From Wikipedia article on deformation, the shear strain is defined as the angle of the deformation. I had always thought of it as the limiting ratio of the difference in perpendicular displacement of the beginning and end of a line element with the length of that line element.
Where $u_y$ is the displacement of a point in the $y$ direction. In this sense, the definition would follow similarly to that of normal strain. That is, a ratio of change in length to that of original length. Why is it that it is defined as the angle instead?
I understand that in very small lengths (differential lengths) the two are the same. For pure shear stress,
But why is it defined as the angle and not the ratio?