A cross-section analysis procedure to rationalise and automate the performance of GBT-based structural analyses

• A novel procedure to perform a GBT “cross-section analysis” is developed and illustrated.
• The algorithm handles arbitrary sections and its implementation can be easily automated.
• The deformation modes are hierarchically ordered within structurally meaningful families.
• Simple formulae to calculate the number of deformation modes in each family are provided.
• The illustrative examples presented and discussed cover all types of flat-walled cross-sections.

When analysing the structural behaviour of a thin-walled member by means of Generalised Beam Theory (GBT) – a one-dimensional folded-plate theory expressing the member deformed configuration as a linear combination of cross-section deformation modes with amplitudes varying along its length – the performance of the so-called “cross-section analysis” is the key step. Indeed, it consists of determining the deformation modes and evaluating the corresponding modal mechanical properties. However, the available procedures to perform this task are strongly dependent on the cross-section geometry type, a feature precluding its general, efficient and systematic numerical implementation. In order to overcome this difficulty, this paper presents the development and illustrates the application of a novel procedure to perform “GBT cross-section analyses” that (i) is able to handle arbitrary (flat-walled) cross-section shapes, (ii) can be numerically implemented in a systematic and straightforward fashion, and (iii) provides a rational set of deformation modes, which are hierarchically organised into several families, each with well-defined structural/mechanical characteristics. Both the analytical derivations and the underlying mechanical reasoning are explained in detail, and the selected illustrative examples cover the various types of relevant cross-section geometries.