Abstract
Columns of stepwise variable bending stiffness are encountered in the engineering practice quite often. Two different load cases can be distinguished: firstly, the axial force acting only at the end of the column; secondly, besides the force acting at the end, the additional force acting at the place where the section changes suddenly. Expressions for critical forces for these two cases of loading are required to correctly design such columns. Analytical formulae defining critical forces for pin-ended columns are derived and presented in the paper. Derivations were based on the Euler-Bernoulli theory of beams. The energetic criterion of Timoshenko was adopted as the buckling criterion. Both formulae were derived in the form of Rayleigh quotients using the Mathematica® system. The correctness of formulae was verified based on one the of transcendental equations derived from differential equations of stability and presented by Volmir. Comparisons to results obtained by other authors were presented, as well. The derived formulae on the critical forces can be directly used by designers in procedures leading to the column’s buckling resistance assessment. The relatively simple procedure leading to buckling resistance assessment of steel stepped columns and based on general Ayrton-Perry approach was proposed in this work. The series of experimental tests made on steel, stepped columns and numerical simulations have confirmed the correctness of the presented approach.
Highlights
IntroductionPublisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations
The presented paper provides closed formulae on critical forces acting on the twosegment stepped columns of general geometrical data and the stiffness distribution
The correctness of derived formulae was verified based on the exact analytical solution presented by Volmir [2] in the form of the transcendental equation
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. In this case when the crane girder is present, the column is loaded at the end and at the place of the sudden change of section. Buckling forces and corresponding equivalent lengths of both segments of stepped columns are required to the assessment of buckling resistance of the column This problem was considered first by Barnes and Mangelsdorf [22] and by Castiglioni [23,24]. In the present work the comparatively easy approach, leading to the buckling resistance assessment of stepped steel columns, was proposed. Numerical simulations in which material parameters obtained in performed material tests were used, have confirmed the correctness of the proposed procedure as well
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