The Work of Wiryanto Dewobroto

Banyak orang, juga enginer (di negeri ini tentunya) yang berpendapat, bahwa hanya dengan tindakan nyata, maka mereka telah berbuat yang besar. Sehingga memandang rendah para teoritis yang hanya berkutat pada angka-angka dan tulisan.  Jika belum berkeringat, belum berpanas-panas dan belum mewujud dalam bentuk fisik maka dianggap belum berkarya.

Bagaimanapun, memang dengan karya nyata, maka duitnyapun nyata adanya. Inilah saya kira tujuan sebagian besar para calon-calon engineer yang sedang menempuh perkuliahan awal. Bahkan ada yang sekolah lagi dengan tujuan agar mendapat pekerjaan yang lebih baik lagi. Selanjutnya jika sudah dapat bekerja dan mempunyai ilmu, maka mereka pikir karena ilmu itulah yang membuat mereka ‘punya’, maka perlu dijaga ketat, sehingga hanya mereka sajalah yang ‘punya’. Konsep seperti ini yang ‘mencegah’ mereka untuk menularkan ke yang lain, apalagi mau mempublikasikan secara tertulis ke khalayak ramai.

Jadi, . . .  meskipun jika mau merunut ke belakang, banyak juga insinyur-insinyur besar di Indonesia, yaitu berdasarkan bangunan-bangunan fisik yang ditinggalkannya, seperti Borobudur, Prambanan dsb-nya, tetapi pada kenyataannya ‘apa-apa’ yang ingin dipelajari oleh seorang calon insinyur (di sini ) pada umumnya adalah berasal dari barat.

Kenapa ?

Karena itu tadi, mereka-mereka yang sukses tadi tidak suka meninggalkan tulisan tentang falsafah pengalamannya. Mereka simpan sendiri dengan maksud yang seperti saya ungkapkan di atas. Mungkin itu asumsi negatif, positipnya adalah bahwa mereka memang terbukti dapat berkarya nyata, tetapi tidak mau atau tidak mampu membuat karya tulis.

Untuk memberi bukti tersebut, maka ada baiknya kita membaca biografi insinyur-insinyur besar penentu di bidang rekayasa struktur yang namanya sering kita dengar berdasarkan formula atau metoda-metoda yang dibuatnya.

Dengan mengetahui biografi mereka, siapa tahu anda tertarik untuk menulis juga, dan tidak hanya berfokus pada materi yang sifatnya jangka pendek. Ingat yang membuat mereka dikenang, sehingga ditulis dan dibaca lagi seperti ini adalah berdasarkan publikasi karya tulisnya dan bukan karena kekayaannya.

Karya tulis yang mereka publikasikan ternyata dapat mengubah cara kita berpikir dan akhirnya dapat berpengaruh di dunia nyata (fisik).

“If you would not be forgotten, as soon as you are dead and rotten, either write things worth reading, or do things worth the writing.”
~ B. Franklin

Biografi didasarkan materi tulisan yang di copy-and-paste dari buku Karl-Eugen Kurrer – “The History of the theory of structure“.

Catatan : Sorry masih dalam bahasa Inggris.  😦

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B E T T I , E N R I C O
*21.10.1823 near Pistoia, Italy,
†11.8.1892 Pisa, Italy

After his father died when Enrico was very young, his mother brought him up alone. He later successfully completed studies in mathematics and physics at the University of Pisa. Under Mossotti’s leadership he fought in the battles of Curtatone and Montanara for Italian independence. Betti taught mathematics at Pistoia Grammar School and was invited to become professor at the University of Pisa.

He remained loyal to his Alma Mater until his death and also served as rector; he also headed the Pisa Teacher Training College. He became a member of parliament in 1862 and was a senator from 1884 onwards. For a few months in 1874 he worked as second permanent secretary in the Ministry for Public Education.

However, his talents brought forth more fruits in other fields: he was a skilled teacher and scientist and so he played a important role in mathematics and elastic theory after the Risorgimento. His reciprocal theorem formulated in 1872 proved critical for the development of elastic theory and structural theory: “If in an elastic, homogeneous body two displacement systems are in equilibrium with two groups of loads applied to the surface, then the sum of the products of the force components of the first system multiplied by the displacement components at the same point of the second system is equal to the sum of the products of the force components of the second system multiplied by the displacement components of the first system at the same point” [Betti, 1872].

This theorem, which represents a generalisation of Maxwell’s theorem [Maxwell, 1864/2], had already been incorporated by Mohr [Mohr, 1868]; in 1887 Robert Land had developed the reciprocal theorem independently from the work theorem, recognised its fundamental importance to classical structural theory and based his kinematic theory on this [Land 1887/2]. Betti’s contributions to algebra and the theory of functions were equally important.

Main contributions to the structural analysis :

• Teorema generale intorno alle deformazioni che fanno equilibrio a forze che agiscono alla superficie [1872];
• Sopra l’equazioni d’equilibrio dei corpi elastici [1873–75];
• Teoria della elasticità[1913];
• Opere matematiche [1903–13]

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C A S T I G L I A N O , A L B E R T O
*8.11.1847 Asti, Italy,
†25.10.1884 Milan, Italy

Alberto Castigliano grew up in poor circumstances.  After completing his studies at the newly founded Istituto Industriale, Sezione di Meccanica e Costruzioni in Asti, he obtained an engineering diploma from the Reale Istituto Industriale e Professionale in Turin with the financial support of wealthy citizens.

In 1873 he graduated with distinction in civil engineering from the Reale Scuola d’Applicazione degli Ingegneri, despite the difficult  circumstances of his life. In the course of a legal dispute with Luigi Federico Menabrea (1809–96), which investigated Castigliano’s diploma thesis Intorno ai sistemi elastici (on elastic systems), he wrote the extensive essay Nuova teoria intorno all’equilibrio dei sistemi elastici (new theory of equilibrium of elastic systems) in 1875, which was to become the core of his main work Théorie de l’Équilibre des Systèmes Élastiques et ses Applications published in 1879.

