DETERMINATION OF THE MOMENT OF INERTIA OF THE BEAM WEB STIFFNESS ELEMENT

Abstract

The subject matter of the article is the shear buckling behavior of a thin-walled beam web in an aircraft structure reinforced by longitudinal stiffeners under transverse shear loading. Particular attention is paid to the influence of the stiffener's rigidity on the critical shear stresses and the web's load-carrying capacity. The aim of the article is to develop an analytical approach for determining the required second moment of area of longitudinal stiffeners based on the conditions of global and local shear buckling of the beam web, and to provide a theoretical justification for widely used empirical design relations. The tasks to be solved are: to formulate a mechanical model of a stiffened beam web represented as an orthotropic plate with equivalent stiffness characteristics; to derive analytical expressions for critical shear stresses under global buckling conditions; to solve the inverse stability problem for determining the required stiffener second moment of area; to analyze local shear buckling of elementary web panels bounded by stiffeners; to establish a condition for simultaneous occurrence of global and local buckling; and to compare the obtained analytical results with known empirical formulas used in aerospace engineering practice. The methods used in the study are based on the classical theory of stability of thin-walled structures, in particular, the theory of shear buckling of orthotropic plates developed in fundamental NACA works, as well as analytical methods of structural mechanics and stability analysis. The following results were obtained: an analytical model describing the shear stability of a stiffened beam web was developed; closed-form expressions for determining the required stiffener second moment of area under global shear buckling conditions were derived; a relationship ensuring simultaneous satisfaction of global and local buckling criteria was established; it was shown that the obtained solutions provide a clear physical interpretation of the influence of geometric and material parameters on structural stability; and it was demonstrated that the derived analytical expressions reproduce the characteristic power-law dependence between stiffener rigidity and applied shear load observed in engineering practice. Conclusions. The developed analytical approach enables direct evaluation of the required stiffness of longitudinal stiffeners at the preliminary design stage of aircraft structures, accounting for both global and local shear buckling modes. The obtained results can be effectively used for rational structural design and optimization of thin-walled beam elements. The scientific novelty of the results obtained is as follows: an analytical solution to the inverse problem of determining the stiffener second moment of area based on global shear buckling conditions was proposed; a unified criterion for simultaneous consideration of global and local shear buckling was formulated; and a theoretical justification of empirical design dependencies widely used in aerospace engineering was provided on the basis of classical stability theory.