Stresses in constant tapered beams with thin-walled rectangular and circular cross sections

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.

Analytical determination of the influence of geometric and material design parameters on the stress and strain fields in non-prismatic components of wind turbines

“…Many other scholars tackled the task of evaluating the shear stresses in tapered beams, e.g. Krahula in 1975 [19] and Cortinez in 1994 [20], as well as Bertolini et al [21] and Balduzzi et al [22] recently. In all cases the study regarded the derivation of a shear formula by the equilibrium of a slice of a tapered beam with symmetric cross-sections, the assumption of Navier's formula to hold, and the limitation of the study to the case of small displacements.…”

Stress recovery of laminated non-prismatic beams under layerwise traction and body forces

“…In addition to the internal forces and the bending load, N � (x) contributes to the shear stress profile of laminated beams. In homogeneous media, N ′ vanishes if the external load is generalized through the cross-section (Taglialegne 2018;Bertolini et al 2019;Bertolini and Taglialegne 2020;Vilar et al 2021a)…”

“…(Zhou et al 2016(Zhou et al , 2020b predicted the shear stress of asymmetric linearly tapered beams with box girder and rectangular crosssections, respectively. Moreover, Taglialegne (2018) and Bertolini et al (2019) derived the stress field of symmetric linearly tapered thin-walled beams. Subsequently, Bertolini and Taglialegne (2020) proposed a similar methodology to include taper in the width direction.…”

“…In general, classical beam models generalize the external load through the entire crosssection. This hypothesis, although not best representing surface forces and partial cross-sectional loads, is widely accepted in beam modeling approaches (Masjedi et al 2019;Weaver 2020a, b, 2022;Masjedi et al 2021;Doeva et al 2020aDoeva et al , b, 2021Doeva et al , 2022Balduzzi et al 2019;Bertolini et al 2019;Bertolini and Taglialegne 2020;Chockalingam et al 2020Chockalingam et al , 2021Vilar et al 2021a). Another issue not addressed in analytical laminated beam formulations is for cases where the stiffness distribution is different from the transverse and axial load distributions, which gives rise to non-classical transverse stresses.…”

“…Moreover, Taglialegne ( 2018 ) and Bertolini et al. ( 2019 ) derived the stress field of symmetric linearly tapered thin-walled beams. Subsequently, Bertolini and Taglialegne ( 2020 ) proposed a similar methodology to include taper in the width direction.…”