Page 44 - Aircraft Stuctures for Engineering Student

1.16 Experimental measurement of surface strains 29

Fig. 1.1 5 Strain gauge rosette.

the form of a rosette, as shown in Fig. 1.15. Suppose that and are the principal
strains at the point, then if E,, &b and E, are the measured strains in the directions 8,
(8 + a), (8 + a + p) to we have, from the general direct strain relationship of
Eq. (1.3 1)
E, = E~COS 8 + cII sin 2 8 (1 SO)
2
since E, becomes E~ becomes qI and -yxy is zero since the x and y directions have
become principal directions. Rewriting Eq. (1.50) we have
2 )
1 + COSM 1 - cos 28
%=EI( 2 )+EII(
or
E, = $ + + 4 - cII) COS 28 (1.51)
Similarly

&b = $ (€1 + EII) + $ (E1 - EII) cos 2(8 + a) (1.52)
and
E, = ; + EI1) + 4 (EI - EII) cos 2(e + a + p) (1.53)
(EI
Therefore if E,, &b and E, are measured in given directions, i.e. given angles a and p,
then and 8 are the only unknowns in Eqs (lSl), (1.52) and (1.53).
The principal stresses are now obtained by substitution of and in Eqs (1.47).
Thus
1
&I = - (Cq - vq1) (1.54)
E
and

(1.55)

Solving Eqs (1.54) and (1.55) gives
E
+
9
01 = - %I) (1.56)
-
(&I