Calculating the Transformed Strain for a Differential Plane Strain Element

February 27, 2017 Abdul Siraj, P.E.

In this post, I will go over the first example in our mechanics of materials course covering strain transformation. The goal of this example is to calculate the transformed strain 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 = 600 x 10^-6
Strain in the normal y direction = -400 x 10^-6
Shear strain in the x-y direction = 300 x 10^-6

 

Find the equivalent strain on this element if it oriented 30 degrees clockwise from the original position.