Basic Linear Strain Gage

It is not possible (currently) to measure stress directly in a structure. However, it is possible to measure strain since it is based on displacement. There are a number of techniques to measure strain but the two more common are extensometers (monitors the distance between two points) and strain gages.

Strain gages are constructed from a single wire that is wound back and forth. The gage is attached to the surface of an object with wires in the direction where the strain is to be measured.

The electrical resistance in the wires change when they are elongated. Thus, the voltage change in the wires can be collaborated to the change in strain. Most strain gage measurement devices automatically collaborate the voltage change to the strain, so the device output is the actual strain.

Strain Gage Rosette at Arbitrary Angles

Since a single gage can only measure the strain in only a single direction, two gages are needed to determine strain in the ε_x and ε_y. However, there is no gage that is capable of measuring shear strain.

There is a clever solution to finding shear strain. Three gages are attached to the object in any three different angles. Recall, any rotated normal strain is a function of the coordinate strains, ε_x, ε_y and γ_xy, which are unknown in this case. Thus, if three different gages are all rotated, that will give three equations, with three unknowns, ε_x, ε_y and γ_xy. These equations are,

Any three gages used together at one location on a stressed object is called a strain rosette.

To increase the accuracy of a strain rosette, large angles are used. A common rosette of three gages is where the gages are separated by 45^o, or θ_a = 0^o, or θ_b = 45^o, or θ_c = 90^o. The three equations can then be simplify to

Solving for ε_x, ε_y and γ_xy gives,

Similarly, if the angles between the gages are 60^o, or θ_a = 0^o, or θ_b = 60^o, or θ_c = 120^o., the unknown strains, for ε_x, ε_y and γ_xy will be,