Engineering Rock Mechanics

Strain analysis 421

1

125

.sx=-=8O0Op or e,, = SOOOp

E =-=zoo0 ps or err = 2OOOp

1

500

yxy=-= 9000ps or exy = 4500p.

1000

Compute the local components of strain if 8 = 30" (cos 6 = 0.866, sin 8
= 0.5)

e:, = (8000 x 0.750) + (2000 x 0.250) + (2 x^4500 x 0.866 x 0.500)

= 10400ys

e'yy = (8000 x 0.250) + (ZOO0 x 0.750) - (2 x^4500 x 0.866 x 0.500)

-400 US

e& = 4500(0.750 - 0,250) - (SO00 - 2000) x 0.866 x 0.500

= -350 US

or

Principd directions and principul strains

Just as for stresses, does there exist a value of 8 for whic.. e& (or yxy) = O?
There is, and let us call us the angle fi-
By analogy with the stress tensor,