A closed-form formula for the critical buckling load of a bar with one end fixed and the other pinned
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Anastasselou, Eleni
Ioakimidis, Nikolaos
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Abstract
The classical problem of elastic buckling of a bar with one end fixed and the other pinned is reconsidered and a closed-form formula for the critical buckling load is derived. This is achieved through the closed-form solution (in terms of two regular integrals) of the transcendental equation tan u = u, to which this problem is reduced. The method of solution of this equation is too simple and based on a generalized form of the Cauchy theorem in complex analysis; yet the sought root of this equation does not contain complex quantities. Finally, numerical results verifying the validity of the derived formula are presented.
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Keywords
Bars, Buckling, Critical buckling load, Roots, Zeros, Closed-form formulae, Closed-form solutions, Transcendental equations, Cauchy Theorem, Complex analysis