Engineering Rock Mechanics

Strain analysis 41 1

Using Mohr's circle to determine stresses on u plune

Follow points 1,2,3 and 5 of the method for determining principal stresses,
then:

4. Draw an element of the correct orientation relative to the x-y-axes, and
   mark on positive of, of, zYyr and vf. Write down the sense (positive
   anticlockwise) and the magnitude of the rotation x-axis to x'-axis.


5. Mark this rotation on the circle, measuring from the (ax, zy) point,
   remembering that you do twice as much on the circle as you do in real
   life.


6. The new point is (q, zdyt). Draw the diameter to determine (ay,, vi).

Example. What are the stresses on an element rotated 30" anticlockwise
relative to the element in the previous example?

ux8 = c + r cos(@ - 60)

= 26. I6MPa

0.. = c - r cos(0 - 60)

I ;7 \

\ =3.84MPa

I\ \ / T..... = r sin(@ - 60)

Strain analysis

If we apply stresses to a body, by how much does it deform? Obviously, it

depends on the stress state, the material the body is composed of, and the

size of the body. This last problem is resolved if, instead of absolute

deformations, we talk about relative deformations, relative to the body. This

is what strain is: deformation normalized to make it independent of the

size of the body.

Anulysis of displacement

Consider this situation:

X X