Complete generalization of the Ayrton-Perry formula for beam-column buckling problems

The Ayrton-Perry (or Perry-Robertson) formula based stability resistance model (APF) is very popular in steel structural design standards. Although the original version of the model is more than 100 years old, it is still frequently used and continuously researched due to its simplicity and adaptability. The original and most widely accepted version of the APF is valid only for the flexural buckling of compression members yielding the basic formulation of the column buckling curves of several structural design codes. Recently there were more successful attempts for the extension of the APF type resistance model for other buckling modes such as torsional buckling or lateral-torsional buckling. The paper continues this research by deriving a complete closed-form universal APF type solution for steel beam-column stability problems. Rigorous mathematical solution is given for the so-called “fundamental case” which is defined by a simply supported prismatic beam-column with arbitrary cross-section subjected to uniform compression and biaxial bending. The exact interpretation and the universal form of the member slenderness, imperfection and reduction factors are presented for all possible buckling cases. The results of the paper can widen significantly the field of applicability of APF based design methods providing a theoretically consistent physical model for the beam-column stability problems.