Theoretical Study of Stability Criteria for X-Bracing Systems

Using a theoretical approach, stability criteria for X-bracing systems are formulated. For two different end constraints, simple closed-form relationships are presented for calculating the critical compressive load. As a design aid, curves of the effective length factor versus the ratio T/P, where T and P are tension and compression brace axial forces, respectively, are given. Criteria are formulated for the general case where the tension and compression braces may have different material and geometrical properties. Some important characteristics are revealed: the ratio T/P increases as the effective length factor k decreases; after a certain value at which the compression brace buckles in the second mode, it will remain unchanged. As the flexural rigidity, EtIt of the tension brace increases, the ratio T/P at which buckling occurs in the second mode decreases, and the effective length factor k also decreases. Therefore, it is possible for the compression brace to snap through in the first buckling mode due to a total loss of the tension brace flexural rigidity. However, when the tension brace flexural rigidity reaches a certain value, the compression brace buckles in the second mode.