Strain Gauge Fundamentals

What a Strain Gauge Actually Measures

A resistance strain gauge is a fine metallic grid bonded to the surface of a structure. When the surface strains, the grid strains with it, and its electrical resistance changes. The relationship between resistance change and strain is characterised by the gauge factor. The gauge measures the average strain in the direction of its grid conductors — the sensitive direction — over the area covered by the grid. It does not measure stress. It does not measure strain in any other direction. It does not measure strain below the surface. It measures one thing: the average extensional strain along its grid axis, over its grid length, at the surface to which it is bonded. Everything else — stress, principal strain, load — is derived from that single measurement by post-processing and assumption.

Why It Matters

Understanding exactly what a strain gauge measures — and what it does not — is essential for test–analysis correlation. The FE model produces a full strain field at every point in every direction. The strain gauge produces a single scalar value in a single direction at a single location. The correlation is only valid if the FE result is processed to represent exactly what the gauge measures: the strain in the gauge direction, at the gauge location, averaged over the gauge length. An engineer who compares a gauge reading against an FE von Mises stress, or against the maximum principal strain, or against the strain at the nearest node without directional transformation, is not correlating — they are comparing two unrelated numbers.

A strain gauge measures one thing: average extensional strain along its grid axis, over its grid length, at its bonded surface. Correlate the FE result to that, or do not correlate at all.

The Gauge Factor

The gauge factor is the fundamental calibration constant of a strain gauge. It relates the fractional change in resistance to the strain along the grid axis. For metallic foil gauges, the gauge factor is typically around 2.0. The gauge factor is supplied by the manufacturer for each gauge lot, and it should be entered into the data acquisition system so that the recorded microstrain is correct. Using a default gauge factor instead of the supplied value introduces a systematic error of a few percent into every measurement — a common and avoidable source of correlation discrepancy.

Gauge factor:

GF  =  (ΔR / R)  /  ε

where:
GF  =  gauge factor (dimensionless, typically ~2.0 for metallic foil)
ΔR  =  change in resistance due to strain
R   =  nominal gauge resistance (e.g. 120 Ω or 350 Ω)
ε   =  axial strain along the grid direction

Rearranged:  ε  =  (ΔR / R)  /  GF

The Wheatstone Bridge

The resistance change produced by structural strain is tiny — a gauge of 120 ohms with a gauge factor of 2.0 at 1000 microstrain changes resistance by only 0.24 ohms. Measuring this directly is impractical. The Wheatstone bridge converts this small resistance change into a voltage output that can be amplified and measured. The bridge has four arms; one or more arms contain strain gauges, and the remainder contain fixed or dummy resistors. The configuration — quarter, half or full bridge — determines the sensitivity, the temperature compensation and the ability to cancel unwanted strain components such as bending or axial load.

Microstrain and Typical Magnitudes

Strain is dimensionless — it is a ratio of length change to original length. Because structural strains are small, the working unit is the microstrain: one microstrain is one part per million, or 10 to the minus 6 strain. A strain of 1000 microstrain corresponds to a length change of one thousandth of the original length — 1 millimetre per metre. For typical structural metals with a modulus of around 70 to 200 GPa, the elastic strain at yield is of the order of 1000 to 4000 microstrain. Test strains in a correlation exercise are therefore typically in the range of tens to a few thousand microstrain. An engineer who sees a reported strain of 0.001 should recognise this as 1000 microstrain — and an engineer who sees a strain of 50,000 microstrain in a metal under a supposedly elastic load should immediately suspect an error.

Relationship between strain, microstrain and stress (elastic):

ε  =  ΔL / L          (dimensionless strain)
με =  ε × 10⁶          (microstrain)
σ  =  E × ε            (Hooke's law, elastic)

Example:  E = 70 GPa (aluminium),  ε = 1000 με = 0.001
          σ = 70,000 × 0.001 = 70 MPa

Installation: The Gauge Is Only as Good as Its Bond

A strain gauge measures the strain of its backing material, which measures the strain of the adhesive layer, which measures the strain of the structure surface. If any of these interfaces is poor, the gauge does not measure the structure — it measures the bond. Surface preparation is therefore critical: the surface must be clean, degreased, abraded to a consistent finish, and conditionened with the correct primer. The adhesive must be applied in a thin, uniform layer, with the correct curing schedule. The gauge must be pressed firmly and uniformly during cure. A gauge bonded to poorly prepared surface, or with a thick or bubbly adhesive layer, will under-read, will be sensitive to transverse strains it should reject, and will drift. Installation quality is not a detail; it is the measurement.

MISTAKE: Bonding a strain gauge to a poorly prepared or contaminated surface. The gauge then measures the bond behaviour, not the structure behaviour — and no amount of post-processing will recover the true strain.

