Chapter 26 Experimental Evaluation of the Warping Deformation in Thin-Walled Open Section Profiles Sandro Cammarano, Giuseppe Lacidogna, Bartolomeo Montrucchio, and Alberto Carpinteri Abstract The analysis of thin-walled open section beams can be performed by means of Vlasov’s theory of the sectorial areas. It is well-known that this type of profiles, when subjected to torsional actions, are characterised by the warping deformation and, consequently, by a further stress state whose intensity is comparable with that produced by mere flexural deformations. In the literature many papers are focused on the structural behaviour of these elements, but, to the Author’s best knowledge, none proposed an experimental technique to evaluate first-hand this particular behaviour. In order to verify the classical theory of the sectorial areas, in the present paper an experiment regarding a thin-walled open section profile subjected to flexural and torsional loads is performed. With the help of a specific optical device, suitable for precision measurements, the warping displacements of a U-shaped section are easily acquired. These are compared to those derived, first, from an analytical formulation, originally devised to deal with vertical thin-walled bracings belonging to the structural core of a tall building, and, secondly, from a FE program, in which the steel profile is modelled by means of thin-shell elements. The numerical comparison confirms the reliability of the analytical formulation. Keywords Thin-walled section • Warping deformation • Vlasov’s theory • Experimental evaluation • Optical device 26.1 Introduction Thin-walled open section profiles are usually employed in high-rise buildings to provide the adequate horizontal resistance against the effects derived from earthquakes and wind. The limits imposed by legislation in terms of lateral displacements of these constructions have caused the appearance of several resistant systems. Among all, open section bracings prove to be particularly convenient since, in addition to contributing to the total stiffness, they can house elevator shafts and stairwells, which are necessary for the functional needs required by the building occupants and useful for a rapid usability of the floor spaces. When subjected to torsional actions, the transversal section of such elements undergoes an out-of-plane distortion, known in literature as warping deformation. Associated with this phenomenon, the bimoment action produces a further stress state, similar to that generated by flexural actions, which cannot be disregarded especially when their structural contribution is decisive for the lateral stability of the building. Timoshenko [1] and Vlasov [2] were the pioneers in the analysis of thin-walled open section profiles. In particular, a comprehensive theory was proposed by Vlasov who demonstrated that the well-known Saint Venant’s theory was actually a very particular case of a more general formulation. Many authors tried to extend his original approach, which, however, represents a milestone in the study of structural mechanics. To the authors’ best knowledge, papers regarding experimental tests for the assessment of the warping deformation of thin-walled open section beams are almost absent in literature. Some of them, based on Vlasov’s theory, are related to the S. Cammarano (*) • G. Lacidogna • A. Carpinteri Department of Structural, Geotechnical and Building Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy e-mail: sandro.cammarano@polito.it; giuseppe.lacidogna@polito.it; alberto.carpinteri@polito.it B. Montrucchio Department of Control and Computer Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy e-mail: bartolomeo.montrucchio@polito.it H. Jin et al. (eds.), Advancement of Optical Methods in Experimental Mechanics, Volume 3: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06986-9_26, #The Society for Experimental Mechanics, Inc. 2015 231
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