Abstract
Dynamic buckling of an elastic column under compression at constant speed is investigated assuming the first buckling mode. Two cases are considered: (1) an imperfect naturally curved column (Hoff’s statement) and (2) a perfect column with an initial lateral deflection. The range of parameters where the maximum load supported by a column exceeds the Euler static force is determined. In this range, the maximum load is represented as a function of the compression rate, slenderness ratio, and imperfection/initial deflection. We answer the following question: “How slowly should the column be compressed in order to measure static load-bearing capacity?” This question is important for the proper setup of laboratory experiments and computer simulations of buckling. Additionally, we show that the behavior of a perfect column with an initial deflection differs significantly from the behavior of an imperfect column. In particular, for a perfect column the dependence of the maximum force on the compression rate is non-monotonic. The analytical results are supported by numerical simulations and available experimental data.
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