Stresses in constant tapered beams with thin-walled rectangular and circular cross sections. (April 2019) - Bertolini, P.; Eder, M.A.; Taglialegne, L.; Valvo, P.S.
Abstract: Tapered beams are widely employed in efficient flexure dominated structures. In this paper, analytical expressions are derived for the six Cauchy stress components in untwisted, straight, thin-walled beams with rectangular and circular cross sections characterised by constant taper and subjected to three cross-section forces. These expressions pertain to homogeneous, isotropic, linear elastic materials and small strains. In fact, taper not only alters stress magnitudes and distributions but also evokes stress components, which are zero in prismatic beams. A parametric study shows that increasing taper decreases the von Mises stress based fatigue life, suggesting that step-wise prismatic approximations entail non-conservative designs. Abstract : Highlights: Stresses in thin-walled rectangular and circular beams are analytically determined. Taper alters all the six stress tensor components with respect to prismatic beams. For the same load, negative taper induces a higher shear stress than positive taper. Ignoring the taper effects can lead to non-conservative design under static and fatigue loads.