The tool SM-06 computes the strain components ε_{x}, ε_{y}, ε_{z}
from the readings of a strain gauge rosette, which is a cluster of three strain gauges. The tool also gives the principal strains and maximum in-plane shear strain.

In addition, a tutorial on how to use the tool in computation is provided and a subject review on fundamental theories and useful formulas is presented.

**Example: A 45 ^{o} Strain Rosette**

The input in the tool is

After clicking "Run", the results will be shown as follows in another page.

Computed strain components:

Normal strain ε_{x} = 6.0000E-5

Normal strain ε_{y} = 1.0000E-4

Shear strain γ_{xy} = 9.0000E-5

Principal strains:

ε_{1} = 1.29244E-4 with angle θ_{p1} = 56.9812 degree

ε_{2} = 3.0756E-5 with angle θ_{p2} = -33.0188 degree

Maximum in-plane shear strain:

γ_{max} = 9.8489E-5 with angle θ_{s} = 11.9812 degree and 101.9812 degree

On the plane of γ_{max}, average normal strain ε_{avg} = (ε_{x}+ε_{y})/2 = 8.0000E-5

A single wire strain gauge can only measure strain in one direction. In a plane strain problem, three strain components at a point on the surface of a
body can be determined by a strain rosette, which is a cluster of three electrical-resistance strain gauges arranged in a special pattern; see Fig.1. As shown in the figure,
the axes of the three gauges are arranged at the three different angles θ_{a}, θ_{b}, and θ_{c}, with respect to the *x* axis,
and each strain gauge can only measure the normal strain along its axis.

**Figure 1. ** A strain gauge rosette

Let ε_{a}, ε_{b}, ε_{c} be the normal strain readings from the strain gauges. The strain components ε_{x},
ε_{y}, γ_{xy} at the point in the xy plane are related to the strain readings by

Equation (1) is obtained by strain transformation; see the subject review of the tool SM-10. This leads to the xy-plan strain components expressed in terms of the strain readings

Table 1 lists two commonly used strain rosettes and related formulas for strain computation.

**Table 1.** 45^{o} strain rosette and 60^{o} strain rosette

For more information about strain transformation and principal strains, please check the subject review in the tool SM-10.

1. Bedford, A., and Liechti, K. M., 2000, Mechanics of Materials, Prentice Hall, Upper Saddle River, New Jersey.

2. Yang, B., 2005, Stress, Strain, and Structural Dynamics: An Interactive Handbook of Formulas, Solutions, and MATLAB toolboxes, Elsevier Science, Boston.