Principal Sectorial coordinate system
Tóm tắt
The use of Sectorial coordinates is unavoidable when studying thin-walled elements with open cross sections. The torsional behavior of this type of elements is governed by some fundamental sectorial properties such as the position of the principal pole, i.e., the shear center, and the warping constant or sectorial moment of inertia. However, and despite being a fundamental concept, the definition of the Principal Sectorial coordinate system has not been clearly presented in the literature, and some errors can be found in the diagrams of sectorial areas in well-known text books. Moreover, the Principal Sectorial coordinate system is used, but the location of the principal origin is usually avoided. In this paper, a compact and alternative procedure to obtain the principal sectorial coordinate system is presented. Authors propose to put aside the traditional definition of Principal Origin and consider instead the value of the sectorial area at an extreme of the contour line. Several examples are developed.
Tài liệu tham khảo
Vlasov, V.Z.: Thin Walled Elastic Beams. Israel Program for Scientific Translations. Jerusalem (1961)
Nishino, F., Kasemset, C., Lee, S.L.: Variational formulation of stability problems for thin-walled members. Ing Archiv 43(1), 58–68 (1973)
Lazić, J.D., Lazić, V.B.: Theory of open thin-walled composite and prestressed beams. Arch. Appl. Mech. 61, 532–547 (1991)
Vo, T.P., Lee, J.: Geometrical nonlinear analysis of thin-walled composite beams using finite element method based on first order shear deformation theory. Arch. Appl. Mech. 81(4), 419–435 (2011)
Vukasović, M., Pavazza, R., Vlak, F.: Analytic solution for torsion of thin-walled laminated composite beams of symmetrical open cross sections with influence of shear. Arch. Appl. Mech. 87(8), 1371–1384 (2017)
Shama, M.A.: Calculation of Sectorial Properties, Shear Center and Warping Constant of Open Sections. Alexandria Press, New York (1974)
Chen, W.F., Atsuta, T.: Theory of Beam-Columns. Space Behavior and Design, vol. 2. J. Ross Publishing, New York (2008)
Timoshenko, J.N., Goodier, S.P.: Theory of Elasticity, 3rd edn. McGraw-Hill, New York (1970)