Shear stress distribution in tapered I-beams: Analytical expression and finite element validation

Shear stress distribution in tapered I-beams is remarkably different from that of prismatic beams as it is largely influenced by the vertical components of the inclined flange forces. Tapered I-beams can have a linear (or nonlinear) variation of web depths or flange widths or a combination of both, with monosymmetric or bisymmetric cross-sections. Evaluation of shear stress distribution at a section in tapered I-beams is a challenging task, and also closed form expressions have not been reported in literature. Hence, this paper presents a mechanicsbased approach to arrive at a closed-form analytical expression for evaluating the shear stress distribution in generic 3D tapered I-beams. The major highlight of the proposed approach is that it accurately predicts the shear stress distribution in I-beams with simultaneously tapering web and flanges. The proposed approach was validated with 3D finite element models for a range of problems, and it was observed that the errors are always less than 4% at sections with L/D ratio greater than 3 and with flange inclination less than 10?. In particular, for the case of bisymmetric web-tapered beams and flange-tapered beams, the errors were less than 1%. Finally, the proposed approach lends itself to an explicit algebraic expression that will be useful for design engineers.