Bracing Design Method Of Longitudinal Column-Bracing System Under Vertical Loading

Braces are widely used to increase the stability of steel structures. The longitudinal column-bracing systems of one-story industrial building usually consist of diagonal bracings and horizontal bracing bars whose primary roles are to maintain the longitudinal stability and reduce the out-of-plane effective length of columns and transfer the longitudinal horizontal loads. In past studies on the design methods of bracings, most experimental researches and theoretical analyses were focused on a single column-brace model by the foreign scholars. In our country, the researches were mainly focused on the theoretical studies of longitudinal column-bracing system under equally top vertical loading. The analysis of mid-height horizontal bracing forces under unequally top vertical loads on the braced columns has not been seen. Moreover, the related experimental data on the longitudinal column-bracing systems have not been found in the domestic and abroad.The initial imperfections of both the columns and the horizontal bracing bars are random variables in the longitudinal column-bracing systems, and the random combination of the initial imperfections between the columns and the horizontal bracing bars can lead to the randomness of horizontal bracing bars in compression or in tension. However, in past studies, the longitudinal column-bracing systems were usually analyzed according to the worst combination of the above two initial imperfections and the horizontal bracing bars were only assumed to be in compression, so it was't in conformity with actual situations. Therefore, the various analyses on the longitudinal column-bracing systems with random distributions of the initial imperfections should be carried out and the rational design method should be seeked.A small amount of verification tests and a large number of finite element parametric analyses on the various problems of the longitudinal column-bracing systems under vertical loading were systematically conducted in this paper. In the finite element parametric analyses, the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. Aiming to the design application, the simplified formulas have been proposed based on numerical calculations, parametric analyses and probability statistics. It is very useful for code revision and design application.A series of static experimental studies have been conducted on the three kinds of test models of longitudinal column-bracing systems with different distributions of the initial imperfections. The three kinds of test models are one-story longitudinal column-bracing systems with pin-ended column bases, two-story longitudinal column-bracing systems with pin-ended column bases and two-story longitudinal column-bracing systems with fixed-ended column bases, respectively. The ultimate load carrying capacity, instability modes and randomness of horizontal bracing forces in compression or tension were obtained. Moreover, the finite element models were developed according to the tests, and results from the finite element analysis by ANSYS agreed well with the experimental data. The reliability of finite element analysis has been verified, which established well foundation for the further theoretical study.A large number of simulation analyses for one-story longitudinal column-bracing systems under vertical loading have been studied using the ANSYS finite element program, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. According to the analysis results, three kinds of instability modes of one-story longitudinal column-bracing systems have been found, triple-normal probability density function of the bracing forces for top bracing bars was proposed through probability statistics, and the design bracing forces for the top bracing bars were also obtained. Moreover, a check method based on the vertical loads analysis was supplied for the top bracing bars which are usually designed by the longitudinal horizontal loads. The results indicate that the random combination of the initial imperfections between the columns and the top bracing bars leads to the randomness of the top bracing forces in compression or intension or zero, so that the design bracing forces can be more reasonably determined.A large number of simulation analyses for two-story longitudinal column-bracing systems with pin-ended column bases have been studied using the ANSYS finite element program, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. According to the analysis results, four kinds of instability modes of two-story longitudinal column-bracing systems have been found, probability density function of the bracing forces for the mid-height horizontal bracing bars was proposed through probability statistics, and the design bracing forces for the mid-height horizontal bracing bars were also obtained. The results indicate the above design bracing forces are much smaller than that proposed by the related codes in the domestic and abroad.The design requirements of the mid-height horizontal bracing bars for two-story longitudinal column-bracing systems with fixed-ended column bases have been obtained, in which the random combination of the initial imperfections between the columns and the horizontal bracing bars was well considered by the Monte Carlo method. The comparative studies on the design requirements of the mid-height horizontal bracing bars were carried out between the systems with fixed-ended column bases and pin-ended column bases, and the reasons that the latter are higher than the former were analyzed also. This conclusion is different from the existing researches.The researches on the design requirements of the mid-height horizontal bracing bars for two-story longitudinal column-bracing systems with pin-ended column bases under unequally top vertical loads on the braced columns were carried out, the above design requirements were compared with that under equally top vertical loading, and the corresponding design recommendations were proposed also. The analysis results indicate that the instability of the longitudinal column-bracing systems is caused by the individual buckling failures of bigger vertically loaded columns, not by the all columns reaching their ultimate load carrying capacity simultaneously. The conclusion is different from the existing national code.The stiffness requirements of the diagonal bracings for one-story and two-story longitudinal column-bracing systems were obtained based on maintaining the longitudinal frame stability under the vertical loading. A check method based on the vertical loading analysis was supplied for the diagonal bracings which are usually designed by the longitudinal horizontal loads.