Stability of axially loaded tapered columns/Centriškai gniuždomų trapecinių kolonų stabilumas

Abstract

In this paper, theoretical analysis of tapered column's bearing capacity is presented. A slender axially loaded column loses stability, when it achieves critical load (1). Critical load for uniform column can be calculated using L. Euler's formula (3). But this formula is only for uniform members. When we have non-uniform member, column's moment of inertia about strong axis (Fig 3) chances according to law (4). A. N. Dinik [4] suggested a differential equation (6) for non-uniform axially loaded member. So the critical load of tapered column can be calculated as for uniform member with additional factor K using (7) formula. Factor K depends only on the moments of inertia ratio (5) of column ends. In this paper, critical load of tapered column was calculated using FE program COSMOS/M. A lot of simulation were carried out with a wide range of moments of inertia ratio. From these simulations factor K was calculated (Fig 4 and Table 1) for axially loaded pin-end column. By computer simulation it was determined that factor K for pin-end column can also be used for other types of column support. After determining critical load, column slenderness (10) can be calculated using column's smallest cross-section A₁. Tapered column must satisfy (12) condition. A couple of examples (Table 2) with various moments of inertia ratio was solved. Three calculation methods were used: the author's suggested (Fig 5 curve 1): using [1, 2] method as for uniform member with the smallest column's cross-section geometrical characteristics (Fig 5 curve 2); and using [1, 2] method as for uniform member with average column's cross-section geometrical characteristics (Fig 5 curve 3). From Fig 5 we see that calculation of tapered column using methods for uniform members with average cross-section geometrical characteristics is not safe.

Article in Lithuanian.

First Published Online: 26 Jul 2012