Following his studies, it was not long before he became head of the design office of the Italian Railway Company, where as member of the board of directors he reorganised the pension fund. Unfortunately, he was unable to complete his planned multi-volume Manuale pratico per gli ingegneri (practical manual for engineers) before his death.

Main contribution to structural analysis :

• Intorno ai sistemi elastici [1875/1];
• Intornoall’equilibrio dei sistemi elastici [1875/2];
• Nuovateoria intorno all’equilibrio dei sistemi elastici[1875/3];
• Théorie de l’Équilibre des SystèmesÉlastiques et ses Applications [1879];
• Intorno aduna proprietà dei sistemi elastici [1882];
• Theoriedes Gleichgewichtes elastischer Systeme und derenAnwendung [1886];
• The Theory of Equilibriumof Elastic Systems and its Applications [1966]

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C L A P E Y R O N , B E N O Î T- P I E R R E – E M I L E
*26.1.1799 Paris, France,
†28.1.1864 Paris, France

In 1820, after finishing their studies at the Ecole Polytechnique and the Ecole des Mines Clapeyron and his friend Gabriel Lamé left Paris to teach pure and applied mechanics, chemistry and design theory at the St. Petersburg Institute of Engineers of Ways of Communication for a period of 10 years. Together with Lamé he acted as a consulting engineer on numerous projects, including St. Isaac Cathedral and the Alexander Column in St. Petersburg as well as suspension bridges and the Schlüsselburg locks.

Following the Paris July Revolution of 1830, Clapeyron returned to France and quickly rose to be a leading railway engineer. In 1844 he was appointed professor of steam engine construction at the Ecole des Ponts et Chaussees

The theoretical consequences of his practical experience in bridge-building found their way into his famous Mémoire (1857) in the form of calculations for continuous beams. This book and another Mémoire on energy conservation in elastic theory (Clapeyron’s theorem) published one year later earned him membership of the Académie des Sciences in Paris, where he succeeded Augustin-Louis Cauchy.

Main contribution to structural analysis :

• Mémoire sur la stabilité des voûtes [1823];
• Mémoire sur la Construction des Polygones Funiculaires [1828];
• Note sur un théorème demécanique [1833];
• Mémoire sur l’équilibreintérieur des corps solides homogènes [1833];
• Calcul d’une poutre élastique reposant librementsur des apppuis inégalement espacés [1857];
• Mémoire sur le travail des forces élastiques dansun corps solide élastique déformé par l’action deforces extérieures [1858]

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C O U L O M B , C H A R L E S A U G U S T I N
*14.6.1736 Angoulême, France,
†23.8.1806 Paris, France

Charles Augustin Coulomb attended lectures at the Collège Mazarin and the Collège de France; in 1757 he became an associate member of the Société des Sciences de Montpellier, to which he contributed several articles on astronomy and mathematics. Afterwards he studied at the Ecole du Génie de Mézière, from where he graduated in 1761 with the rank of lieutenant en premier des Corps du Génie. It was while studying here that he established his lifelong friendship with his mathematics teachers Jean Charles Borda and Abbé Charles Bossut. His first activities as an officer in the engineering corps were in Brest and the French colony of Martinique (1764–72), where he was in charge of building fortifications.

Coulomb transformed his practical experiences into a book of theory which he presented to the Académie des Sciences in 1773; after favourable reviews by the academy members Borda and Bossut, his theories were published in 1776 under the title Mémoires de mathématique et de physique presentés à l’académie royale des sciences par divers savants [Coulomb, 1773/1776].

In his book, Coulomb solved Galileo’s beam problem and developed a forward-looking earth pressure and masonry arch theory. Coulomb’s 40-page Mémoire rounds off the preparatory period in structural theory quite conclusively and to some extent anticipates the theories of the coming consolidation period. However, the ideas of his Mémoire were not adopted until 40 years later. Coulomb also led the way in theories on electricity, magnetism and friction. In the meantime, Coulomb had been promoted to lieutenant-colonel, and in 1776 his proposal to restructure the Corps du Génie into a “Corps a talent” (Coulumb) was backed by the reform plans of the Turgot government.

In 1781 he became a member of the Académie des Sciences and had a decisive influence on the profile of that institution until it was abolished in August 1793. He was critical of the French Revolution: prudently, he withdrew to his small estate near Blois in 1792. Only after the downfall of the Jacobins’ “Reign of Terror” did he return to Paris and from 1795 onwards was responsible for experimental physics as an elected member of the newly founded Institut de France.

In 1801 Coulomb became president of this highly respected scientific establishment. From 1802 until his death he was general inspector of all public education and in this capacity contributed significantly to creating the French system of Lycées.

Main contribution to structural analysis :

• Essai sur une application des règles des Maximiset Minimis à quelques Problèmes de statiquerelatifs à l’Architecture [1773/1776]

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C R E M O N A , A N T O N I O   L U I G I   G A U D E N Z I O    G I U S E P P E
*7.12.1830 Pavia, Italy;
†10.6.1903 Rome, Italy

Immediately after completing his education in his home town in 1848, Cremona joined the “Free Italy Battalion” in the fight against the Austrian rulers and took part in the defence of Venice, which ended in capitulation on 24 August 1849.

In that same year he began studying civil engineering at the University of Pavia, from where he graduated with a doctor’s degree in 1853. Following various teaching posts in Pavia, Cremona and Milan, Cremona became a professor at the University of Bologna in 1860.

This was followed by a professorship in higher geometry at Milan Polytechnic (1867–73); it was during this period that he established the mathematical basis of his graphical statics, based on the Maxwell duality, which formed the practical foundation of Cremona’s graphical analysis and was very quickly adopted in the teaching of the theory of structures and engineering practice: “Cremona therefore furnished a reason for constructing dual force diagrams for the graphical analysis of certain trussed frameworks which in general terms left no stone unturned” [Scholz, 1989, p. 198].

Together with Culmann and Maxwell, Cremona represents the graphical statics enhanced by projective geometry. In 1873 Minister Sella nominated him founding rector of the newly formed Technical University in Rome per decree, where he was responsible for graphical statics until 1877. Afterwards, he was professor of mathematics at the University of Rome until his death.

