Hardy Cross

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 contributions to structural analysis:

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

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. 724