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):