Page 45 - Aircraft Stuctures for Engineering Student

30 Basic elasticity

Fig. 1.16 Experimental values of principal strain using Mohr's circle.

and
(1.57)

A typical rosette would have Q = ,O = 45" in which case the principal strains are
most conveniently found using the geometry of Mohr's circle of strain. Suppose
that the arm a of the rosette is inclined at some unknown angle 8 to the maximum
principal strain as in Fig. 1.15. Then Mohr's circle of strain is as shown in Fig.
1.16; the shear strains +yay +yb and 7, do not feature in the analysis and are therefore
ignored. From Fig. 1.16
oc= +(&,+Ec)

CN =E, -0C =;(E, -E,)
QN= CM = ~ b +E,)
-OC=E~ -$(E,
The radius of the circle is CQ and

CQ = dCN2 + QN2
Hence

which simplifies to
1 J(
E,
CQ=~ - qJ2 + (E, - Eb)2
Therefore which is given by
= OC + radius of circle
is

(1.58)