@article{Jacek2009CALCULATION,
title={CALCULATION OF FIRST NATURAL FREQUENCY OF STEEL COLUMNS WITH VARIABLE CROSS-SECTIONS PART I DERIVATION OF FORMULAS},
author={ Jaworski, Jacek and Boniecka, Marta and Nycz, Marcin},
journal={Acta Sci. Pol. Architectura},
abstract={An approximated method for calculations of the natural period for towers and columns (after PN-77/B-02011 standard) is evolved in the paper using the integration instead of the summation of products of concentrated masses and squares of deflections. Formulas for calculations of first natural frequency (period) for columns shaped like frustum of cone or pyramid are derived. The special case of tube columns shaped like a cone (or pyramid) when generating lines of external and internal cone are crossing the cone (or pyramid) axis in the same point is also solved. Examples of calculations and a comparison of results will be published in the second part.},
volume={8},
number={1},
pages={8},
year={2009}.
url={https://www.architectura.actapol.net/volume8/issue1/_1_.pdf}
}