# Strain Gauge

#### Civilian2

How does one work just out of interest?

I use it when loading a steel beam to see the strain induced in the web of a chanel section.

can't figure out how it would work

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#### FredGarvin

Science Advisor
For lack of a better description, it is a continuous wire that zig-zags back and forth. The wire is embedded in a foil that holds it in place and allows mounting of the gauge.

You mount the strain gauge, ideally, so that the long lengths of wire are perpendicular to the applied load. When the load is applied, the strain gauge distorts slightly. That slight distortion causes the internal resistance of the gauge to change. That change in resistance is proportional to the strain induced. Each strain gauge comes with a proper calibration for it's intended use range.

You'll also have to delve into a Wheatstone bridge. That is the electrical workings and where the actual signal reading is taken from.

Here's a quick intro:
http://www.sensorland.com/HowPage002.html
http://www.omega.com/techref/strain-gage.html
http://www.omega.com/techref/pdf/Positioning_Strain_Gages.pdf

#### Gokul43201

Staff Emeritus
Science Advisor
Gold Member
Very simplistically speaking :

$$R = \frac{\rho l}{A}$$

A tensile strain increases l and decreases A (through the Poisson ratio), causing R to increase. This change in R is calibrated against variations in l.

#### Civilian2

thanks for the reply. Thats interesting, though I probably should have thought it would be along those lines.

What factors then do you think would cause it to have a different strain reading than theoretically calculated results useing bending theory?

Besides stress raisers and innacurate cross section values.

#### faust9

What kind of strain gauge are you using exactly? This is probably a day late and a dollar short, but if you use a rosette strain gauge, it is much easier to determine the various strains. Google rosette strain gauge and you'll find loads of information I'm sure.

Anywho, differences between measured and theoretical can come from strain gauge error--do you know this for the gauge readings in questionor incorrect positioning of the gauge. As for the beam itself, one would have to know the exact configuration, shape, and force perameters to make a truely educated guess as to where inaccuracies would come from IMHO. Did you model your beam using a thin walled approximation, or did you model the beam using the true shape/size? Did you account for all of the moments in the beam---actualyy a more important question is how are you modeling this beam? Are you using software or pencil and paper? If you used pencil and paper, then did you make any assumptions/approximations I.E. bending causes negligible change in length or shape. If you did then there is a little error. How far off are you? You'll be hard press to get 5% or less error unless you are paying big  for materials of known and verified quality/composition/shape. Are there and stress reliefs in your real beams not accounted for in you model? Small filets will change the stresses within a beam fairly drastically.

What "beam theroy" equations did you use. In this regard, you could analyze a beam using simple external force/moment analysis or you could use change in potential energy analysis; moreover, 2D vs 3D analysis can also be done. The various analysis can each add error depending on how you accounted for different variables.

I can probably list two dozen other things and still be 873568736238746 items short of a full list of possible sources of error for a general beam problem. One needs to know the details to give a better account of variables to help you along.

Sorry for being vague, but it's kind of tough pin pointing an exact source of error w/out knowing the methodology used to determine the stresses.

Good luck w/ you analysis though.

#### Civilian2

Thanks very much for the depth of your reply. It has helped me alot in terms of my investigation and the right questions to dwell upon.

Actually I am fairly close, I am about 8% out with one method - strain = my/EI where EI was calculated by measuring the deflection and from that obtaining the curvature (the beam has two point loads therefore has a section of constant moment ie constant curvature between them). EI is found by plotting moment vs curvature.

And I'm about 12% out with using strain = kx
where k is the curvature. Although I believe this value should be closer to the strain gauge readings.

Therefore I am investigating what I haven't taken into account in regards to the strain gauge itself and the beam. I think self-weight is my next stop.

Cheers.

PS> Sorry for not addressing all your concerns as I am in a hurry to be somewhere.

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#### FredGarvin

Science Advisor
PS...don't forget if you are using a beam in a school lab, there's nothing saying that at one time that beam wasn't permanently deformed or is not homogeneous.

#### Civilian2

FredGarvin said:
PS...don't forget if you are using a beam in a school lab, there's nothing saying that at one time that beam wasn't permanently deformed or is not homogeneous.

Interesting point.

If a beam has been plasticly deformed at some stage in its life and then bent back and unloaded....

Will elastic bending theory of the likes of f= my/I still work the next time it is loaded in what was its elastic range of load?

#### Gokul43201

Staff Emeritus
Science Advisor
Gold Member
Civilian2 said:
Interesting point.

If a beam has been plasticly deformed at some stage in its life and then bent back and unloaded....

Will elastic bending theory of the likes of f= my/I still work the next time it is loaded in what was its elastic range of load?
Yes it will. But the elastic limit may not be the same as before, though it will be very close.

#### Abolfazl Rostamzadeh

Hello,

I will be appreciated with your suggestions and comments regard to Weight Measurement possibility & its precision using Strain Gauge (or better suggested sensor) at 0-1.0000 and 0-10.0000 grams ranges.

Best Regards,
Abolfazl Rostamzadeh

#### Gokul43201

Staff Emeritus
Science Advisor
Gold Member
I'm not at all familiar with any strain gages or load cells that go to such low loads with any accuracy. But I know for a fact that these exist.

The reason I know this is that you can buy a good electronic balance with an accuracy of 0.0001g. I know that Wiggen Hauser makes these.

You probably know the principal sources in error in a load cell : thermal fluctuations, creep, hysteresis and off-centering.

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