( ... continued )

When the rosette is installed on a test part subjected to an arbitrary strain state, the variables on the right-hand side of Eqs. ( 515.2 ) are unknown. But the strains , , and can be measured. Thus, by solving Eqs. (515.2) simultaneously for the unknown quantities , , and , the principal strains and angle can be expressed in terms of the three measured strains. Following is the result of this procedure:

   (515.3)

   (515.4)

If the rosette is properly numbered, the principal strains can be calculated from Eq. (515.3) by substituting the measured strains for , , and . The plus and minus alternatives in Eq. (515.3) yield the algebraically maximum and minimum principal strains, respectively. Unambiguous determination of the principal angle from Eq. (515.4) requires, however, some interpretation, as described in the following. To begin with, the angle represents the acute angle from the principal axis to the reference grid of the rosette. In the practice of experimental stress analysis, it is somewhat more convenient, and easier to visualize, if this is re-expressed as the angle from Grid 1 to the principal axis. To change the sense of the angle requires only reversing the sign of Eq. (515.4). Thus:

     (515.5)

The physical direction of the acute angle given by either Eq. (514.4) or Eq. (514.5) is always counterclockwise if positive, and clockwise if negative. The only difference is that is measured from the principal axis to Grid 1, while is measured from Grid 1 to the principal axis. Unfortunately, since , the calculated angle can refer to either principal axis; and hence the identification in Eq. (515.5) as . This ambiguity can readily be resolved (for the rectangular rosette) by application of the following simple rules:

(a) if > , then = .
(b) if < , then = .
(c) if = and < , then = = -45 degrees.
(d) if = and > , then = = +45 degrees.
(e) if = = , then is indeterminate (equal biaxial strain).

The reasoning which underlies the preceding rules becomes obvious when a sketch is made of the corresponding Mohr's circle for strain, and the rosette axes are superimposed as shown previously .

( continued ... )

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