Geometrically non-linear analysis with stiffness reduction for the stability design of stainless steel structures: Application to members and planar frames

This paper focuses on the development of beam-column flexural stiffness reduction factor (tau(MN)) applicable to the in-plane stability design of stainless steel beam-columns and frames with compact cold-formed square and rectangular hollow sections. The proposed tau(MN) accounts for the deleterious influence of material non-linearity, residual stresses and member out-of-straightness. The use of a Geometrically Non-linear Analysis (GNA) with the proposed tau(MN) eliminates the need for member buckling strength checks and thus, only cross-sectional strength checks are required. The proposed approach, aligned to AISC standards, is aimed at facilitating greater and more efficient use of stainless steel. Two types of tau(MN) are proposed: analytical and approximate. The analytical tau(MN) presumes knowing the maximum internal second order moment (M-r2) within a member. It is developed by means of extending the formulations for evaluating the elastic second order effects to the inelastic range. The accuracy of the analytical tau(MN) is verified for beam-columns and sub-assemblages. Since in practical design M-r2 is not known in advance, an approximate expression of tau(MN), which is more likely to be used relative to the analytical tau(MN) , is proposed by fitting variables to the analytically determined (MN). The accuracy of the approximate tau(MN) is verified for frames with different geometrical and loading configurations. Furthermore, the proposed approach is compared against the Direct Analysis Method (DM). Results show that, compared to the DM, GNA coupled with the approximate tau(MN) provides improved estimations, since the proposed tau(MN) can more accurately capture stiffness reduction resulted from material non-linearity and well capture additional second order effects due to material nonlinearity.