He joined the Senate in 1879 and was one of its most highly respected members. The universities of Berlin, Stockholm
and Oxford (among others) awarded him honorary doctorates for his pioneering work in geometry.

Main contributions to structural analysis :

• Le figure reciproche nella statica grafica[1872];
• Opere matematiche [1914–17]

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C R O S S , H A R D Y
*10.2.1885 Nansemond County, USA,
†11.2.1959 Virginia Beach, USA

In 1902 Hardy Cross gained a Bachelor of Arts in English and in 1903 a Bachelor of Science at Hampden-Sydney  College. For the next three years he taught English and mathematics at Norfolk Academy.

At the age of just 23, he gained a Bachelor of Science in civil engineering at the Massachusetts Institute of Technology (MIT) and subsequently worked for two years in the bridge-building department of the Missouri Pacific Railroad in St. Louis. In 1911 Havard University awarded him the academic grade of Master of Civil Engineering. After that, Cross worked as assistant professor at Brown University and then, following a short period in practice, was promoted to professor of civil engineering at the University of Illinois in 1921.

From 1937 until he was granted emeritus status in 1951, he taught and performed research at Yale University and was head of the Department of Civil Engineering.

In his 10-page contribution to the Proceedings of the American Society of Civil Engineers (ASCE) in 1930, Cross solved the Gordian knot of the consolidation period of the theory of structures. His stroke of genius was to calculate statically indeterminate systems by iterative means using the simplest form of  arithmetic [Cross, 1930]. The Cross method was admirably suited to analysing systems with a high degree of static indeterminacy, as is common in the design of high-rise buildings, for example.

With one fell swoop, Cross ended the search which had characterised the application phase of structural theory – the hunt for suitable methods of calculation for solving systems with a high degree of static indeterminacy by rational means. The Cross method initiated not only an algorithmisation of structural theory, which was without precedent in the 20th century, but also raised the rationalisation of structural calculations to a new level.

It is therefore not surprising that in the wake of his work a flood of lengthy discussion articles appeared in the Transactions of the ASCE [Cross, 1932]. His ingenious iterative method provoked countless engineers – well into the innovation phase of structural theory – to describe the Cross method and develop it further. Indeed, so much has been written that it would easily fill the medium-sized private library of any academic! And the Cross method was not just confined to theory of structures; it was also quickly accepted in disciplines such as shipbuilding and aircraft design. Cross himself transferred the basic idea of his iterative method to calculations of steady-state flows in pipework – the Hardy Cross method – and there, too, achieved a phenomenal breakthrough. The honours he received are too numerous to mention.

Main contribution to structural analysis :

• Analysis of continuous frames by distributingfixed-end moments [1930];
• Analysis of continuousframes by distributing fixed-end moments[1932/1];
• Continuous Frames of ReinforcedConcrete [1932/2];
• Analysis of continuous framesby distributing fixed-end moments [1949];
• Engineers and Ivory Towers [1952];
• Arches, Continuous Frames, Columns and Conduits:Selected Papers of Hardy Cross [1963]

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E N G E S S E R , F R I E D R I C H
*12.2.1848 Weinheim, Baden,
†29.8.1931 Aachen, Germany

Friedrich Engesser studied at Karlsruhe Polytechnic from 1865 to 1869. Afterwards, he first worked on several structures for Black Forest Railways and then functioned as a central inspector for Baden State Railways in Karlsruhe.

In 1885 he succeeded Prof. Hermann Sternberg at Karlsruhe TH, where he remained for 30 years as lecturer and researcher in structural engineering and theory of structures. For example, in 1889 he worked out the difference between deformation energy Π and deformation complementary energy Π* and in doing so opened up the theory of structures for the quantitative dominance of non-linear material behaviour.

In the same year Engesser published an article explaining the mechanical cause behind the deviation of buckling trials from the Euler curve. However, it was not until 1895 – after he had concluded trials to verify the buckling theory of Considère (1889) – that he specified his modified Euler equation for the non-elastic buckling zone within the scope of a discussion with Jasiński published in a Swiss building journal, and frankly admitted he had made a mistake in 1889 [Nowak, 1981, pp. 147–148].

His contributions to the theory of secondary stresses and theory of frameworks also had a lasting effect on structural theory in the consolidation period. Together with Müller-Breslau and Mohr, Engesser forms the triple star in the firmament of classical structural theory. He contributed to the underlying theories of structural steelwork more than any other. His outstanding achievements were rewarded in many ways, including a doctorate from Braunschweig TH.

Main contribution to structural analysis :

• Über statisch unbestimmte Trägersysteme beibeliebigem Formänderungsgesetz und überden Satz von der kleinsten Ergänzungsarbeit[1889];
• Über die Knickfestigkeit gerader Stäbe[1889];
• Die Zusatzkräfte und Nebenspannungeneiserner Fachwerkbrücken [1892/1893];
• Über dieBerechnung auf Knickfestigkeit beanspruchterStäbe aus Schweiß- und Gußeisen [1893];
• ÜberKnickfragen [1895];
• Über die Knickfestigkeit vonStäben mit veränderlichem Trägheitsmoment[1909];
• Die Berechnung der Rahmenträger mitbesonderer Rücksicht auf ihre Anwendung [1913]

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G A L L A G H E R , R I C H A R D  HUGO
*17.11.1927 New York City, USA,
†30.9.1997 Tucson, Arizona, USA

Richard Hugo Gallagher was born into a Catholic family. His father was of Irish descent, but his mother had been born in Bohemia – the attributes of a true American! Following his secondary education at the Cardinal Hayes High School and military service in the US Navy, Gallagher studied structural engineering at New York University was awarded a bachelor degree in 1950. For the next five years he worked as a field engineer for the US Department of Commerce and thereafter as a design engineer in the New York offices of the Texas Corporation. During this period he studied structural engineering as an external student at New York University and upon completion was awarded a masters degree.

