Principal Sectorial coordinate system

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.