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.

[1]  Recovery of Stresses in a Beam from those in a Cone , 1998 .

[2]  J. L. Krahula.  Shear formula for beams of variable cross section , 1975 .

[3]  E. H. Atkin.  Tapered Beams: Suggested Solutions for Some Typical Aircraft Cases , 1938 .

[4]  J. Michell.  The Stress in an Æolotrophic Elastic Solid with an Infinite Plane Boundary , 1900 .

[5]  O. Basquin.  The exponential law of endurance tests , 1910 .

[6]  Mario C. Cirillo,et al.  On the use of the normalized mean square error in evaluating dispersion model performance , 1993 .

[7]  Bruno A. Boley,et al.  On the Accuracy of the Bernoulli-Euler Theory for Beams of Variable Section , 1963 .

[8]  Josef Eberhardsteiner,et al.  Non-prismatic beams: A simple and effective Timoshenko-like model , 2016 .

[9]  Erich Hau,et al.  Wind Turbines: Fundamentals, Technologies, Application, Economics , 1999 .

[10]  Changyou Li,et al.  Fatigue Life Estimation of Medium-Carbon Steel with Different Surface Roughness , 2017 .

[11]  Dewey H. Hodges,et al.  The Effect of Taper on Section Constants for In-Plane Deformation of an Isotropic Strip , 2008 .

[12]  George C. Lee,et al.  Design of Tapered Members. , 1971 .

[13]  A. Paglietti,et al.  Remarks on the Current Theory of Shear Strength of Variable Depth Beams , 2009 .

[14]  Josef Füssl,et al.  Stress recovery from one dimensional models for tapered bi-symmetric thin-walled I beams: Deficiencies in modern engineering tools and procedures , 2017 .

[15]  Nicholas S. Trahair,et al.  In-plane behaviour of web-tapered beams , 2016 .

[16]  Ken P. Chong,et al.  SHEAR ANALYSIS OF TAPERED BEAMS , 1976 .

[17]  S. Carothers.  XXVI.—Plane Strain in a Wedge, with Applications to Masonry Dams. , 1914 .

[18]  Barna A. Szabó,et al.  Torsional Response of Tapered I-Girders , 1967 .

[19]  Dewey H. Hodges,et al.  Stress and strain recovery for the in-plane deformation of an isotropic tapered strip-beam , 2010 .

[20]  Carlos E. S. Cesnik,et al.  VABS: A New Concept for Composite Rotor Blade Cross-Sectional Modeling , 1995 .

[21]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[22]  Ferdinando Auricchio,et al.  Planar Timoshenko-like model for multilayer non-prismatic beams , 2018 .