Probabilistic modelling of residual stress in advanced analysis of steel structures

• Residual stress is modeled as by applying a scale factor to a common distribution.
• Statistical information of residual stress is obtained from the literature.
• Error minimization is used to determine the scale factors.
• The effects of different residual stress patterns on frame ultimate strength are examined.
• The proposed method is demonstrated by a number of case studies.

This paper outlines a method for the probabilistic modelling of residual stress in the advanced analysis of steel structures. An extensive survey of literature on a large number of experimental measurements of residual stress in hot-rolled I-sections is presented. An error minimization is then performed to obtain appropriate scale factors to apply to common residual stress patterns to obtain the best agreement with available experimental data. The statistical distributions of the scale factors are derived. Frames with deterministic and random residual stresses are then analysed by advanced geometric and material nonlinear analysis using the proposed scale factors to determine the influence of residual stress and its different patterns on the ultimate strength and reliability of steel frames. It is shown that the strength of steel frames comprising columns with a range of slenderness values is generally much less influenced by residual stress than individual columns.