Error due to strain measurement in non-principal sections

Abstract

It often happens that we measure principal strains in cross-sections which, for one reason or another, are not precisely parallel to the intended principal section. An equation is here derived which gives the error due to measuring principal strains in non-principal sections. This error is a function of the axial ratio of the strain ellipsoid and the orientation of the measured section relative to the principal plane. The practical value of this analysis is enhanced by considering the cases of maximum and minimum error, so that the error may be bounded using estimates of the axial ratio and the angle between the measured principal direction and the true principal direction. Limiting error values are presented in both tabular and graphical form. As might be expected, deformations with low axial ratios are the most tolerant of measurements made in sections which are not parallel to a principal plane.