Estimation of the minimum beam length for the static, dynamic, and stability problems

Abstract

The calculation results of extended elements of structures according to the theory of beam will be correct if the condition for their length is met, which, as is known, should be much more transverse dimensions. The absence of an exact relationship between the transverse dimensions and the length of the beam is caused by the characteristics of the behavior under a load of various types and shapes of cross-sections: open, closed, thin-walled, etc. In this paper, the ratio of the length of the beam to its transverse dimensions is considered, which provides correct results during its static and dynamic loading, as well as during the loss of stability. To do this, two forms of thin-walled cross-sections are selected: circular and rectangular. The problem solution was carried out both analytically and by the finite element method. The results showed that the most stringent requirements are introduced by the theory of stability, according to which the length should be 15 or more times the largest transverse dimension.