Engineering Rock Mechanics

Stress analysis 403

If the global stresses are

what are the local stresses?

TSY, oy, 0.

Ox’ 0 Ty’x’ 0 0,. “1

If we think in terms of a small cubic element rotating about the z-axis,

Calculating of, o,, and qY, is more difficult and is done like this:

we can see that q = of.

The rotated element is positioned

over the original element such that

the vertical sides (remember it is a

cube) A and B touch two of the

original faces. If we now cut off the

prism OAB from the original ele-

ment and examine the resulting

free body diagram resolving stress

components onto resolved areas:

X

As usual, write down the equations of static equilibrium:

-Y