Three-Element Rectangular (45-degree) Rosettes

When the directions of the principal axes are unknown, three independent strain measurements are required to completely determine the state of strain. For this purpose, a three-gage rosette should be used, and the rectangular rosette is generally the most convenient form.

If the transverse sensitivity of the gage elements in the rosette is other than zero, the individual strain readings will be in error, and the principal strains and stresses calculated from these data will also be incorrect.

Correction for the effects of transverse sensitivity can be made either on the individual strain readings or on the principal strains or principal stresses calculated from these. Numbering the gage elements consecutively, elements (1) and (3) correspond directly to the two-gage, 90-degree rosette, and correction can be made with Equations (509.6) and (509.7), or (509.6a) and (509.7a), or (by properly setting the gage factor control on the strain indicator) with Equations (509.6b) and (509.7b). The center gage of the rosette requires a special correction relationship since there is no direct measurement of the strain perpendicular to the grid. The correction equations for all three gages are listed here for convenience:

     Eq. (509.10)

    Eq. (509.11)

    Eq. (509.12)

where:

   = indicated strains from the respective gage elements.
   = corrected strains along the gage axes.

Note : The Equations (509.10), (509.11), and (509.12) are based upon the assumption that the transverse sensitivity is the same, or effectively so in all gage elements, as it is in stacked rosettes. This may not be true for planar foil rosettes, since the individual gage elements do not all have the same orientation with respect to the direction in which the foil was rolled. It is common practice, however, to etch the rosette in a position of symmetry about the foil rolling direction, and therefore the transverse sensitivities of gage elements (1) and (3) will be nominally the same, while that of element (2) may differ. Correction equations for rosettes with nonuniform transverse sensitivities among the gage elements are given in the Appendix .

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