440 Nonorthogonal solution for thin-walled members — applications and modelling considerations 1 R. Emre Erkmen and Magdi Mohareb Abstract: In a companion paper (R.E. Erkmen and M. Mohareb. 2006. Canadian Journal of Civil Engineering, 33: 421–439.), three finite elements based on the Vlasov thin-walled beam theory were formulated using a nonorthogonal coordinate system. Although the associated derivations are more elaborate than in more conventional solutions based on orthogonal coordinates, the new elements offer more modelling capabilities and flexibility in modelling structural steel members, a feature that is illustrated in this paper. In this context, the current paper presents four details in steel construction that were conveniently modelled within the new solution scheme. The applications involve thin-walled members with coped flanges, rectangular holes reinforced with longitudinal stiffeners, and eccentric supports. Comparisons with established shell finite element models using ABAQUS suggest the validity of the new solution. Key words: open sections, finite element analysis, thin-walled members, coped flanges, rectangular holes, eccentric supports. Résumé : Dans un article connexe (R.E. Erkmen and M. Mohareb. 2006. Canadian Journal of Civil Engineering, 33 : 421– 439.), trois éléments finis fondés sur la théorie de Vlasov sur les poutres à parois minces ont été formulés dans un système de coordonnées cartésiennes orthogonales. Bien que les dérivées connexes soient plus élaborées que celles dans des solutions plus conventionnelles basées sur les coordonnées cartésiennes orthogonales, les nouveaux éléments offrent plus de capacités et de flexibilité de modélisation lors de la modélisation d’éléments structuraux en acier, une caractéristique qui est examinée dans le présent article. Dans cet ordre d’idées, cet article présente quatre détails d’une construction en acier modélisés dans le nouveau schéma de solution. Les utilisations impliquent des poutres à parois minces munies de semelles en contre-profilé, de trous rectangulaires renforcés par des éléments de charpente de renforcement et des supports excentriques. Les comparaisons aux modèles établis d’éléments finis de l’enveloppe dans le logiciel ABAQUS attestent la validité de la nouvelle solution. Mots clés : profils ouverts, analyse par éléments finis, poutres à parois minces, semelles en contre-profilé, trous rectangu- laires, supports excentriques. [Traduit par la Rédaction] Overview of companion paper In the companion paper (Erkmen and Mohareb 2006), three finite elements were developed based on the Vlasov thin-walled beam theory (Vlasov 1961). The solutions adopted nonconven- tional coordinate systems in contrast to conventional formula- tions in which orthogonal coordinate systems are used S x =  A x dA = 0, S y =  A y dA = 0 Received 1 December 2004. Revision accepted 6 February 2006. Published on the NRC Research Press Web site at http://cjce.nrc.ca/ on 2 June 2006. R.E. Erkmen and M. Mohareb. 2 Department of Civil Engineer- ing, University of Ottawa, Ottawa, ON K1N 6N5, Canada. Written discussion of this article is welcomed and will be received by the Editor until 31 August 2006. 1 This article is one of a selection of papers published in this Special Issue on Steel Research. 2 Corresponding author (e-mail: mmohareb@uottawa.ca). S ω =  A ω dA = 0, J xy =  A xy dA = 0 J ωx =  A ωx dA = 0, J ωy =  A ωy dA = 0 Coordinates x = x(s),y = y(s) are those of a point located on the section midsurface denoted by a curvilinear coordinate s measured from an arbitrary sectorial origin s 0 on the midsur- face. The sectorial coordinate ω = ω (s 0 ,s) is twice the area en- closed by the fixed radius Os 0 (where O is an arbitrarily selected origin point in the plane of the cross section), mobile radius Os , and curved sector s 0 s (see Erkmen and Mohareb 2006, Fig. 1). All integrals are performed over the cross-sectional area A. The first element, nonorthogonal Vlasov element based on exact shape functions, with 14 degrees of freedom (NOVEE14), is based on shape functions that exactly satisfy the coupled form of the Vlasov homogeneous form of the differential equations of equilibrium. As a result, it is expected to yield nodal displace- ments in exact agreement with those based on an exact solution of the Vlasov equations. The second element, nonorthogonal Vlasov element based on cubic shape functions, with 14 degrees Can. J. Civ. Eng. 33: 440–450 (2006) doi: 10.1139/L06-027 © 2006 NRC Canada