1Mechanics of Materials

Axial stress:

Strain:

Poisson ratio:

Modulus elasticity:

L

dLstrainaxial a

D

dDstraintransverse t

A

Fa

a

t

E

2Strain Gauges Strain gauges: for measuring force, pressure, torque, and strain.

How ? Convert these forms of input into mechanical strain using an elastic member,

which is then converted into resistance change.

Resistance change is converted into voltage using a bridge circuit, ie.Wheatstone bridge circuit

Must be properly calibrated first.

3Strain Gauges Strain gauges changes resistance due to tension/compression in the

longitudinal direction

4Strain Gauges

Electrical resistance:

Resitance relationship to strain:

A

LR

5Strain Gauges: Calculation Example

6Strain Gauges: Calculation Example

7Strain Gauges: Data Example

8Strain Gauges Typical Values

Electrical Resistance, R 120 Ohm or 350 Ohm

1000 Ohm with plastic materials

A high Gage Factor is desirable because a large change in R is producedfor a given strain

Metal GF= 1.6 to 4 Resistivity does not change with the strain

Semiconductor GF= 80 to 200 Fragile and sensitive to changes in temperature

Axial strain range = 10-6 to 103

dR=0.00024 Ohm to 0.24 Ohm Notice how small this dR

Need to utilize Wheatstone bridge circuit

9Strain Gauges: Gauge Factor Table

Most GF decreases as temperature increase (NTC)

10

Potential Error Sources with Strain Gauges

Application errors:

Gauge may be damaged during installation

Need to verify resistance before stress

Electrical and magnetic field noise

Uneed shielded lead wires and insulated coatings

Utilize twisted lead wires

Temperature effects

Thermal expansion of material

Self heating of strain gages

11

Wheatstone Bridge Circuit

Balanced condition (EAC=0) when R1R3=R2R4or consider R1=R2 =R3 = R4

12

Wheatstone Bridge Circuit: One Active Arm

13

Wheatstone Bridge Circuit: Two Active Arms

14

Wheatstone Bridge Circuit: Two Active Arms

Temperature compensation:

15

Wheatstone Bridge Circuit: Four Active Arms