Engineering Rock Mechanics

Stress unalysis 405

Example

X

e = 300 3 sin e = 0.500, COS e = 0.866

:. of = 20 x (0.866)2 + 10 x (0.500)' +2 x 10 x 0.500 x 0.866 = 26.16 MPa

oY, = 20 x (0.500)2 + 10 x (0.866)' - 2 x 10 x 0.500 x 0.866 = 3.84 MPa

zIy = 10 (0.866' - 0.500") - (20 - 10) x 0.866 x 0.500 = 0.67 MPa.

An interesting check of the arithmetic is that

(0, + cy) = (0,. + 43.

So in this case

ox + oy = 30 MPa

and

ox, + = 26.16 + 3.84 = 30.00 MPa.

Notice that T~~~ is very low in comparison to zv. We may be tempted to
ask whether there exists for x'y' an orientation such that zxtyt = 0. Well
there is.

Principal directions and principal stresses

t

't -

.X

From this - To this -