Wilhelm Fränkel

As the adopted son of Oskar Schlöhmilch (1823–1903), professor of mathematics at Dresden Polytechnic, Wilhelm Fränkel’s CV was more or less preordained: studies in civil engin- eering at the Polytechnic School in Dresden, where from 1865 he served as assistant to Prof. Johann Andreas Schubert and carried out work for Saxony State Railways. Concurrently with Winkler and Mohr, he worked on the principles of the theory of influence lines (1867). In 1870 he was offered the chair of theory of structures and bridge-building (established in 1868) and in 1871 the Polytechnic School in Dresden was raised to the status of a Polytechnic. Fränkel remained here until he died; his successors were: Georg Christoph Mehrtens (1895–1912), Willy Gehler (1913–45), Kurt Beyer (1919–52) and Gustav Bürgermeister (1952–71). It may have been Winkler’s theorem of the line of thrust in masonry arches [Winkler, 1879/1880, p. 128] that inspired Fränkel to derive (1882) – independently of Menabrea and Castigliano – the principle of Menabrea on a plane frame with n degrees of static indeterminacy and linearelastic continuum from the principle of virtual forces and furnish proof of Winkler’s theorem. He was aware that his “principle of the least work of elastic systems … would permit a consistent understanding of a whole series of structural theory problems” [Fränkel, 1882, p. 63]. Unfortunately, Fränkel’s groundwork in the dispute over the fundamentals of the theory of structures (1883–89) was not fully adopted by either Müller-Breslau or Mohr – they could have helped clarify matters. T. M. Charlton paid tribute to Fränkel’s pioneering contributions to classical structural theory [Charlton, 1982]. Fränkel invented the strain gauge named after him which was used for the experimental investigation of iron bridges; he later added the deflection gauge as well as the horizontal and vertical vibration gauges. He had thus created the instruments required to verify bridge engineering theories and classical structural theory. His chapter on moving bridges in the Handbuch der Ingenieurwissenschaften [Schäffer & Sonne, 1888/1] remained unequalled for two decades.

Main contributions to structural analysis:

Berechnung eiserner Bogenbrücken [1867]; Zur Theorie der elastischen Bogenträger [1869]; Vorträge über Schiebebühnen und Drehscheiben [1872]; Anwendung der Theorie des augenblicklichen Drehpunktes auf die Bestimmung der Formänderung von Fachwerken – Theorie des Bogenfachwerkes mit zwei Gelenken [1875]; Über die ungünstigste Einstellung eines Systems von Einzellasten auf Fachwerkträger mit Hilfe von Influenzkurven [1876]; Das Princip der kleinsten Arbeit der inneren Kräfte elastischer Systeme und seine Anwendung auf die Lösung baustatischer Aufgaben [1882] 

Source: Kurrer, Karl-Eugen The History of the Theory of Structures, Wilhelm Ernst & Sohn Verlag für Architektur und technische Wissenschaften GmbH, Berlin (Deutschland), ISBN 3-433-01838-3, 2008; p. 731