Out-of-plane Inelastic Stability Of Tapered Members

Tapered members are very widely used in portal frames, and out-of-plane flexural-torsional buckling is the main instability mode of thin-walled structures, which is more complicated than the flexural bucking or the torsional buckling. Technical specification for steel structure of light-weight buildings with gabled frames.(CECS 102:2002) has a few problems for checking out-of-plane stability of tapered beam-columns, axial force and sectional properties are taken from the smaller end of tapered members, but moment and sectional properties are taken from the larger end. When tapered columns degenerate into uniform sections, formula in the "specification" (CECS 102:2002) can't degenerate into the formula in Code for design of steel structures. (GB50017-2003), leading to non-consistent among codes. Stability coefficient of beams is from formula of elastic critical moment, then must be reduced considering inelastic. However, flexural-torsional buckling of actual beams is no longer the problem of bifurcating buckling but rather the problem of limit point buckling because of initial imperfection and residual stress. In addition, there are many different methods and disputes for calculating stability coefficient of beams having unequal moments at home and abroad. Now formula of out-of-plane stability can be improved even for members of constant section. For example, when Msmall/Mlarge is equal to-1, thenβ3tx is equal to 0.3, moments are reduced significantly. Then the formula of out-of-plane stability is in control if the axial force is big, while the strength is in control if the moment is big.This paper focuses on the out-of-plane elastic-plastic stability of tapered members. Firstly, on the basis of Vlasov's thin-walled beam assumptions, the total strain energy of tapered bending members is figured out, considering both the axial force and moment, and the angleαcs between Shear center axis and centroidal axis of monosymmetrical tapered members in the whole derivation process, which is not only suitable for doubly symmetric tapered members but also for monosymmetrical tapered members. Secondly, stiffness matrices are derived from the total potential energy using finite element method, analysis of examples is taken to verify the validity of this theory by using FEA software Ansys. Besides this paper mainly studies out-of-plane inelastic stability of tapered beams and bending members which are affected on unequal moments, the maximum stress ratio between the smaller end and the larger end is equal to-1.0,-0.5,0,0.5 and 1.0. A new formula of the stability factor is obtained by the results of Ansys considering initial imperfection and two residual stress models. At the same time, a smooth curve of axial force-moment interaction and a new formula of out-of-plane stability are proposed based on the results of analysis on the inelastic stability of tapered bending members.