On the tallest column (Q554091)

The problem of the strongest heavy column subject to elastic instability was formulated by \textit{F. I. Niordsen} [Q. Appl. Math. 23, 47--53 (1965; Zbl 0127.16103)]. Their solution was successively questioned by \textit{S. J. Cox} and \textit{C. M. McCarthy} [SIAM J. Math. Anal. 29, No. 3, 547--554 (1998; Zbl 0913.34072); ibid. 31, No. 4, 940--940 (2000; Zbl 0957.34073)] who remarked that the existence of an optimal column cannot be granted in advance. In the present paper the author shows, with arguments of monotonicity, that the solution exists and is unique. The result is interesting, but a restrictive assumption on the quadratic relationship between the area of the cross-section and its moment of inertia excludes a wide class of technically relevant cases.