Calculating the Principal Strains and Associated Orientation for a Differential Plane Strain Element

February 27, 2017 Abdul Siraj, P.E.

In this post, I will go over the second example in our mechanics of materials course covering strain transformation. The goal of this example is to calculate the principal strains and associated orientation for a differential plane strain element.


The engineering problem statement states,


The differential element shown in the figure below experiences a state of plane strain.


Strain in the normal x direction = -400 x 10^-6
Strain in the normal y direction = 200 x 10^-6
Shear strain in the x-y direction = 100 x 10^-6


Find the principal strains at this point and the associated orientation of the element.