BUCKLING ANALYSES OF A HEAVY COLUMN CONSIDERATED IN WATER

Abstract

In 1744, the critical buckling load with the assumption of uniform cross-section without weight of column were computed by Euler. Whenever an economical solution is required, the weight of column must be considered for solution of buckling analyses. In literature, the critical buckling load and asymptotic behaviour of heavy column in condition of atmosphere have inverstigated for ten different support types. When this literature is examined, it is stated that the differential equations of for four different suppport types in condition of water is similar to condition of atmosphere. However, the differential equations of other four different suppport types in condition of water is different from to condition of atmosphere. And it is stated that the critical buckling load these different suppport types in condition of water is not calculated from condition of atmosphere. The goals of this paper are to develop self weight buckling of column at its top fixed and lower end fixed-roller supported in condition of water. This paper, presents a analytical method for calculating the critical buckling load of the heavy column.

Keywords

• Buckling in water, Bessel-Hankel functions, Dimensionless critical buckling load, Dimensionless, Critical length.

SU iÇERiSiNDE AGIRLIGI DiKKATE ALINAN BiR KOLONUN BURKULMA ANALiZi

Öz

EULER, 1744 yılında sabit enine kesitli çubukların kritik burkulma kuvvetlerini, çubuk agırlıgını ihmal ederek hesaplamıstır. Daha ekonomik çubuklar için, çubuk agırlıgının da dikkate alınması ve çözüm yapılması gerekir. Literatürde, 10 degisik mesnetleme durumu için çubuk agırlıgı da dikkate alınarak hava ortamında kritik burkulma kuvvetleri ve asimptotik burkulma kuvvetleri hesaplanmıs ve bu kuvvetlerden hareketle 4 mesnetleme durumu için sudaki kritik kuvvetlerin bulunabilecegi, diger 6 mesnetleme durumuna ait sudaki kritik burkulma kuvvetlerinin ise hava ortamındakinden hesaplanamayacagı belirtilmistir. Bu çalısmada, bugüne kadar kritik burkulma kuvvetleri hesaplanmamıs, su içerisinde, üst ucu ankastre mesnetli alt ucu ankastreli kayıcı mesnetli çubuk için çözüm verilmistir.

Anahtar Kelimeler

• Suda burkulma, Bessel-Hankel fonksiyonları, Boyutsuz kritik burkulma kuvveti, Boyutsuz çubuk uzunlugu.

References

1. Euler, L. 1744. De Curvis Elasticis, Lausanne und Genf.
2. Bernitsas, M.M. and Kokkinis, T. 1984. Asymptotic behavior of heavy column and rise stability boundaries. Trans. ASME 51, 560-565.
3. Özdamar, A. 1996. Das Knicken Schwerer Gestänge, Yayınlanmış Doktora Tezi, VWF Verlag für Wissenschaft und Forschung, Berlin.
4. Plunkett, R. 1967. Static bending stresses in catenaries and drill strings. J. Eng. Ind., Trans. ASME 89, 31-36.
5. Sugiyama, Y., Ashida, K. and Kawagoe, H. 1978. Buckling of long columns under their own weight. Bulletin of the ASME 158-5, 1228-1235.
6. Watson, G.N. 1966. A Treatise on the Theory of Bessel Functions. Cambridge University Press, Second Edition.
7. Willers, F.A. 1941. Das knicken schwerer gestänge. Z. Angew Math. Mech. 21, 43-51.