A kurtosis-based parameter for classifying elliptical hollow sections under bending

Abstract

A novel section parameter termed normalized excess kurtosis of a section, inspired by the same parameter used in probability distributions, is introduced to characterize the rotation capacity of a hollow section under bending. The proposed normalization accounts for variations in yield stress and Young’s modulus too. A linear relationship is observed between rotation capacity and the normalized excess kurtosis of circular hollow sections (CHS), rectangular/square hollow sections (RHS) and elliptical/oval hollow sections (EHS), under constant and linearly varying moment conditions, based on experimental and finite element model (FEM) data. It is found that, the rotation capacity variation of hollow sections is better explained by using normalized excess kurtosis than by the conventional section slenderness. The gradient of the above linear relationship varies with the section type and provides an estimate of the rotation capacity of a hollow section with a known shape and aspect ratio. It also provides insights into the section classification of EHS sections, with aspect ratios closer to unity (0.67 < a/b < 1.5) being suitable for an equivalent diameter approach and those with aspect ratios further from unity (a/b < 0.5 and a/b > 2.0) for an equivalent RHS approach. The difference between the moment and rotation capacities of linearly varying moment conditions (3-point bending) and constant moment conditions (4-point bending) is also elucidated.