We can define shear strain exactly the way we do longitudinal strain: the ratio of deformation to original dimensions. In the case of shear strain, though, it's the amount of deformation perpendicular to a given line rather than parallel to it. The ratio turns out to be tan A, where A is the angle the sheared line makes with its original orientation. Note that if A equals 90 degrees, the shear strain is infinte.
Note that we are not concerned about the line changing length. That's longitudinal strain. With shear strain we are only concerned about the change in angles.
- Any time an object is deformed, shear occurs. For example, in the top row a block is deformed without changing area. It looks like the only deformation involved is compression and extension.
- However, if we examine the diagonals of the block (bottom row) we see that there is indeed shear because the angle between the diagonals changes. This sort of shear is called pure shear.
- Pure shear is harder to see than simple shear because there is no stationary frame of reference. Imagine that you have planted your feet firmly along one of the diagonals of the block. As the block deforms, you see the other diagonal rotate just as you did with simple shear. To an outside observer, you also rotate, but from your perspective the two situations look identical.
- Even the principal strain directions look the same. In the simple shear case above, the major and minor axes of the deforming ellipse rotate clockwise as strain progresses. The same thing happens under pure shear as well.
Fig: Pure Shear
COMPARISON OF SIMPLE AND PURE SHEAR:
- Simple Shear:
- One direction remains constant and everything else rotates relative to it. Approximates the situation in a shear zone.
- Pure Shear
- Directions of greatest compression and extension are constant. The major and minor axes of the deforming ellipse remain constant. All other lines rotate.