Strain gauges · Measurement

Bridge Signal to Strain Calculator (mV/V)

Convert a measured bridge signal in mV/V into strain and uniaxial stress, with correction of the quarter-bridge non-linearity per eq. 4.7.

DMSKeil 2017

Inputs

Bridge signal U_M/U_B [mV/V]Gauge factor kBridge factor BYoung's modulus E [N/mm²]

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

Results

Enter values and run the calculation.

Method

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)

Limits

Assumptions and typical mistake

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

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.

Inputs

What you enter – and where the values come from

Bridge signal U_M/U_B [mV/V]: The bridge signal is what the amplifier delivers as raw value: the Wheatstone bridge output divided by the excitation, in millivolts per volt. A typical strain-gauge transducer delivers 1 to 2 mV/V at rated load; 1000 µm/m on a single gauge with k = 2 give 0.5 mV/V. Source: amplifier reading in mV/V mode after zero balancing, or a transducer test certificate.
Gauge factor k: The gauge factor is the sensitivity of the strain gauge: it states how much the electrical resistance changes when the gauge is stretched (ΔR/R = k·ε). Without it no strain can be computed from an electrical signal. Source: printed on every gauge package or in the manufacturer datasheet, typically 2.0 to 2.1 for constantan foil gauges; valid at room temperature. The same value must be set in the amplifier.
Bridge factor B: The bridge factor states how many times the strain of a single gauge is contained in the signal – it depends only on the wiring: 1 for a single gauge (quarter bridge), 2 for two gauges top/bottom in bending, 4 for four gauges in bending or torsion, 2(1+ν) ≈ 2.6 for two longitudinal and two transverse gauges on a tension rod. Source: read from your own wiring or determine with the ‘quarter, half and full bridge’ calculator. Note: if B is already set in the amplifier it displays strain directly – then enter 1 here.
Young's modulus E [N/mm²]: Young's modulus describes how stiff the part's material is – how much stress it takes to produce a given strain (σ = E·ε). It is needed to turn measured or computed strains into stresses and vice versa. Source: material tables or datasheet; steel ≈ 210 000 N/mm², aluminium ≈ 70 000 N/mm², titanium ≈ 110 000 N/mm². E drops at elevated temperature.

Context

What this calculator is for

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

What comes next

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

Results

How to read the results

The strain applies to one single active gauge; for full bridges it is not the sum of the four gauges.
Adopt σ = E·ε only for uniaxial loading along the gauge; for biaxial states measure two strains and use the principal-stress calculator.

Result quantities

What each value means

Strain ε (linear) [µm/m]: Strain at one active strain gauge calculated from the raw signal. Use it for the subsequent stress or load calculation; for a full bridge it is not the sum of all four gauges.
Strain ε, quarter bridge exact (eq. 4.7) [µm/m]: Quarter bridge only (B = 1): strain per the exact bridge equation. The difference from the linear approximation is about the strain itself (0.1 % at 1000 µm/m).
Resistance change ΔR/R [‰]: Corresponding relative resistance change of the active gauge in per mille. It is mainly a plausibility value for sensor checks and troubleshooting; use strain for subsequent component calculations.
Stress σ = E·ε (uniaxial) [N/mm²]: Stress along the gauge per σ = E·ε. Valid only if no stress acts transverse to the gauge (tension rod, outer fibre in bending). For biaxial states use the principal-stress calculator.

Source

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.

FAQ

Frequently asked questions

How large is the non-linearity at 0.5 mV/V?

ΔR/R₀ = 4·0.0005/(1−0.001) = 2.002 ‰ instead of 2.000 ‰, i.e. 0.1 %.

What if the amplifier reads µm/m?

Then it has already applied its gauge and bridge factors; only deviations need correcting (ε = ε_reading·k_instrument/k_gauge).

Can I compute σ this way for bending?

Yes, the outer-fibre stress is uniaxial; ε must be the bending strain of one gauge, not B times it.

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