strain gauges example: bone has a young’s modulus e of about 100,000 psi. 10 psi of stress will...

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Strain Gauges ample: Bone has a Young’s modulus E of about 100,000 psi. psi of stress will stretch a 20 inch femur Compare to F = K*Δx … Hooke’s Law

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Page 1: 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

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

Page 2: 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

Page 3: 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

Consider incompressible material (constant volume…)

Transverse Strain and Poisson’s ratio

Page 4: 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

Page 5: 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

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…

Page 6: 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

Another deformation: torsional twist

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

Page 7: 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

Page 8: 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

Page 9: 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

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.

Page 10: 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

from www.sensorland.com

from www.natmus.dk

Page 11: 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

Page 12: 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

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:

Page 13: 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

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.

Page 14: 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

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 …

Page 15: 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

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

http://me.queensu.ca/courses/MECH215/documents/MECH215-Week06Lecture1-StrainMeasurement-Introduction.pdf

http://me.queensu.ca/courses/MECH215/documents/MECH215-Week06Lecture1-StrainMeasurement-Introduction.pdf

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

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

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

Page 16: 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

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

Web viewPENDIDIKAN MATEMATIKA. PROGRAM . PASCASARJANA . ... δV δy mendekati turunan dV dy . Begitu pula, dengan δx mendekati 0, sehingga x + δx mendekati x

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