FEM STABILITY ANALYSIS OF TAPERED BEAM‐COLUMNS

This paper deals with a theoretical and a numerical analysis of tapered beam‐columns subjected to a bending moment and an axial force. A standard FEM code COSMOS/M has been used for a numerical estimation of a critical load multiplier. It has been assumed that the critical force of an axially loaded tapered column could be calculated in an analogous way as for uniform member just with an additional correction factor αn. Similarly, a critical bending moment of the tapered column subjected to a pure bending could be determined by using a correction factor αm. A large number of simulations carried out within a wide range of the ratios of second moments of area allowed to determine the proper values of theses two factors. For practical engineers, solution of such kind of problems can be easier when an equivalent cross‐sectional height htr is used.

STABILITY OF AXIALLY LOADED TAPERED COLUMNS/CENTRIŠKAI GNIUŽDOMŲ TRAPECINIŲ KOLONŲ STABILUMAS

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 Kdepends 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 A 1. 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.

STRAIN-STRESS EXPERIMENTAL BEHAVIOUR OF TAPERED COLUMNS IN SINGLE-SPAN FRAMES/TRAPECINIŲ KOLONŲ VIENANAVIUOSE RĖMUOSE DEFORMACIJŲ-ĮTEMPIŲ BŪVIS

Two single-span frame tests were carried out. The width of frame is 6m, column's height 4.17m. Frame supports are pinned. Connection between column and beam is rigid. Beam of the frame was loaded with two vertical and one horizontal loads. The stability of tappered columns was analysed in frame plane and in perpendicular plane, according to [1] and [2] methods. All deflections were calculated taking into account support movements. During the first frame test R1-1 the tapered column collapsed at the load 2V=400kN and H=200 kN (vertical and horizontal loads). During the second test R1-2 the tapered column collapsed at the load 2V=390 kN and H=175 kN. In both tests columns collapsed in lateral-torsional buckling way. Because the column's web is very thin at the load 2V=300 kN and H=150 kN the column's web achieved local buckling. But the column was still carrying the load. During both tests at the load 2V=300 kN and H=150 kN the column began to twist in the middle of its height about the longitudinal axis and to bend about the weak axis. In test R1-1, the vertical experimental deflection (in point 6, see Fig 1 a) is about 17.5% smaller than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 11.6% smaller than the theoretical one. In test R1-2, vertical experimental deflection (in point 6, see Fig 1 a) is about 21.1% bigger than the theoretical one. The horizontal experimental deflection (in point, see Fig 1 a) is about 29.6% smaller than the theoretical one. In test R1-1, an experimental compression stresses in section A-A (see Fig 2) are about 11.2% smaller than the theoretical one. Experimental tension stresses in section A-A are about 8.65% smaller than the theoretical one. In test R1-2, an experimental compression stresses in section A-A is about 0.43% bigger than the theoretical one. An experimental tension strain in section A-A is about 1.73% smaller than the theoretical one.