Study on mid-height horizontal bracing forces considering random initial geometric imperfections

• Buckling mode of columns for different column base influences the bracing forces.
• Bracing forces increase with an increase of the slenderness ratio of the column.
• Random initial geometric imperfections lead to the randomness of bracing forces.
• The design bracing forces proposed in this paper are smaller than relevant codes.

In order to investigate the different mid-height horizontal bracing forces of column–bracing system between pin-ended column base and fixed-ended column base, a large number of column–bracing systems with pin-ended column base and fixed-ended column base have been modeled and analyzed using finite element method, in which the random combination of the initial geometric imperfections between columns and braces was well considered by the Monte Carlo method. Based on the above comparative study, the probability density function of mid-height horizontal bracing forces was found through probability statistics and the design bracing forces were also obtained. It is founded that the buckling mode of columns for pin-ended column base is three half-waves of bending while the buckling mode of columns for fixed-ended column base is two half-waves of bending, so that the ultimate load-carrying capacity and the mid-height horizontal bracing forces of column–bracing systems with pin-ended column base are higher than those of column–bracing systems with fixed-ended column base, and the relative high ultimate load-carrying capacity of the former more significantly increases its mid-height horizontal bracing forces. The results also indicate that random combination of the initial geometric imperfections between columns and braces leads to the randomness of mid-height horizontal bracing forces in compression or in tension, so that the design bracing forces can be reasonably reduced which are smaller than those stipulated in GB50017-2003, Eurocode3-1992 and AS4100-1998. Moreover, practical design formulas of mid-height horizontal bracing forces are proposed.