Gallagher worked in the Structural Systems Department of Bell Aero Systems in Buffalo from 1955 to 1967, initially as assistant chief engineer. It was here that Gallagher continued to develop the FEM Turner and others had been working on at Boeing. “The opportunities offered by the finite element method fired his imagination and led to much creative research” [Zienkiewicz et al., 1997, p. 904]. Gallagher, working with J. Padlog and P. P. Bijlaard, wrote a paper in which tetrahedron elements appear as early as 1962 [Gallagher et al., 1962] – the very first publication concerning three-dimensional elements. He completed his doctorate at Buffalo University in 1966 with a dissertation on curved (finite) elements for thin shells, and from 1967 to 1978 was professor for civil and environmental engineering at Cornell University, teaching and researching alongside the well-known structural steelwork professor George Winter (1907–82); Gallagher took over from him as chairman of the faculty of engineering in 1969.

It was at Cornell University that Gallagher was able to continue the work on stability theory and shell theory he had begun at Bell Aero Systems, extend this work considerably and apply FEM to fluid mechanics. He used his visiting professorship at the University of Tokyo in the autumn of 1973 and his research semester at University College, Swansea (UK), to prepare his main work, Finite Element Analysis Fundamentals [Gallagher, 1975], which was translated into German (1976), French (1977), Chinese (1979), Russian (1985) and Turkish (1994) as well as other languages. In historico-logical terms, this monograph can be regarded as a brilliant introduction to the diffusion phase of structural mechanics (1975 to date). Together with J. T. Oden, T. H. H. Pian, E. L. Wilson and O. C. Zienkiewcz, Gallagher visited China in 1981 in order to consolidate scientific contacts in the field of FEM (Gallagher was to return to China on a number of occasions); Shanghai Technical University awarded him an honorary doctorate in 1992 for his services to the development of scientific cooperation with China.

Gallagher served as dean of the College of Engineering at the University of Arizona from 1978 to 1984, thereafter, until 1988, he was provost and vice-president of academic issues at Worcester Polytechnic Institute, and he rounded off his academic career as president of Clarkson University in 1995. The ASME Medal (1993) and honorary membership of ASCE are just two of the many honours and awards he received.

Main contributions to structural analysis :

• The stress analysis of heated complex shapes[1962];
• A Correlation Study of Matrix Methodsof Structural Analysis [1964];
• Theory andPractice in Finite Element Structural Analysis[1973];
• Finite Element Analysis Fundamentals[1975];
• Finite Elements for Thin Shellsand Curved Members [1976];
• IntroductoryMatrix Structural Analysis [1979];
• OptimumStructural Design [1979];
• New Directionsin Optimum Structural Design [1984]

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K H A N , FA Z L U R RAHMAN
*3.4.1929 Faridpur, India (today: Bangladesh)
†27.3.1982 Jeddah, Saudi Arabia

It was 1950 when Fazlur Rahman Khan graduated as a bachelor of science from the Bengal Engineering College of the University of Dhakar as the best student of his year. Benefiting from a Fulbright scholarship, he gained a masters
degree in structural engineering and applied mechanics at the University of Illinois in 1952, and three years later was awarded a doctorate in structural engineering at the same university. He joined the Chicago-based architectural practice of Skidmore, Owings & Merill (SOM) later in 1955 and remained there for the rest of his career apart from a two-year interlude (1957–59).

He was promoted to participating partner as early as 1961, associate partner in 1966 and, finally, general partner in 1970. During those one-and-a-half decades, Khan developed innovative structural systems for high-rise buildings: framed tube, tube-in-tube system, bundled tubes and diagonalised tube (see [Sobek, 2002]; [Mufti & Bakht, 2002]).

The basic concept of the framed tube idea is a structural system consisting of a fixed-based vertical tube braced by the horizontal floor plates, which maximises the internal lever arm of the high-rise building cross crosssection.

One example of this structural system was the World Trade Center in New York, which was completed in 1973 but unfortunately totally destroyed following the all-too-well-known terrorist attack of 11 September 2001. As a result of the shear lag effect, under horizontal loading those parts of the framed tube parallel to the plane of loading behave like a giant lattice frame.

“The columns at the corners attract considerably more load than the columns in the middle of the sides, which means they therefore carry heavier loads than would be expected according to the principles of the practical bending theory” [Sobek, 2002, p. 425]. Like Eric Reissner had shown in 1941 that the shear lag effect governs the design of the thin-wall box beams of aircraft wings [Reissner, 1941], this is also the case for the framed tube, but in a totally different order of magnitude – and that is precisely the challenge of an innovative loadbearing system development. Khan first increased the efficiency of the framed tube by coupling the service core (inner tube) with the outer tube by means of the floor plates (tube-in-tube system) and increased it still further by using the multi-cell high-rise building cross-section (bundled tube).

For example, the cross-section of Sears Tower in Chicago (442 m high, completed in 1975) consists of a group of nine individual cross-sections; in structural terms, this skyscraper can be modelled as a vertical cantilever beam with a nine-cell cross-section. Khan, together with B. Graham, realised Myron Goldsmith’s design for the John Hancock Center (344 m high, completed in 1970) [Sobek, 2002, p. 430]. The prominent German structural engineer and architect Werner Sobek has acknowledged Khan’s innovations in loadbearing structures with an impressive quick look at the history of skyscrapers and has called him the “vanguard of the 2nd Chicago School” [Sobek, 2002].

Khan’s objective was to combine architecture and structural engineering. He was a conscious thinker and active citizen, and set up the Bangladesh Liberation Movement in the USA as early as 1971. He was awarded many honours, including honorary doctorates from Northwestern University (1973), Lehigh University (1980) and Zurich ETH (1980).

In an obituary of this great engineering personality written in the journal Engineering News Record it says: “The consoling facts are that his structures will stand for years, and his ideas will never die” (cited in [Sobek, 2002, p. 433]). In this sense, his daughter, Yasmin Sabina Khan, has provided us with a living memorial in the shape of her book Engineering Architecture: the vision of Fazlur R. Khan [Khan, 2004].

