melan's contribution -- 2.9.2 Suspension bridges become stiffer -- 2.9.3 Arch bridges become more flexible -- 2.9.4 The differential equation for laterally loaded struts and ties -- 2.9.5 The integration of second-order theory into the displacement method -- 2.9.6 Why do we need fictitious forces? -- 2.10 Ultimate load method -- 2.10.1 First approaches -- 2.10.2 Foundation of the ultimate load method -- 2.10.3 The paradox of the plastic hinge method -- 2.10.4 The acceptance of the ultimate load method -- 2.11 Structural law - Static law - Formation law -- 2.11.1 The five Platonic bodies -- 2.11.2 Beauty and law -- 3 The first fundamental engineering science disciplines: theory of structures and applied mechanics -- 3.1 What is engineering science? -- 3.1.1 First approximation -- 3.1.2 Raising the status of engineering sciences through philosophical discourse -- 3.1.3 Engineering and engineering sciences -- 3.2 Revoking the encyclopaedic in the system of classical engineering sciences: five case studies from applied mechanics and theory of structures -- 3.2.1 On the topicality of the encyclopaedic.

3.2.2 Franz Joseph Ritter von Gerstner's contribution to the mathematisation of construction theories -- 3.2.3 Weisbach's encyclopaedia of applied mechanics -- 3.2.4 Rankine's Manuals, or the harmony between theory and practice -- 3.2.5 Föppl's Vorlesungen über technische Mechanik -- 3.2.6 The Handbuch der Ingenieurwissenschaften as an encyclopaedia of classical civil engineering theory -- 4 From masonry arch to elastic arch -- 4.1 The geometrical thinking behind the theory of masonry arch bridges -- 4.1.1 The Ponte S. Trinità in Florence -- 4.1.2 Establishing the new thinking in bridge-building practice using the example of Nuremberg's Fleisch Bridge -- 4.2 From the wedge to the masonry arch - or: the addition theorem of wedge theory -- 4.2.1 Between mechanics and architecture: masonry arch theory at the Académie Royale d'Architecture de Paris (1687 - 1718) -- 4.2.2 La Hire and Bélidor -- 4.2.3 Epigones -- 4.3 From the analysis of masonry arch collapse mechanisms to voussoir rotation theory -- 4.3.1 Baldi -- 4.3.2 Fabri -- 4.3.3 La Hire -- 4.3.4 Couplet -- 4.3.5 Bridge-building - empiricism still reigns -- 4.3.6 Coulomb's voussoir rotation theory -- 4.3.7 Monasterio's Nueva Teórica -- 4.4 The line of thrust theory -- 4.4.1 Gerstner -- 4.4.2 The search for the true line of thrust -- 4.5 The breakthrough for elastic theory -- 4.5.1 The dualism of masonry arch and elastic arch theory under Navier -- 4.5.2 Two steps forwards, one back -- 4.5.3 From Poncelet to Winkler -- 4.5.4 A step back -- 4.5.5 The masonry arch is nothing, the elastic arch is everything - the triumph of elastic arch theory over masonry arch theory -- 4.6 Ultimate load theory for masonry arches -- 4.6.1 Of cracks and the true line of thrust in the masonry arch -- 4.6.2 Masonry arch failures -- 4.6.3 The maximum load principles of the ultimate load theory for masonry arches.

4.6.4 The safety of masonry arches -- 4.6.5 Analysis of a masonry arch railway bridge -- 4.7 The finite element method -- 4.8 On the epistemological status of masonry arch theories -- 4.8.1 Wedge theory -- 4.8.2 Collapse mechanism analysis and voussoir rotation theory -- 4.8.3 Line of thrust theory and elastic theory for masonry arches -- 4.8.4 Ultimate load theory for masonry arches as an object in the historical theory of structures -- 4.8.5 The finite element analysis of masonry arches -- 5 The beginnings of a theory of structures -- 5.1 What is the theory of strength of materials? -- 5.2 On the state of development of structural design and strength of materials in the Renaissance -- 5.3 Galileo's Dialogue -- 5.3.1 First day -- 5.3.2 Second day -- 5.4 Developments in the strength of materials up to 1750 -- 5.5 Civil engineering at the close of the 18th century -- 5.5.1 Franz Joseph Ritter von Gerstner -- 5.5.2 Introduction to structural engineering -- 5.5.3 Four comments on the significance of Gerstner's Einleitung in die statische Baukunst for theory of structures -- 5.6 The formation of a theory of structures: Eytelwein and Navier -- 5.6.1 Navier -- 5.6.2 Eytelwein -- 5.6.3 The analysis of the continuous beam according to Eytelwein and Navier -- 6 The discipline-formation period of theory of structures -- 6.1 Clapeyron's contribution to the formation of classical engineering sciences -- 6.1.1 Les Polytechniciens: the fascinating revolutionary élan in post-revolution France -- 6.1.2 Clapeyron and Lamé in St. Petersburg (1820 - 1831) -- 6.1.3 Clapeyron's formulation of the energy doctrine of classical engineering sciences -- 6.1.4 Bridge-building and the theorem of three moments -- 6.2 From graphical statics to graphical analysis -- 6.2.1 The founding of graphical statics by Culmann -- 6.2.2 Rankine, Maxwell, Cremona and Bow.

6.2.3 Differences between graphical statics and graphical analysis -- 6.2.4 The breakthrough for graphical analysis -- 6.3 The classical phase of theory of structures -- 6.3.1 Winkler's contribution -- 6.3.2 The beginnings of the force method -- 6.3.3 Loadbearing structure as kinematic machine -- 6.4 Theory of structures at the transition from the discipline-formation to the consolidation period -- 6.4.1 Castigliano -- 6.4.2 The foundation of classical theory of structures -- 6.4.3 The dispute about the fundamentals of classical theory of structures is resumed -- 6.4.4 The validity of Castigliano's theorems -- 6.5 Lord Rayleigh's The Theory of Sound and Kirpichev's foundation of classical theory of structures -- 6.5.1 Rayleigh coefficient and Ritz coefficient -- 6.5.2 Kirpichev's congenial adaptation -- 6.6 The Berlin school of structural theory -- 6.6.1 The notion of the scientific school -- 6.6.2 The completion of classical theory of structures by Heinrich Müller-Breslau -- 6.6.3 Classical theory of structures takes hold of engineering design -- 6.6.4 Müller-Breslau's students -- 7 From construction with iron to modern structural steelwork -- 7.1 Torsion theory in iron construction and theory of structures from 1850 to 1900 -- 7.1.1 Saint-Venant's torsion theory -- 7.1.2 The torsion problem in Weisbach's Principles -- 7.1.3 Bach's torsion tests -- 7.1.4 The adoption of torsion theory in classical theory of structures -- 7.2 Crane-building at the focus of mechanical and electrical engineering, structural steelwork and theory of structures -- 7.2.1 Rudolph Bredt - the familiar stranger -- 7.2.2 The Ludwig Stuckenholz company in Wetter a. d. Ruhr -- 7.2.3 Bredt's scientific-technical publications -- 7.2.4 The engineering industry adopts classical theory of structures -- 7.3 Torsion theory in the consolidation period of structural theory (1900 - 1950).

7.3.1 The introduction of an engineering science concept: the torsion constant.