Engineering Rock Mechanics

Strain analysis 425

(a) Delta rosette

E~ = c + r COS 28

Q = c + r COS (28 + 120)

ER = c + r cos (28 + 240).

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

EQ = c + r {cos 28 cos 120 - sin 28 sin l2O>

= c + r {- YZ cos 28 - % sin 20) (2)

ER = c + r {cos^28 cos^240 - sin^28 sin 240)

= c + r {- YZ cos 28 + 6,~ sin 28). (3)

Adding (l), (2) and (3):

hence

c = '/3 (&p + &Q + ER).

Subtracting (2) from (3):

2&p - (Ea + ER) = 3v cos 20.

hence

(5)

('R - 'Q)

tan20 =

2EP - ('Q + 'R )