Basic strain-gauge bridge equation: signal from four strains

What is calculated?

With equal nominal resistances in all arms, eq. 4.1 yields the basic equation 4.6. Its numerator shows the sign rule: strains in arms 1 and 3 count positive, in 2 and 4 negative. The denominator carries the sum of all resistance changes – if non-zero the bridge becomes non-linear, which matters most with a single active arm.

Equations

U_M/U_B = (ΔR₁−ΔR₂+ΔR₃−ΔR₄) / (2(2R₀+ΔR₁+ΔR₂+ΔR₃+ΔR₄)) (Keil Gl. 4.6)

U_M/U_B ≈ k/4·(ε₁ − ε₂ + ε₃ − ε₄) (linearisiert, Keil Gl. 4.10 ff.)

ΔRᵢ/R₀ = k·εᵢ

Step by step

1. Assign each arm its strain (fixed resistors and compensation gauges: 0).
2. Enter gauge factor and excitation.
3. Compare linearised and exact signals; for large strains evaluate with the exact value.

Typical mistake

Entering compensation gauges with their temperature apparent strain although it is equal in all arms and cancels – or forgetting the sign of compression.

Application and limits

Designing transducer circuits, checking temperature compensation (equal strain in all arms gives zero) and assessing quarter-bridge non-linearity on plastics or in the elasto-plastic range.

Equal nominal resistances and gauge factors in all arms, constant-voltage excitation, unloaded output.

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 4.2, eqs. (4.2)–(4.8); sec. 4.5, eqs. (4.10)–(4.18).

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
• Quarter, half and full bridge: bridge factor and signal

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