Abstract:
Studies the stability of an X-brace system with out-of-plane support using theoretical analysis and numerical calculation, and proposes a simple and efficient calculation method. An out-of-plane brace is connected at the intersection of the two diagonals of the X-brace. The elastic buckling of an asymmetric cross bracing system with out-of-plane struts is considered, i.e., continuous diagonals of different lengths, sections and loads. Out-of-plane struts and X-brace planes can have different angles, and the intersection point of the X-brace is not fixed in the middle of the span. The eigenvalue matrix of any linear elasticity in the middle of the double-span compression member fixed at both ends is established, and the buckling load is calculated by an iterative algorithm and the buckling of the new X-brace system is described in details. The calculation formula for the rotational stiffness of a double-span tension (compression) member fixed at both ends is deduced at any position in the span, and the influence of the rotational stiffness of different force forms on the buckling length coefficient of the X-brace is discussed based on numerical calculation, which shows that the influence of the rotational stiffness on the buckling load is negligible in actual structure. Then proportional load buckling analysis is carried out to establish the relationship between the effective length factor of the compression member and the force ratio of the compression member and the tension member. The numerical solution of the effective length factor of the asymmetric cross bracing system at any position is obtained, and its effectiveness is verified using the results in the literature. The theoretical value of buckling length coefficient is recommended to engineering practice.