History of a "Paradox" for Thin-Walled Members with Variable, Open Cross-sections

This paper describes the development of research conducted in the theory of thin-walled members with variable, open cross-sections. Special attention is paid to the torsional stability of centrally compressed I-columns with some references to the closely related problem of torsional vibration. The particular contributions of the author in those fields are highlighted. He discovered that in the case of variable, bisymmetric I-sections, the critical torsional buckling loads (and, recognized even earlier in the context of the frequencies of torsional vibration) fell outside the range determined by values relevant for similar enveloping constant, minimum and maximum, cross-sections — thus becoming "paradoxical". Later investigations of different scholars concentrated more on the torsional buckling aspect alone. They confirmed that "paradox" but, until now, no convincing reasoning was produced. The author recalls the problems and issues in order to activate further discussion.