Analytical solution of the stresses in doubly tapered box girders

Lengthwise geometrical variations such as taper, are widely employed in engineering structures, e.g. in wind turbine blades, aircraft wings and bridges. Notwithstanding the effects of taper on the mechanical behaviour of beams, it is common design procedure to model such structures as prismatic beams. Indeed, the derivation of analytical solution of the stress components in tapered beams is not a trivial task. This work provides the above-mentioned analytical solution of the stresses in tapered box girders, whose width and height are varying along the longitudinal axis of the beam. The proposed solution deals with any arbitrarily oriented external forces and it is based on the hypothesis of homogeneous isotropic material. The analytical solution shows that a combination of even small vertical and horizontal tapers highly influences the stress distribution. A parametric study of the relation between taper and the von Mises stress was investigated. Furthermore, it is evinced that disregarding taper effects might lead to an overestimation of the fatigue lifetime of the structures up to 12%.