Main Contributions to structural analysis :

• Computer design of 100-story John HancockCenter [1966/1];
• On some special problemsof analysis and design of shear wall structures [1966/2];
• 100-story John Hancock Center inChicago – a case study of the design process [1972];
• New structural systems for tall buildings and their scale effects on cities [1974]

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M O H R , O T T O
*8.10.1835 Wesselburen, Holstein, †2.10.1918 Dresden, German Empire

During his father’s period of office as the local mayor, the young Otto met Friedrich Hebbel, who was later to become famous as an author but at that time was the 14-year-old scribe employed in his father’s office. At the age of 16 Mohr went to the Polytechnic School in Hannover.

After completing his studies he worked for Hannover State Railways and afterwards Oldenburg State Railways. Around 1860 he is supposed to have developed the method of sections for analysing a statically determinate frame (attributed to August Ritter) in working on a design for the first iron bridge with a simple triangulated frame at Lüneburg. A little later the young Mr. Mohr gained attention among his profession by publishing a paper on the consideration of displacements at the supports during the calculation of internal forces in continuous beam.

But his work din’t stop there : he introduced influence lines at the same time as Winkler in 1868 and discovered the analogy since named after him, which gave graphical statics an almighty helping hand.

He was appointed professor of structural mechanics, route planning and earthworks at Stuttgart Polytechnic in 1867. Six years later, Mohr accepted a post at Dresden Polytechnic as successor to Claus Köpcke (1831–1911) and taught graphical statics plus railway and hydraulic engineering there until 1893. After the departure of Gustav Zeuner in 1894, he took on the subjects of structural mechanics and strength of materials in conjunction with graphical statics.

Mohr gave up teaching in 1900, but continued working on the development of structural mechanics and theory of structures. His work on the fundamentals of theory of structures based on the principle of virtual forces (1874/75) meant that he – alongside the work of Maxwell [Maxwell, 1864/2] – made the greatest contribution to classical theory of structures.

Through his work, Mohr, like no other, provided impetus to the classical period of the discipline-formation period and the first half of the consolidation period of structural theory. Mohr argued with Müller- Breslau over the foundations of structural theory and later over priority issues regarding essential definitions, theorems and methods in the theory of structures. Numerous personalities from the world of science and engineering, e. g. Robert Land, Georg Christoph Mehrtens, Willy Gehler, Kurt Beyer and Gustav Bürgermeister, were influenced by the founder of the Dresden school of structural mechanics.

Hannover TH awarded him a doctorate. After lengthy deliberations, Mohr accepted the post of Working Privy Counsellor with the title “Excellency”, which he had been awarded by the Saxony government.

Main contributions to the structural analysis :

• Beitrag zur Theorie der Holz- und Eisenkonstruktionen [1868];
• Beitrag zur Theorie derBogenfachwerksträger [1874/1];
• Beitrag zurTheorie des Fachwerks [1874/2];
• Beiträge zurTheorie des Fachwerks [1875];
• Die Berechnungder Fachwerke mit starren Knotenverbindungen[1892/93];
• Abhandlungen aus dem Gebiete derTechnischen Mechanik [1906, 1914, 1928]

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M Ö R S C H , E M I L
*30.4.1872 Reutlingen, German Empire, †29.12.1950 Weil im Dorfe near Stuttgart, Federal Republic of Germany

Emil Mörsch studied civil engineering at Stuttgart TH from 1890 to 1894. Upon graduating he worked as a senior civil servant and superintendent in the Ministerial Department for Highways & Waterways, and afterwards was employed in the bridge unit of Württemberg State Railways.

He joined the Wayss & Freytag company in Neustadt, Palatinate, in early 1901 and it was here, commissioned by the company, that he published the first edition of his book Der Betoneisenbau. Seine Anwendung und Theorie, which later underwent numerous reprints (substantially enlarged) under the title of Der Eisenbeton. Seine Theorie und Anwendung.

This book set standards in reinforced concrete writing during the consolidation period of structural theory. Its theory based on practical trials made it the standard work of reference in reinforced concrete construction for more than half a century.

In 1904 Mörsch was appointed professor of theory of structures, bridge-building and reinforced concrete construction at Zurich ETH. However, four years later he returned to the board of Wayss & Freytag AG.

From 1916 onwards, Mörsch worked as professor of theory of structures, reinforced concrete construction and masonry arch bridges at Stuttgart TH. He adhered rigorously to elastic theory for designing reinforced concrete components right up until his death. Among his numerous honours are honorary membership of the Concrete Institute (today: Institutution of Structural  Engineers) (1913) and honorary doctorates from Stuttgart TH (1912) and Zurich ETH (1929).

Main contributions to the structural analysis :

• Der Betoneisenbau. Seine Anwendung und Theorie [1902];
• Berechnung von eingespanntenGewölben [1906];
• Der Eisenbetonbau. Seine Theorie und Anwendung [1920]

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M Ü L L E R – B R E S L A U , H E I N R I C H
*13.5.1851 Breslau, Prussia, †23.4.1925 Berlin- Grunewald, Germany

Following service in the Franco-Prussian War of 1870–71, the young Müller, who a few years later was to change his name to Müller-Breslau, left the place of his birth to study at the Berlin Building Academy. However, the birth of a son in December 1872, who was also christened Heinrich (1872–1962), forced him to start earning money.

He tutored his fellow students at the Building Academy in theory of structures in readiness for the dreaded state examination set by Schwedler, although he himself did not sit the examination. Müller-Breslau, however, turned duty into a virtue by publishing his theory of structures notes as a book in 1875 and setting himself up as an independent civil engineer.

In October 1883 he was appointed assistant and lecturer at Hannover TH and in April 1885 professor of civil engineering at the same establishment before succeeding Emil Winkler in the chair of theory of structures, building and bridge design at Berlin TH in October 1888. Taking the theorems of Castigliano and Maxwell’s frame theory as his starting point, Müller-Breslau worked out a consistent theory of statically indeterminate frames between 1883 and 1888 which, just a few years later, officially became the force method. Müller-Breslau’s completion of classical theory of structures brought to a close the discipline-formation period of structural theory.

