Engineering Rock Mechanics

426 Appendix A: Stress and strain analysis

rearranging (4) gives

(b) Rectangular rosette

0

.cP = c + r cos 28

% = c + r cos (28 + 90)

ER = c + r cos (28 + 180).

Using the double angle formulae on the expressions for EQ and E~:

EQ = c + r {COS~~COS 90 -sin 28sin 90) = c + r {-sin 28) (2)

cR = c + r {cos 28 cos 180 - sin 28 sin 180) = c + Y {- cos 28). (3)

Adding (1) and (3):

hence

c = 1/2 (Ep + Ed.

Subtracting (3) from (1):

~p - ER = 2r cos 28.

Divide (5) by (4):

(‘P + ‘R) - 2EQ

‘P - ‘R

= tan28.

Rearranging (4):