Chapter 2 - Stress and Strain Transformation

Abstract

Stress and strain states at any point within the solid body have six distinctive components, that is, three normal and three shear components, with respect to an arbitrary coordinate system. The values of these six stress and/or strain components at the given point would change with the rotation of the original coordinate system. It is therefore important to understand how to perform stress or strain transformation between two coordinate systems and to be able to determine the magnitudes and orientations of the resulting stress or strain components. One key reason for stress or strain transformation is that the strains, normally measured in the laboratory along particular directions, are to be transformed into a new coordinate system before the relevant stresses can be calculated within the new coordinate system using stress–strain relation formulae. In this chapter, we discuss the stress/strain transformation principles and the key role they play in the stress calculation of a drilled well at any point of interest whether vertical, horizontal, or inclined.