Strain Gauges

Example: Bone has a Young’s modulus E of about 100,000 psi. 10 psi of stress will stretch a 20 inch femur

Compare to F = K*Δx …

Hooke’s Law

stress-strain curve:stiffness, yield strength, fracture

www.tpub.com/doematerialsci/materialscience22.htm

Consider incompressible material (constant volume…)

Transverse Strain and Poisson’s ratio

What to expect on the strain gauge quiz:

www.solware.co.uk/blog

Given stress, Young’s modulus, gain, Vex, Poisson’s ratio, calculate Vout…

Another deformation: torsional twist

http://home.gna.org/getfem/shots.html

What about the piezoresistivity term?It is normally not zero. In fact for some semiconductors it dominates the expression on the right of the equation. For metals, with a Poisson ratio around 0.3, nonzero piezoresistivity of 0.4*ε basically results in approx:

In the Strain Gage Quiz the gauge factor will be 2.

from www.sensorland.com

from www.natmus.dk

Unknown material properties vs strain gauge material properties:

Gauge factor: of the strain gaugePoisson’s ratio: of the unknownstrain: of the unknownYoung’s modulus = Ym… Young’s modulus: of the unknown > Ym of SG

Next consider a Wheatstone bridgemade with 4 strain gauges… Two voltage dividers to consider:

That is the term to finish the expression for Vout = G*Vex*ΔR/4R for one longitudinal strain gauge in a "positive" location in the bridge.

R1 LG TG LR TRR2 LG TG LR TRR3 LG TG LR TRR4 LG TG LR TR

tension -1 1 1 -1 0.25 -0.25 -0.25 0.25 -1 1 1 -1 0.25 -0.25 -0.25 0.25CW bend 1 -1 -1 1 -0.25 0.25 0.25 -0.25 -1 1 1 -1 0.25 -0.25 -0.25 0.25

Sign of influence on Vout given SG placement:

Table reads: if R1 is the LG strain gauge then how does Vout change? *dR/4R …

SG web links: • http://me.queensu.ca/courses/MECH215/documents/MECH215-Week06Lec

ture1-StrainMeasurement-Introduction.pdf

• http://www.eidactics.com/Downloads/Refs-Methods/NI_Strain_Gauge_tutorial.pdf

• http://www.thorlabs.com/images/TabImages/Strain%20Tutorial.pdf

FINAL REPORT TO THE NATIONAL OPERATING COMMITTEE ON STANDARDS FOR ATHLETIC EQUIPMENT (NOCSAE) 1999

“THE USE OF SHOE ORTHOTICS TO REDUCE BONE STRAIN RATE”

http://www.nocsae.org/research/rep/Burr_final.htm