At a point subjected to plane strain, the normal and shear strain components measured along axes rotated by an angle theta from a reference (x-y) system are given by transformation equations analogous to those for plane stress, with shear strain gamma appearing as gamma/2 in place of shear stress tau; differentiating these equations with respect to theta yields the principal strains (maximum/minimum normal strain, occurring where shear strain is zero) and the maximum/minimum shear strains (occurring at 45 degrees from the principal strain directions), which can equivalently be determined graphically via Mohr's circle of strain plotted on epsilon and gamma/2 axes. This theory in strength of materials parallels and extends the earlier treatment of principal stresses and Mohr's circle of stress, establishing sign conventions for normal strain (elongation positive) and shear strain (angle decrease positive) needed for consistent transformation and graphical construction.
At a point subjected to plane strain, the normal and shear strain components measured along axes rotated by an angle theta from a reference (x-y) system are given by transformation equations analogou…