Engineering Rock Mechanics

Strain analysis 427

In summary then:

Delta rosette

1

c=- &,+EQ+€,

l( 3

d3(ER -'Q)

tan28 =

Rectangular rosette

c=- E,+&,

2 l( )

('P +'R)-'&Q

tan28 =

Example. In a delta rosette the three measured strains are J+ = 8E-4,
EQ = -8E4 and = 2E4. What are the principal strains and their
orientation to E~?

) = 0*7873

)

4 3(2E - 4 - -8E - 4

tan28 =

hence

28 = 38.2" -141.80 remember

-180 < 8 < 180

c = V3 (8 - 8 + 2)E4 = 0.667E - 4

2E -4- -8E - 4

= 9.333E - 4.

= .i 3sin(38.2)

Use whichever value of 20 gives positive r.
Hence

= c + r = 10.000E-4

and
= c - r = -8.667B-4.

Now choose the value of 0 which is compatible with these values

near to E~, which seems

midway between Q and E~, which cannot

= 10E-4, EQ = -8E-4, ER = 2E4). Hence 8 = 19.1" and the

of .sl and E~. In this case, 8 = 19.1" puts
reasonable. 8 = -70.9" puts
be correct
solution is: