1. Strain Gages
By Dr. Sotiris Omirou

2. The electrical resistance strain is a metal wire or metal foil strip which is wafer-like and can be stuck onto surfaces like a postage stamp.
Strain-gauge

3. Typical bonded strain gages

4. When a strain gauge is bonded to an object, and the object changes in size, the resistance of the strain gauge will change. The resistance R is given by the expression:
R= ρ l/A
Where:
l is the length of the wire in meters
ρ is the resistivity of the material in ohm meters
A is the cross-sectional area of the filament in m2

5. Mechanical strain ε = ΔL / L Electrical strain ΔR/R= G . ΔL/L
When strain gauges measure the changing dimensions of an object, they are measuring strain. Strain is the ratio of the change in dimension of an object to the original dimension
Mechanical strain ε = ΔL / L
When subject to strain, its resistance R changes, the fractional change in resistance ΔR/R being proportional to the mechanical strain i.e.
Electrical strain ΔR/R= G . ΔL/L
where G is the gauge factor (1.8 – 2.2)
R varies between 50 Ω and 2KΩ

6. Potential Divider

7. Potential Divider with differential amplifier

8. Wheatstone Bridge
The four arms of the bridge circuit are formed by the resistance R1 to R4.
The corner points 1 and 4 are connected to the input voltage Vin
The corner points 2 and 3 are connected to the output voltage Vo. 1 2 4 3 R2 R1 R3 R4 Vo
Vin

9. Quarter strain gauge bridge with differential amplifier

10. Half strain gauge bridge with differential amplifier

11. Full strain gauge bridge with differential amplifier

12. Interpretation of results (Example 1)
Meter reading

13. (Example 2)
Meter reading

14. Strain Gages - review Strain = Elongation / Original Length
Change in length = Change in electrical resistance
Electrical Resistance change is very small, too small to be accurately measured using ordinary voltmeters

15. Wheatstone Bridge
Converts a change in electrical resistance from a strain gage to a change in voltage
Changes in strain are linearly related to a change in voltage output
Voltage change is too small to be accurately measured and for this reason an amplifier is used