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About the Tool

The tool SM-06 computes the strain components εx, εy, εz 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.

Tutorial

Example: A 45o 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 εx = 6.0000E-5

Normal strain εy = 1.0000E-4

Shear strain γxy = 9.0000E-5


Principal strains:

ε1 = 1.29244E-4 with angle θp1 = 56.9812 degree

ε2 = 3.0756E-5 with angle θp2 = -33.0188 degree


Maximum in-plane shear strain:

γmax = 9.8489E-5 with angle θs = 11.9812 degree and 101.9812 degree

On the plane of γmax, average normal strain εavg = (εxy)/2 = 8.0000E-5

Subject Review

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 θa, θb, and θc, 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 εa, εb, εc be the normal strain readings from the strain gauges. The strain components εx, εy, γxy 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. 45o strain rosette and 60o strain rosette

45 strain rosette and 60 strain rosette

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


References

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.