Simplified buckling analysis of skeletal structures

A simplified approach is proposed for buckling analysis of skeletal structures, which employs a "rotational spring analogy" for the formulation of the geometric stiffness matrix. The benefit of this analogy is that it offers an intuitive framework, which is based on the common notions of linear structural analysis. Assuming that the structural deflections prior to buckling are negligible, a linear eigenvalue problem, utilising the geometric and material stiffness matrices, can be easily formulated and solved for the critical buckling loads. This can be further simplified using an assumed mode, where the rotational spring analogy is shown to provide considerable computational benefits and significant insight into the buckling of various forms of skeletal structure. In this context, the use of different assumed modes can be conceived as a process of probing the structure to establish the most likely mode for buckling and the corresponding critical load. It is also shown that the approximation inherent in the assumed mode approach together with the discrete form of the rotational spring analogy can be significantly improved through modal combinations and increasing the number of elements, respectively, where convergence to the exact buckling solution is demonstrated. Several illustrative examples are provided in the paper, which highlight the simplicity of the proposed approach, its application using a linear structural analysis tool, and its ability to shed significant light on important issues in buckling analysis of skeletal structures.