Culmann, Karl

(b. Bergzabern, Lower Palatinate, Germany, 10 July 1821; d. Zurich, Switzerland, 9 December 1881)

graphic statics.

After preliminary schooling by his father, an evangelical clergyman, Culmann enrolled at the engineering and artillery school in Metz (an uncle was professor there) to prepare for entrance to the Ecole Polytechnique in Paris. He learned of the graphical methods introduced by J. V. Poncelet and studied in Metz before a case of typhoid fever caused him to return home. Following a long convalescence, he attended the Polytechnikum at nearby Karlsruhe. On graduation in 1841 he joined the Bavarian civil service as cadet bridge engineer and was assigned to the Hof railway construction division; he continued to study under the guidance of Schnürlein, a student of Gauss’s. To prepare for a study trip abroad, he arranged in 1847 for transfer to the railway bureau in Munich, in order to extend his mathematical training and perfect his English.

Taking leave in 1849, Culmann visited England, Ireland, and the United States, returning in 1851 with detailed observations for two reports. The first dealt with the wooden bridges of the United States, the second with iron bridges in England and America. These reports present what is probably the most complete story of American bridges of the first half of the nineteenth century: American achievement lay in the largely empirical design of wooden bridges. To compare American and European designs Culmann developed new methods for the analysis of truss systems and approximate procedures for indeterminate structures, such as the Town lattice-truss and Burr archtruss bridges.

Culmann was called to Zurich in 1855 as professor of engineering sciences at the newly founded polytechnic institute (the present ETH), a post he held until his death twenty-six years later, declining an offer to move to the Munich Polytechnikum in 1868. From 1872 to 1875 he was also director of the institute.

As a teacher Culmann drew high praise for his rich experience, excellent theoretical knowledge, and sympathetic understanding; but it is on his principal work, Die graphische Statik (1866), that his fame now rests. His youthful exposure to the developments of Poncelet and other French geometers is reflected in his reports on American bridge practice, in which his independent extensions of graphical methods are already evident. It was the custom to analyze a particular design with equations; but Culmann chose another route to the solution, geometric constructions of a fundamental and widely applicable nature.

Culmann presented the graphical calculus as a symmetrical whole, a systematic introduction of graphical methods into the analysis of all kinds of structures—beams, bridges, roof trusses, arches, and retaining walls. Among other things, he introduced the general use of force and funicular polygons, the method of sections, and the diagram of internal forces based on the equilibrium conditions of successive joints.

The methods, first used by his students, were quickly assimilated by bridge and structural designers, who appreciated the time saving of the graphical methods over the current procedures involving simultaneous equations of analytical mechanics. The contents of the first edition of Die graphische Statik was thus known when it was published, and the book was eagerly accepted by a wide circle. For example, graphical analysis was applied to the Eiffel Tower by its structural designer, Maurice Koechlin, a student of Culmann’s. Further advances appeared in the first part of the second edition (1875), with more planned for the second volume, which was never published because of Culmann’s death. His work was carried forward by a Zurich colleague, W. Ritter (who is not to be confused with his contemporary A. Ritter, a prominent structural engineer who was also professor of mechanics at the Polytechnikum in Aachen). Further developments came from E. Winkler, O. Mohr, L. Cremona, and H. Müller-Breslau, among others.

In his work on beams Culmann showed how the stresses at any point can be analyzed graphically and developed a stress circle for the uniaxial shear state, a particular case of the more general, and later, Mohr circle (1882). With this he was able to draw the stress trajectories of flexural members.

On seeing sections of human bones prepared by Hermann von Meyer, professor of anatomy at the University of Zurich, Culmann noted that in some the trabeculae forming the cancellous tissue (spongiosa) followed the principal stresses on assuming beam loading of the bone, as in the head of the femur. Just how this arrangement is related to the mechanical conditions of loading is not yet clear, even though Meyer’s trajectorial theory of bone formation has been the subject of discussion since 1867.

Although modern structural analysis is no longer governed by graphical methods, Culmann’s work was fundamental to the present analytical procedures that represent complements and extensions of the older, physical approach.

BIBLIOGRAPHY

I Original Works. Culmann’s writings are “Der Bau der hölzernen Brucken in den Vereinigten Staaten von Nordamerika,” in Allgemeine Bauzeitung (Vienna), 16 (1851), 69–129; “Der Bau der eisernen Brücken in England and Amerika,” ibid., 17 (1852)163–222; “Bericht über die Untersuchung der schweizerischen Wildbäche in den Jahren 1858–1863,” in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich (1864); Die graphische Statik (Zurich, 1866; 2nd ed., pt. 1, 1875); and “Ueber das Parallelogram and über die Zusammensetzung der Kräfte,” in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich (1870).

II. Secondary Literature. On Culmann’s work see A. J. du Bois, Graphical Statics (New York, 1875); F. G. Evans, Stress and Strain in Bones (Springfield, III., 1957); H. von Meyer, “Die Architektur der Spongiosa,” in Archiv für Anatomie, Physiologie and wissenschaftliche Medizin, 47 (1867); W. Ritter, Anwendungen der graphischen Statik (Zurich, 1888); and D’Arcy W. Thompson, on Growth and Form, repr. of 2nd ed. (Cambridge, 1952), pp. 975–979, 997.

Obituaries are in Zeitschrift für Bau-und Verkehrswesen (17 Dec.1881); and Vierteljahrsschrift der Naturforschenden Gesellschaftr in Zürich, 27 (1882).

Biographical sketches are C. Matschoss, Männer der Technik (Berlin, 1925); W. Ritter, in Allgemeine deutsche Biographie, XLVII (1903); M. Rühlmann, Vorträge über Geschichte der technischen Mechanik (Berlin, 1885); Fritz Stüssi, in Neue deutsche Biographie, III (1957); S. Timoshenko, History of Strength of Materials (New York, 1953); and Viertel jahrsschrift der Naturforschenden Gesellschaft in Zürich, 41 (1896), Jubelband 1.

R. S. Hartenberg