Strain and stress from the bridge signal (mV/V)

What is calculated?

The amplifier displays the bridge voltage ratio. Gauge factor and bridge factor turn it into strain; for the quarter bridge the exact eq. 4.7 yields a slightly larger strain than the linear approximation at large signals. Converting to stress is valid only for a uniaxial stress state – biaxial states need two strains and Hooke's law per eqs. 9.27/9.28.

Equations

ε = 4·(U_M/U_B)/(k·B) (aus Keil Gl. 4.8)

Viertelbrücke exakt: U_M/U_B = ΔR/(2(2R₀+ΔR)) ⇒ ΔR/R₀ = 4s/(1−2s) (Keil Gl. 4.7)

σ = E·ε (einachsig)

Step by step

1. Enter the signal in mV/V, gauge factor and bridge factor of the circuit used.
2. For quarter bridges above 1 mV/V use the exact value.
3. Adopt σ = E·ε only for uniaxial loading along the gauge.

Typical mistake

Using the amplifier's fixed gauge factor 2.00 although the gauge has 2.08, or entering the signal in mV instead of mV/V.

Application and limits

Evaluating raw signals from data loggers without a strain-gauge mode, converting transducer sensitivities and checking amplifier settings (gauge factor, bridge factor).

Lead resistance, transverse sensitivity and temperature response are excluded; the non-linearity correction applies to one active arm only (B = 1).

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 4.2, eqs. (4.7), (4.8), fig. 4.2; sec. 9.4, eqs. (9.27), (9.28).

The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.

Frequently asked questions

In the same cluster

• Strain-gauge basic equation: resistance change from strain and gauge factor
• Transverse sensitivity: correction for two perpendicular gauges
• Temperature response: apparent strain of a gauge under temperature change
• Bridge excitation voltage and gauge self-heating
• Wheatstone bridge: output voltage of the unbalanced bridge
• Basic strain-gauge bridge equation: signal from four strains

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