New Buckling Analysis of Rotationally Restrained Columns Using the Finite Integral Transform Method

In this paper, the finite integral transform method is employed for the first time to analytically solve the buckling problem of axially compressed columns subjected to rotationally restrained-type boundary conditions (BCs), a topic on which relevant studies remain scarce. In the present solution procedure, the complex buckling problem of compressed columns can be transformed into solving simple matrix eigenvalue problems after straightforward integral transformations, which significantly reduces the mathematical difficulty involved. Based on the proposed method, new and accurate analytical results for the effective length factor of axially compressed columns under elastic rotational constraints are obtained. All the present results show excellent agreement with those reported in the literature, with the maximum deviation being less than 0.5%, verifying the high precision and reliability of the present method. By varying the spring rotational restraint coefficient, the variation law of the column’s effective length during the transition of end constraints from elastic rotationally restrained constraints to simply supported and clamped conditions is further revealed, which provides clear quantitative guidance for engineering stability design.