An investigation into curved beam flange efficiency in thin-walled structure

Abstract

Allowing a structural member to reach its full loading potential is likely the primary focus of structural analysis. Structural area that is ineffective is seen as ’parasitic’, and is eliminated either in the final design iteration, or in a subsequent weight-optimization exercise. Curved beam flange efficiency is the term used to refer to the outstanding flange of a beam, curved in the plane of bending, that is subjected to uniaxial bending along its principal axis. The seminal research articles outlining the phenomenon of curved beam flange efficiency were written in the 1950s; as outlined in a comprehensive literature review herein. These articles shed light on a phenomenon that, to an extent, remains enigmatic amongst structural engineers. Graphs based on seemingly complicated equations are advocated in aircraft structural directives; yet the fundamental mechanism of the true axial stress distribution in an outstanding curved beam flange remains elusive. It is the purpose of the proposed investigation to highlight some aspects of the phenomenon that, as yet, have not received adequate attention through rigorous analysis. Furthermore, relatively ’simple’ linear Finite Element analysis, validated by the aforementioned fundamental research, is shown to adequately capture the phenomenon. Finally, a method is proposed that considers the influence of the corner fillet radius at the connection of the flange to the web, a detail that has not been fully investigated in the literature. The method is outlined for a C section, but can be applied to all thin-walled sections (Z, I and T). The proposed method shows good correlation with current methods found in the literature (for no fillet radius). By fully exploiting the increased stiffness afforded by the corner fillet radius, as well as the concomitant reduction of material, the proposed method, validated by FE analysis, ’recovers’ some of the efficiency ’lost’ by the flange.