Stability Criteria for X-Bracing Systems

Using the energy approach, stability criteria for X‐bracing systems are formulated and verified. By employing the Raleigh‐Ritz method of stationary potential energy, simple closed‐form relationships are obtained for calculating the compression brace critical load, directly for any ratio of Q/P, where Q and P represent the tension and compression brace axial force, respectively. Moreover, as a design aid, curves are generated for the effective length factor as a function of Q/P. The criteria are formulated for the general case where the tension and compression braces are different in section properties and lengths. However, the special case of equal lengths and section properties is also addressed. The analytical expressions for the effective length factor are simple and very amenable to design application. Application of the criteria will result in considerable savings in the weight of the primary bracing members and, hence, the overall cost of the structure. This renders the criteria very attractive.