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The horizontal bracing forces of column-bracing systems derived from past studies and current design codes were considered only located at middle of columns. Actually, the horizontal braces used to reduce the out-of-plane effective column lengths are frequently designed not to locate at middle of columns. In this paper, a large number of column-bracing systems with the horizontal braces unlocated at middle of columns were modelled and analyzed using the finite element method, in which the random initial geometric imperfections of both the columns and the horizontal braces unlocated at middle of columns were well considered by the Monte Carlo method. Based on the numerical calculations, parametric analysis, and probability statistics, the probability density function of the horizontal bracing forces was found, so that the corresponding design forces of horizontal braces unlocated at middle of columns were proposed which were compared with the design mid-height horizontal bracing forces in the previous study and the relevant codes. The results indicate that the design forces of the horizontal braces located at 0.6 column height are smaller than the mid-height horizontal bracing forces in the previous study while the design forces of horizontal braces located at 0.7 column height are larger than the mid-height horizontal bracing forces in the previous study. The proposed design forces of the horizontal braces located and unlocated at middle of columns are both smaller than the mid-height horizontal bracing forces stipulated in GB50017-2017, Eurocode 3-1992, and AS4100-1998. The above conclusions provide references for the engineering applications and further related code revisions.

Design Forces of Horizontal Braces Unlocated at Middle of Columns considering Random Initial Geometric Imperfections