Temperature and Thermal Output

When the temperature changes, a strain gauge reading changes even if the structure is not mechanically strained. This apparent strain — the thermal output — arises from two effects: the gauge alloy changes resistance with temperature, and the gauge and the substrate have different coefficients of thermal expansion, so the gauge is mechanically strained by the differential expansion. Manufacturers supply self-temperature-compensated gauges, where the alloy is selected so that its thermal resistance change partially cancels the differential expansion effect for a specific substrate material. This compensation is not perfect — it reduces thermal output but does not eliminate it. The residual thermal output is provided on the gauge packet as a curve of apparent strain versus temperature. In a test where temperature varies, this apparent strain must be subtracted from the reading, or a bridge configuration that cancels it (a dummy gauge on an unstrained piece of the same material at the same temperature) must be used.

Thermal output sources in a strain gauge:

  Temperature change ΔT
        ↓
  1. Gauge alloy resistance change  →  ΔR_thermal
  2. Differential expansion:        →  ε_thermal = (α_gauge − α_substrate) · ΔT
     gauge vs substrate expand differently
        ↓
  Total apparent strain = ΔR_thermal/(R·GF) + ε_thermal
        ↓
  Self-temperature-compensated gauge:
  alloy selected so the two effects partially cancel
  for a specified substrate — residual is small but nonzero

Gauge Resistance and Lead-Wire Effects

Strain gauges are commonly available in 120 ohm and 350 ohm resistances. The 350 ohm gauge is generally preferred for correlation work because it produces less self-heating for a given excitation voltage and is less sensitive to lead-wire resistance changes. Lead-wire resistance is a particular concern in a quarter-bridge configuration: the lead wires are in series with the gauge, and if their resistance changes with temperature, it appears as apparent strain. A three-wire quarter-bridge configuration cancels the lead-wire temperature effect by placing equal lead resistance in adjacent arms of the bridge. For long cable runs or varying temperatures, three-wire or even six-wire configurations should be used. Ignoring lead-wire effects introduces a systematic error that scales with cable length and temperature variation.

• Use 350 Ω gauges where possible — lower self-heating, less lead-wire sensitivity
• Use 3-wire quarter bridge to cancel lead-wire temperature effects
• Keep lead-wire lengths balanced and away from temperature gradients
• Check bridge balance and zero with the article in the unloaded, stabilised condition
• Record the gauge factor, gauge resistance and bridge configuration for every channel

Transverse Sensitivity

A strain gauge is designed to measure strain along its grid axis, but it also has a small sensitivity to strain perpendicular to the grid — the transverse sensitivity. This arises because the end loops of the grid conductors are strained by transverse strain. The transverse sensitivity is typically a few percent and is supplied by the manufacturer. In a biaxial strain field, the gauge reading includes a small contribution from the transverse strain, and if this is not corrected, the reported strain is slightly in error. The correction is straightforward if the two principal strains or the two orthogonal strains are known (as from a rosette), but it is often neglected in practice. For high-accuracy correlation, the transverse sensitivity correction should be applied.

Transverse sensitivity correction:

ε_reported  =  ε_axial  +  K_t · ε_transverse

ε_corrected  =  (ε_reported − K_t · ε_transverse) / (1 − K_t²)

where:
K_t            =  transverse sensitivity factor (typically 0.01 to 0.05)
ε_axial        =  true strain along grid axis
ε_transverse   =  true strain perpendicular to grid axis

Key Takeaways

• A strain gauge measures average extensional strain along its grid axis, over its grid length, at its bonded surface — nothing else
• The gauge factor (typically ~2.0) converts resistance change to strain; use the supplied value, not a default
• The Wheatstone bridge converts tiny resistance changes to voltage; quarter, half and full bridges trade sensitivity against compensation
• Microstrain (με) is the working unit; structural elastic strains are typically tens to a few thousand microstrain
• Installation quality and temperature compensation are as important as the gauge itself — a poorly bonded or uncompensated gauge measures artefacts, not structure

Key takeaways

• A strain gauge measures surface strain by converting mechanical deformation into a resistance change via the gauge factor — it measures strain in one direction only.
• The Wheatstone bridge converts the tiny resistance change into a measurable voltage; quarter-, half- and full-bridge configurations trade sensitivity against temperature compensation and bending cancellation.
• Microstrain (με) is the working unit of strain measurement — one microstrain is one part per million of deformation, and structural strains are typically tens to a few thousand microstrain.
• Gauge installation quality — surface preparation, bonding, wiring and environmental protection — is as important as the gauge itself; a poorly bonded gauge measures bond behaviour, not structure behaviour.
• Temperature changes produce apparent strain in a gauge through thermal output; self-temperature-compensated gauges and dummy-gauge bridges reduce but do not eliminate this effect.