Universidade Federal do Rio Grande do Sul (UFRGS)
Programa de Pós-Graduação em Engenharia Civil (PPGEC)
12. Strain gages and load cells
12.1. Strain gage principles
12.2. Wheatstone bridge configuration
12.3. Strain gage installation
12.4. Load cell design
12.5. Bridge signal conditioning
Prof. Marcelo M. Rocha, Dr.techn. (ORCID)
Porto Alegre, RS, Brazil
R = 350.
K = 2.1
e = 1/1000.
DR = R*K*e
print(DR)
VA = 5*(350 + DR)/(2*R)
VB = 5*(350 - DR)/(2*R)
G = 128
print(G*(VA - VB))
0.735 1.344000000000051
A Wheatstone bridge can be seen as a double voltage divider. The resistors can be replaced by strain gages as shown below:
For the full bridge with four strain gages the voltage difference, $\Delta V = V_2 - V_1$, between the central nodes are given by:
$$ \Delta V = \frac{1}{4}\left( \frac{\Delta R_A}{R_A} + \frac{\Delta R_B}{R_B} + \frac{\Delta R_C}{R_C} + \frac{\Delta R_D}{R_D} \right) V_{\rm in} $$To maximize this difference, variations $\Delta R_A$ and $\Delta R_C$ must opose the variations $\Delta R_B$ and $\Delta R_D$. In the best case, with all gages subjected to the same strain and with oposition ensured, we get:
$$ \Delta V = K \varepsilon V_{\rm in} $$