During the 1880s, the dispute between Mohr and Müller-Breslau over the fundamentals of theory of structures led to the formation of the Dresden school of applied mechanics and the Berlin school of structural theory, which also gained international recognition.

Müller-Breslau’s appointment as a full member of the Prussian Academy of Sciences in 1901 demonstrates the high status accorded to theory of structures and iron bridge-building – indeed engineering sciences on the whole – by Imperial Germany.

Main contributions to the structural analysis :

• Die neueren Methoden der Festigkeitslehreund der Statik der Baukonstruktionen [1886,1893, 1904, 1913];
• Die Graphische Statik derBaukonstruktionen [1887, 1903, 1892, 1908]

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NAV I E R , C L A U D E – L O U I S – M A R I E – H E N R I
*10.2.1785 Dijon, France,
†21.8.1836 Paris, France

After losing his father – a lawyer in Dijon – at the age of just 14, the young Navier was cared for by his uncle and his wife, Emil and Marie Gauthey. Emil Gauthey taught part-time at the Ecole des Ponts et Chausees and in 1791 was appointed general inspector of the Bridges & Highways Corps. Navier’s uncle therefore became his role model.

He studied at the Ecole Polytechnique and Ecole des Ponts et Chaussess from 1802 to 1806 and afterwards, in addition to practical employment in bridge-building, dedicated himself to preparing a new edition of Gauthey’s Traité des ponts (1813) and Bélidor’s engineering manuals [Bélidor, 1813], [Bélidor, 1819]. In 1819 he was appointed professeur suppleant at the Ecole Des Ponts et Chayssees, which resulted in his Leçons [Navier, 1820].

During the early 1820s, Navier established the principles of elastic theory together with Cauchy and Lamé. In May 1821 Navier submitted a paper to the Académie des Sciences in which he derived the basic equations of elastic theory (to be named after him and Lamé) from the discontinuum (molecular) hypothesis; an extract from this paper was published in 1823 [Navier, 1823/3], but publication of the complete work had to wait until 1827 [Navier, 1827]. The year 1828 was marked by a dispute between Navier and Denis Poisson (1781–1840) in the journal Annales de Chimie et de Physique concerning the principles of elastic theory, which, however, did not supply any clarification because both based their ideas on the molecular hypothesis.

Navier was commissioned by the government to travel to England and Scotland in order to find out about the construction of chain suspension bridges; his findings were published in his famous Rapport, which contained the first theory of suspension bridges [Navier, 1823/1].

Although this publication earned him membership of the Académie in 1824, its implementation in practice resulted in numerous difficulties for Navier in connection with his failed Pont des Invalides suspension bridge project [Stüssi, 1940, p. 204]. At the same time, the 1820s can be seen as his most creative years.

His Résumé des Leçons [Navier, 1826] made Navier the founder of theory of structures; this work was to challenge great minds in the establishment phase of structural theory – like Saint-Venant, who obtained a copy of the third edition and improved on it by adding a grandiose historicocritical commentary [Navier, 1864]. In Germany, Moritz Rühlmann in particular is credited with establishing Navier’s theory of structures [Navier, 1851/1878]. Navier became Cauchy’s successor at the chair of analysis and mechanics at the Ecole Polytechnique, Chevalier de la Légion d’Honneur and section inspector of the Bridges & Highways Corps – all in 1831.

In sociological terms, Navier – like Clapeyron and other prominent scientists and engineers – was committed to the ideas of Saint-Simon and his followers. Therefore, Navier nominated Auguste Comte as his assistant at the Ecole Poltytechnique and played an active part in events in Raucourt de Charleville’s Institut de la Morale Universelle [McKeon, 1981, p. 2]. In this way the classical engineering sciences established in France at that time – in the first place theory of structures and applied mechanics – experienced an implicit sociological significance on which the, as it were, natural positivism of the engineering scientist dedicated to the “scientific paradigms” [Ropohl, 1999, pp. 20–23] could draw sustenance.

Main contributions to structural analysis :

• Leçons données à l’École Royale des Ponts etChaussées sur l’Application de la Mécanique[1820];
• Rapport et Mémoire sur les Pontssuspendus [1823/1];
• Extrait des recherches sur laflexion des planes élastiques [1823/2];
• Sur les loisde l’équilibre et du mouvement des corps solidesélastiques [1823/3];
• Résumé des Leçons donnéesà l’École Royale des Ponts et Chaussées surl’Application de la Mécanique à l’Etablissementdes Constructions et des Machines. 1er partie:Leçons sur la résistance des materiaux et surl’établissement des constructions en terre, enmaçonnerie et en charpente [1826];
• Mémoire surles lois de l’équilibre et du mouvement des corps solides élastiques [1827];
• Résumé des Leçonsdonnées à l’École des Ponts et Chaussées surl’Application de la Mécanique à l’Etablissementdes Constructions et des Machines. 2. Aufl.,
• Vol. 1: Leçons sur la résistance des materiaux et sur l’établissement des constructions en terre, enmaçonnerie et en charpente, revues et corrigées.
• Vol. 2: Leçons sur le mouvement et la résistancedes fluides, la conduite et la distribution des eaux.
• Vol. 3: Leçons sur l’établissement des machines[1833/1836];
• Mechanik der Baukunst (Ingenieur-Mechanik) oder Anwendung der Mechanik aufdas Gleichgewicht von Bau-Constructionen[1833/1878];
• Résumé des leçons données àl‘École des Ponts et Chaussées sur l‘applicationde la mécanique à l‘établissement des constructionset des machines, avec des Notes et desAppendices par M. Barré de Saint-Venant[1864]

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S A I N T- V E N A N T, A D H É   M A R J E A N  C L A U D E   B A R R É D E
*23.8.1797 Villiers-en-Bière, Seine et-Marne, France,
†6.1.1886 St.-Ouen, Loir-et-Cher, France

Napoleon lost the battle of Leipzig in 1813 and Paris faced its downfall. It was in this year that Saint-Venant started studying at the Ecole Poly technique and all the students were mobilised to help defend Paris. The 17-year-old Saint-Venant refused to take part, saying: “My conscience forbids me to fight for a usurper” [Benvenuto, 1997, p. 4]. The young conscientious objector was forced to quit the Ecole Polytechnique and  work as an assistant in the Service des Poudres et Salpêtres (gun powder factories). It was not until 1823 that the government permitted him to resume his studies at the Ecole des Ponts et Chaussées, which he completed in 1825. He worked for the Service des Ponts et Chaussées until 1848 and later as Professeur du génie rurale at the Agricultural Institute in Versailles, where he was involved with typical civil engineering duties. Showing a high awareness of social responsibility, Saint-Venant committed himself to improving the miserable living conditions in the countryside through the targeted application and further development of hydraulic engineering for agriculture (land improvement, irrigation and rational use of ponds).

