Cartesian - co-ordinate system and Cylindrical - co-ordinate system
Cartesian - co-ordinate system: In the Cartesian co-ordinates system, we make use of the axes, X, Y and Z
Let us consider the small element of the material and show the various normal stresses acting the faces
Thus, in the Cartesian co-ordinates system the normal stresses have been represented by sx, syand sz.
Cylindrical - co-ordinate system: In the Cylindrical - co-ordinate system we make use of co-ordinates r, q and Z.
Thus, in the Cylindrical co-ordinates system, the normal stresses i.e components acting over a element is being denoted by sr, sqand sz.
Sign convention : The tensile forces are termed as ( ve ) while the compressive forces are termed as negative ( -ve ).
First sub – script : it indicates the direction of the normal to the surface.
Second subscript : it indicates the direction of the stress.
It may be noted that in the case of normal stresses the double script notation may be dispensed with as the direction of the normal stress and the direction of normal to the surface of the element on which it acts is the same. Therefore, a single subscript notation as used is sufficient to define the normal stresses.