A method for the treatment of second order effects in plastically-designed steel frames

Abstract

The susceptibility of steel frames to global second order effects, also referred to as sway effects, 'P-∆' effects and global geometric nonlinearities, is traditionally assessed through the elastic buckling load amplifier αcr. For elastic analysis, EN 1993-1-1 and other international steel design standards state that second order effects may be neglected provided αcr is greater than or equal to 10. However, when plastic analysis is employed, yielding of the material degrades the stiffness of the structure, and hence a stricter requirement of αcr≥15 is prescribed in EN 1993-1-1 for second order effects to be neglected. Use of a single limit of 15 for any structural system is however considered to be overly simplistic. A more consistent and accurate approach is to determine the degree of stiffness degradation and hence the increased susceptibility to second order effects on a frame-by-frame basis. A parametric analysis to assess the stability of steel frames in the plastic regime is presented herein. A series of frames with varying geometries and load cases has been assessed. Based on the findings, a proposal for the calculation of a modified elastic buckling load factor αcr,mod, which considers the reduction in stiffness following plasticity on a frame-by-frame basis, is presented.

Stability and design of stainless steel structures – Review and outlook

“…The applicability and accuracy of the proposed method has been demonstrated through comparisons with numerical results on a series of stainless steel frames [78]. Comparisons with results from parallel work on carbon steel frames has also yielded similar findings [80]. Further work is currently underway on this topic.…”

“…However, when plastic analysis is employed, yielding of the material degrades the stiffness of the structure, and hence a stricter requirement of cr≥15 is prescribed in EN 1993-1-1 before second order effects can be neglected. Use of a single limit of 15 for any structural system is however considered to be overly simplistic, both for stainless steel and indeed carbon steel frames [80]. A more consistent and accurate approach is to determine the degree of stiffness degradation and hence the increased susceptibility to second order effects on a frame by frame basis, as proposed in [78,80], where a modified elastic buckling load factor cr,mod, which considers explicitly the reduction in frame stiffness following plasticity at a given design load, is presented.…”

“…Use of a single limit of 15 for any structural system is however considered to be overly simplistic, both for stainless steel and indeed carbon steel frames [80]. A more consistent and accurate approach is to determine the degree of stiffness degradation and hence the increased susceptibility to second order effects on a frame by frame basis, as proposed in [78,80], where a modified elastic buckling load factor cr,mod, which considers explicitly the reduction in frame stiffness following plasticity at a given design load, is presented. The method is implemented by performing a first order plastic analysis of the structure and determining the secant stiffness Ks at the design load level, relative to the initial stiffness K, as illustrated in Fig.…”

“…If cr≥10, second order effects may be neglected. Note that the 0.8 factor approximates the further loss of stiffness due to the additional plastification that occurs at the same load level when second order effects are considered, as described in [78,80]. This approach provides a consistent treatment of second order effects for both elastic and plastic analysis.…”

Design of structural stainless steel members by second order inelastic analysis with CSM strain limits

“…The nonlinear material behaviour of stainless steel results in added complexities for traditional design, and makes the opportunities offered by more advanced techniques particularly advantageous. Second order inelastic analysis enables the distribution of internal forces and moments within a structure to be accurately determined since the erosion of stiffness due to buckling and plasticity is directly modelled [2]. Advanced analysis is commonly carried out using beam element finite element models which are incapable of capturing the effects of local buckling directly since cross-section deformation is not possible.…”