State-based buckling analysis of beam-like structures

Beam, column, plate, and any other structure, under full or partial compressive loading, are prone to failure by the buckling phenomenon. At the instant of failure, the structure may be in unpredictable elastic, elastic–plastic, full plastic, cracked, or other forms of deterioration state. Therefore, in spite of so much study, there is no definite solution to the problem. In this paper a unified, simple, and exact theory is proposed where buckling is considered as the change of state of structure between intact and collapsed states, and then the buckling capacity is innovatively expressed via states and phenomena functions, which are explicitly defined as functions of state variable. The state variable is determined by calibration of the structure slenderness ratio. The efficacy of the work is verified via concise mathematical logics, and comparison of the results with those of the others via seven examples.