The stability of compression members is typically assessed through buckling curves, which include the influence of initial geometric imperfections and residual stresses. Alternatively, the capacity may be obtained more directly by carrying out either an elastic or an inelastic second order analysis using equivalent bow imperfections that account for both geometric imperfections and residual stresses. For design by second order elastic analysis, following the recommendations of EN 1993-1-1, the magnitudes of the equivalent bow imperfections can either be back-calculated for a given member to provide the same result as would be obtained from the member buckling curves or can be taken more simply as a fixed proportion of the member length. In both cases, a subsequent M–N (bending + axial) cross-section check is also required, which can be either linear elastic or linear plastic. For design by second order inelastic analysis, also referred to as design by geometrically and materially nonlinear analysis with imperfections (GMNIA) there are currently no suitable recommendations for the magnitudes of equivalent bow imperfections and, as demonstrated herein, it is not generally appropriate to use equivalent bow imperfections developed on the basis of elastic analysis. Equivalent bow imperfections suitable for use in design by second order inelastic analysis are therefore established in the present paper. The equivalent bow imperfections are calibrated against benchmark FE results, generated using geometrically and materially nonlinear analysis with geometric imperfections of L/1000 (L being the member length) and residual stresses. Based on the results obtained, an equivalent bow imperfection amplitude e₀ = αL/150 (α being the traditional imperfection factor set out in EC3), is proposed for both steel and stainless steel elements and shown to yield accurate results. The reliability of the proposed approach is assessed, using the first order reliability method set out in EN 1990, against the benchmark FE ultimate loads, where it is shown that partial safety factors of 1.0 for steel and 1.1 for stainless steel can be adopted.

受压构件的稳定性通常通过屈曲曲线评估，该曲折曲线包括初始几何缺陷和残余应力的影响。可替代地，可以通过使用考虑了几何缺陷和残余应力的等效弓形缺陷进行弹性或非弹性二阶分析来更直接地获得容量。对于通过二阶弹性分析进行设计，按照EN 1993-1-1的建议，可以反算给定构件的等效弓形缺陷的大小，以提供与从构件屈曲曲线获得的结果相同的结果。或者可以更简单地认为是构件长度的固定比例。在这两种情况下，都需要进行后续的M–N（弯曲+轴向）横截面检查，可以是线性弹性或线性塑料。对于通过二阶非弹性分析进行设计（也称为通过具有缺陷的几何和材料非线性分析（GMNIA）进行设计），目前尚无关于等效弓形缺陷大小的合适建议，并且如此处所示，通常不适合使用在弹性分析的基础上发展出等效的弓形缺陷。因此，本文确定了适用于二阶非弹性分析设计的等效弓形缺陷。根据基准有限元结果校准等效弓形缺陷，该结果是使用几何和材料非线性分析得出的 也被称为具有缺陷的几何和材料非线性分析（GMNIA）设计，目前尚无关于等效弓形缺陷的大小的合适建议，如此处所示，通常不适合使用基于缺陷的弓形缺陷开发的等效弓形缺陷弹性分析。因此，本文确定了适用于二阶非弹性分析设计的等效弓形缺陷。根据基准有限元结果校准等效弓形缺陷，该结果是使用几何和材料非线性分析得出的 也被称为带有缺陷的几何和材料非线性分析的设计（GMNIA），目前尚无关于等效弓形缺陷的大小的合适建议，如此处所示，通常不适合使用基于弓形缺陷开发的等效弓形缺陷弹性分析。因此，本文确定了适用于二阶非弹性分析设计的等效弓形缺陷。根据基准有限元结果校准等效弓形缺陷，该结果是使用几何和材料非线性分析得出的 如本文所示，一般不适合使用基于弹性分析得出的等效弓形缺陷。因此，本文确定了适用于二阶非弹性分析设计的等效弓形缺陷。根据基准有限元结果对等效弓形缺陷进行校准，这些结果是使用几何和材料非线性分析得出的，其中几何缺陷为 如本文所示，通常不适合使用基于弹性分析得出的等效弓形缺陷。因此，本文确定了适用于二阶非弹性分析设计的等效弓形缺陷。根据基准有限元结果校准等效弓形缺陷，该结果是使用几何和材料非线性分析得出的L / 1000（L为构件长度）和残余应力。根据获得的结果，对钢和不锈钢元件都提出了等效的弓形缺陷幅度e ₀  =  αL / 150（α是EC3中规定的传统缺陷因子），并显示出准确的结果。使用EN 1990中规定的一阶可靠性方法，对基准FE极限载荷进行评估，评估了该方法的可靠性，结果表明可以采用钢的部分安全系数1.0和不锈钢的部分安全系数1.1。