In 1842 the authority discharged him from his duties and until 1848 he had to make himself available to the authority but on a reduced salary and without any responsibilities. It was during this period that Saint-Venant made his main contributions to the further evolution of structural mechanics [Saint- Venant, 1844], in particular torsion theory [Saint-Venant, 1847].

As the social issue was dramatically revealed in the Paris Revolution of 1848 and the ruling powers struck back with the military, Saint-Venant took sides: a military solution would not improve the social injustices, which mainly affected the unemployed. More charity would be much better for improving the working and living conditions of the lower classes. A short time later a nephew of Napoleon would use the lower classes to set himself up in power and then declare himself Emperor Napoleon III. On the whole, Saint-Venant’s remarks were based on the ideology of religiously motivated socialism, which fought to improve the living conditions of rural populations who had been made “superfluous” by the Industrial Revolution [Benvenuto, 1997, pp. 6–7].

In 1852 Saint-Venant was promoted to Ingénieur en chef and in 1868 was elected Poncelet’s successor in the Mechanics Section of the Académie des Sciences. During the 1850s and 1860s, Saint-  Venant formulated the semi-inverse method [Saint-Venant, 1855] within the scope of his torsion theory and expanded the practical bending theory of Navier [Saint-Venant, 1856].

He published Navier’s Résumé des leçons in a third edition with a comprehensive historico-critical commentary [Navier, 1864]. In his presentation to the Paris Société Philomathique on 28 July 1860, Saint-Venant formulated the compatibility conditions of elastic theory for the first time [Saint-Venant, 1860] and hence completed their set of equations: equilibrium condtions,  material equations, kinematic relationships and compatibility conditions.

Three years before his death, he published Theorie der Elasticität fester Körper [Saint-Venant, 1862] together with Flamant, Clebsch, which contained an extensive appendix [Clebsch, 1883]. Also pioneering are Saint-Venant’s contributions to the theory of viscous fluids, structural dynamics, plastic theory and vector calculus. His work on structural mechanics did not become evident until the structural theory of the consolidation period.

Main contribution to structural analysis :

• Mémoire sur les pressions qui se développent àl’intérieur des corps solides lorsque les déplacementsde leurs points, sans altérer l’élasticité, nepeuvent cependant pas être considérés commetrès petits [1844/1];
• Mémoire sur l’équilibre descorps solides, dans les limites de leur élasticité, et sur les conditions de leur  résistance, quand les déplacements éprouvés par leurs points ne sontpas très-petits [1844/2];
• Note sur l’état d’équilibred’une verge élastique à double courbure lorsqueles déplacements éprouvés par ses points, parsuite l’action des forces qui la sollicitent, ne sontpas très-petits [1844/3];
• Deuxième note: Surl’état d’équilibre d’une verge élastique à doublecourbure lorsque les déplacements éprouvés par ses points, par suite l’action des forces quila sollicitent, ne sont pas très-petits [1844/4];
• Mémoire sur l’équilibre des corps solides, dans leslimites de leur élasticité, et sur les conditions deleur résistance, quand les déplacements éprouvéspar leurs points ne sont pas très-petits [1847/1];
• Mémoire sur la torsion des prismes et sur laforme affectée par leurs sections transversalesprimitivement planes [1847/2];
• Suite au Mémoiresur la torsion des prismes [1847/3];
• Mémoire surla Torsion des Prismes, avec des considérations sur leur flexion, ainsi que sur l’équilibre intérieurdes solides élastiques en général, et des formulespratiques pour le calcul de leur résistance à diversefforts s’exerçant simultanément [1855];
• Mémoiresur la flexion des prismes, sur les glissementstransversaux et longitudinaux qui l’accompagnentlorqu’elle ne s’opère pas uniformément ou en arcde cercle, et sur la forme courbe affectée alorspar leurs sections transversales primitivementplanes [1856];
• Sur les conditions pour que six fonctions des coordonées x, y, z des points d’uncorps élastiques représentent des composantesde pression s’exercant sur trois plans rectangulairesà l’intérieur de ce corps, par suite de petitschangements de distance de ses parties [1860];
• Résumé des leçons données à l‘École des Pontset Chaussées sur l‘application de la mécanique àl‘établissement des constructions et des machines,avec des Notes et des Appendices par M. Barréde Saint-Venant [1864];
• Théorie de l’élasticitédes corps solides de Clebsch. Traduite par M.M. Barré de Saint-Venant et Flamant, avec des Notes étendues de M. de Saint-Venant [1883].

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TA K A B E YA , F U K U H E I
*9.9.1893 Okazaki near Nagoya, Japan,
†24.4.1975 Kamakura, Japan

After completing his education at the 8th state grammar school in Nagoya, Fukuhei Takabeya studied at the Imperial Kyushu University in Fukuoka (1916–19), where he afterwards served as a lecturer until 1921. He gained his doctorate at the Imperial Kyushu University in 1922 with the dissertation On the calculation of a beam encastré at both ends taking special account of the axial force.

Over the years 1921 to 1925 he was an associate professor at the Imperial Kyushu University and in May 1925 he was appointed professor at the Imperial Hokkaido University in Sapporo, but returned to the Imperial Kyushu University in 1947. He was professor at the Japanese Defence Academy from 1954 to 1966 and afterwards worked at the University of Tokai until 1972.

