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So, I am learning about how strain gauges work and I understand that through stretching or compressing resistance of the staring gauge can be changed which can be measured in resistance accurately connected to a wheat stone bridge or some kind of bridge and the voltage difference is amplified by an op amp.

Okay, so far sounds good.

But with the values of resistance and voltage difference, how do you exactly use this information to calculate the force caused by the strain. I couldnt find where to look for this equation or information in general. Maybe I am asking questions about mechanism too much but was just curious to know exactly how strain gauge could be used to calculate force in a load cell for example.

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Gauge Factor is the first element you're looking for.

As described in that link to Wikipedia, the Gauge Factor of a Strain Gauge is the ratio of relative change in electrical resistance \$ R \$ , to the mechanical strain ε, and is defined as:

\$GF = \frac{\Delta R / R}{\Delta L / L} = \frac{\Delta R / R}ε = 1 + 2v + \frac{\Delta \rho / \rho}ε \$
where

  • ε = strain = \$ \Delta L / L_0 \$
    • \$ \Delta L \$ = absolute change in length
    • \$ L_0 \$ = original length
  • ν = Poisson's ratio
  • \$ \rho \$ = resistivity
  • \$ \Delta R \$ = change in strain gauge resistance due to axial and lateral strain
  • \$ R \$ = unstrained resistance of strain gauge

But knowing the gauge factor of your strain gauge(s) is only part of what you need to calculate the force exerted on a load cell.
The mechanical construction of the load cell determines the relationship between the \$ \Delta L \$ of the strain gauge(s) to the amount of force applied to the load cell.
It's been a while since I last worked with mechanical engineers who understood and explained those details to me, but this factor obviously depends on the material the load cell is constructed from and the dimensions & geometry of the construction.

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    \$\begingroup\$ I've read the maximum strain should remain less than 0.1% (1,000 ppm) of the yield point. \$\endgroup\$ – analogsystemsrf May 8 '19 at 3:42

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