Equation (12) in the original article [1] gives the strain from the measured voltage on a full bridge configuration of the four strain gages. The full-bridge is intended to measure tension-compression strain (type III full-bridge), the correct equation is therefore [2]

$$ \begin{array}{@{}rcl@{}} V_{r}(t) = \frac{e(t)}{V_{\text{ex}}} \end{array} $$
(1)
$$ \begin{array}{@{}rcl@{}} \epsilon_{\text{III}}(t) = \frac{2 V_{r}(t)}{\kappa[(1+\nu) -V_{r}(t)(1-\nu)]} \end{array} $$
(2)

and not

$$ \epsilon_{\text{II}}(t) = \frac{2 V_{r}(t)}{\kappa(1+\nu)} $$
(3)

which corresponds to a type II full-bridge for bending measurements (see table 12.2 in [2]). κ is the gage factor, Vr the bridge output and Vex the excitation voltage.

The measurement uncertainty on the strain was given as (see equation (13) in [1]):

$$ \begin{array}{@{}rcl@{}} \left[\frac{u\left( \epsilon_{\text{II}}(t)\right)}{\epsilon_{\text{II}}\left( t\right)}\right]^2 &=&\left[\frac{u\left( \kappa\right)}{\kappa}\right]^2 + \left[\frac{u(\nu)}{1+\nu}\right]^{2}\\ &&+ \left[\frac{u(V_{\text{ex}})}{V_{\text{ex}}}\right]^{2} + \left[\frac{u(e(t))}{e(t)}\right]^{2} \end{array} $$
(4)

which holds only in case of type II full-bridge (Equation 3). For type III full-bridge, from Equation 2 and the rules for expressing uncertainty (see [3]), the uncertainty in the strain is:

$$ \begin{array}{@{}rcl@{}} \left[\frac{u(\epsilon_{\text{III}})}{\epsilon_{\text{III}}}\right]^{2}\! &=& \!\left[ \frac{(1+V_{r})\nu}{(1\!+\!\nu)\!-\!V_r(1\!-\!\nu)} \right]^{2} \left[\frac{u(\nu)}{\nu}\right]^{2}+\left[\frac{u(\kappa)}{\kappa}\right]^{2}\\ &&+ \left[ \frac{1+\nu}{(1\!+\!\nu)\!-\!V_r(1\!-\!\nu)} \right]^{2} \left[\frac{u(e)}{e}\right]^{2}\\ &&+ \left[ \frac{1+\nu}{(1\!+\!\nu)\!-\!V_r(1\!-\!\nu)} \right]^{2} \left[\frac{u(V_{\text{ex}})}{V_{\text{ex}}}\right]^{2} \end{array} $$
(5)

□

A first order asymptotic approximation of Equation 2 gives

$$ \epsilon_{\text{III}} = \frac{2V_{r}}{\kappa(1+\nu)} \left( 1 + o(V_{r}) \right) $$
(6)

Finally, the order of magnitude of Vr during the experiments was of a few thousandth. The consequences of the bridge type error on the results (i.e. strain and measurement uncertainty on the strain) are therefore negligible.