He became an honorary member of the Japanese Society of Civil Engineers (JSCE) in 1963, and honorary professor of the Japanese Defence Academy in 1966. Takabeya developed the iteration methods of Cross and Kani further to form a highly effective computational algorithm at the transition between the invention and innovation phases of structural theory [Takabeya, 1965 & 1967], which was especially useful for analysing systems with a high degree of static indeterminacy in high-rise buildings.

Main contributions to structural analysis :

• On the calculation of a beam encastré at bothends taking special account of the axial force[1924];
• Frame tables [1930/1];
• On the calculationof stresses in plane, encastré flat metal sheets[1930/2];
• Multistorey frames [1965 & 1967]

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T E T M A J E R , L U D W I G  V O N
*14.7.1850 Krompach, Austrian Empire,
†31.1.1905 Vienna, Austria-Hungary

Born in Hungary, the son of the director of the Krompach-Hernader ironworks, Tetmajer studied at Zurich Polytechnic (Zurich ETH) from 1868 to 1872 and then worked for the Swiss Railways Company.

He had already written his habilitation thesis by 1873 and went on to assist Culmann and teach his method of graphical statics. In the late 1870s he turned to materials testing, which at that time was still in its infancy.

Upon Culmann’s death he was appointed professor of theory structures and technology of building materials at Zurich ETH. At the same time he also took charge of the Swiss Building Materials Testing Institute. Thus began the systematic establishment of materials testing in Switzerland, which very soon enjoyed a good international reputation.

In the early years of his professorship he formulated the forwardthinking hypothesis that the mechanical material quality is characterised quantitatively by the internal work; the energy doctrine becoming established in the classical phase of structural theory thus appears in materials testing as well.

Tetmajer published two reports (1883/84) on buckling tests carried out on timber members where for the first time the buckling load was presented as a function of the slenderness of the member and the beginnings of the Tetmajer Line (as it was later called) can be seen [Nowak, 1981, pp. 112–113].

His numerous buckling tests and buckling theory deliberations were brought together analytically in 1890 in the form of an empirical formula (Tetmajer Line) for all the materials he had investigated.

In 1895, following the death of Johann Bauschinger, Tetmajer developed the Bauschinger Conferences on materials testing into the Internationaler Verband für die Materialprüfungen der Technik (now known as the New International Association for the Testing of Materials), and became its first president.

He taught and carried out research at Vienna TH from 1901 onwards, and also served as rector there. He unfortunately did not live to see the founding of a central laboratory for technical materials testing in Austria [Rossmanith, 1990, p. 530]; he died while giving a lecture.

The main contribution to the structural analysis :

• Methoden und Resultate der Prüfung derschweizerischen Bauhölzer [1884];
• Die angewandte Elasticitäts- und Festigkeitslehre[1889];
• Methoden und Resultate der Prüfung derFestigkeitsverhältnisse des Eisens und andererMetalle [1890];
• Die Gesetze der Knickfestigkeitder technisch wichtigsten Baustoffe [1896];
• Die Gesetze der Knickungs- und der zusammengesetztenDruckfestigkeit der technisch wichtigsten Baustoffe [1903];
• Die angewandteElastizitäts- und Festigkeitslehre [1904]

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T I M O S H E N K O , S T E PA N P R O K O F I E V I C H
*22.12.1878 Shpotovka (Poltava), Ukraine, Russia,
†29.05.1972 Wuppertal, Federal Republic of Germany

Timoshenko finished his secondary education at Romenski School in 1896 and five years later he had completed his studies at the Institute of Engineers of Ways of Communication in St. Petersburg; he taught here and at the Petersburg Polytechnic Institute from 1902 onwards. Krylov’s method of analysing engineering problems mathematically using differential equations was to have a considerable influence on Timoshenko’s scientific career.

He was a professor at the Faculty of Civil Engineering at the Polytechnic Institute in Kiev from 1906 to 1911, serving as dean there from 1909. He was dismissed in February 1911 in connection with the dispute between the universities and the tsarist government. But in that same year he was awarded the Zhuravsky Gold Medal of the St. Petersburg Polytechnic Institute for his treatise On the stability of elastic systems. It was at this latter institute that he served as professor of theoretical mechanics from 1913 to 1917 in the place of A. N. Krylov.

According to his former friend A. F. Joffe, Timoshenko joined the group around Maxim Gorki in the years leading up to the revolution and “was probably the most left-wing of the Russian professors” [Joffe, 1967, p. 106]. In 1918  Timoshenko became a professor of the Polytechnic Institute in Kiev as well as director and founder of the Mechanics Research Institute at the reorganised Ukraine Academy of Sciences.

Following an interlude as professor in Zagreb (1921–22), Timoshenko became involved in a wide range of activities in the USA, first at the Westinghouse company, then as a professor at Michigan University (1928–35) and afterwards at Stanford University. He influenced applied mechanics in the 20th century like no other and that had a decisive knock-on effect for theory of structures. For example, in 1921 he published his theory of the shear-flexible  beam, which was later named after him (Timoshenko beam). The American Society of Mechanical Engineers was founded in 1957 and Timoshenko was awarded the society’s first gold medal. Following a leg injury in 1964, he moved to Wuppertal, Federal Republic of Germany, to be with his daughter. He undertook extensive travels in the USSR in 1958 and 1967.

Main contribution to structural analysis :

• On the question of the strength of rails[1915/2001];
• On the correction for shear of thedifferential equation for transverse vibrationof prismatic bars [1921];
• History of strength ofmaterials. With a brief account of the historyof theory of elasticity and theory of structures[1953/1];
• The collected papers [1953/2];
• Ustoichivost’ sterzhnei, plastin i obolochek:Izbrannye raboty (stability of bars, plates andshells: collected works) [1971];
• Prochnost ikolebaniya elementov konstruktsii (strengthand vibrations of construction elements) [1975/1];
• Staticheskie i dinamicheskiezadachi teorii uprugosti (static and dynamicproblems of elastic theory) [1975/2]