The incorporation of warping effects in the analysis of thin-walled framed structures is of primary importance for the realistic assessment of their response. This is particularly true in the linear range for members with warping restraints subject to significant torques, and in the nonlinear range for members subject to lateral torsional instability. This paper presents a new formulation for warping elastic structures composed of open thin-walled members. The new formulation is derived in a local Eulerian system and is based on cubic shape functions for the transverse local displacements and element twist. The derivation presented herein is valid for members with any open thin-walled cross-section, although explicit expressions of element matrices are only provided for symmetric l-sections. Whilst the cubic formulation is essentially linear in the local system, it is implemented within a large displacement global analysis capability which enables its use for the nonlinear analysis of structures subject to lateral torsional instability. Verification examples, using the general purpose nonlinear analysis program ADAPTIC, are presented to demonstrate the accuracy of the proposed formulation, and to illustrate its applicability to the analysis of open thin-walled structures under non-uniform torsion conditions.

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