| name | strain-gauge-measurement |
| description | Strain gauge measurement — gauge factor, Wheatstone bridge, rosette analysis, temperature compensation, principal strains, residual stress measurement, signal conditioning. |
| metadata | {"priority":7,"promptSignals":{"phrases":["strain gauge","strain gage","Wheatstone bridge","rosette analysis","strain measurement","gauge factor"],"minScore":3}} |
Strain Gauge Measurement — Complete Skill
Gauge Factor (GF)
Definition:
GF = (ΔR/R) / ε
ΔR = change in resistance; R = nominal resistance; ε = axial strain
Typical GF: constantan (A-alloy) ≈ 2.0; Karma ≈ 2.1; semiconductor ≈ 100–200
Gauge resistance: standard 120Ω; also 350Ω (lower noise for long leads)
Wheatstone Bridge
Quarter bridge (one active gauge):
V_out = V_ex × GF × ε / 4 (for small ε, linear approximation)
Exact: V_out/V_ex = (ΔR/R) / (4 + 2ΔR/R) ≈ (GF×ε)/4
Half bridge (two active gauges):
V_out = V_ex × GF × (ε₁ - ε₂) / 2
Bending measurement: ε₁ = +ε (tension), ε₂ = -ε (compression) → V_out = V_ex × GF × ε
Full bridge (four active gauges):
V_out = V_ex × GF × ε (maximum sensitivity; full cancellation of thermal effects)
Temperature Compensation
Gauge resistance changes with temperature: apparent strain error
Self-temperature-compensating (STC) gauges:
Matched to specific material thermal expansion; ±5 με/°C typical
STC number matches CTE of substrate (aluminum → STC-13; steel → STC-6)
Dummy gauge method:
Active gauge on test part; dummy gauge on identical unstressed piece at same temperature
Dummy in adjacent bridge arm → thermal changes cancel
Two-gauge (half bridge):
Both gauges at same temperature; mechanically arranged to double response → cancels temperature
Rosette Analysis
Three-gauge rosette measures principal strains when direction unknown
Standard configurations:
- 0°-45°-90° rosette (rectangular): most common
- 0°-60°-120° rosette (delta)
For 0°-45°-90° rosette (gauges A, B, C):
ε_A = εA; ε_B = εB; ε_C = εC (measured strains)
Principal strains:
ε₁,₂ = (εA + εC)/2 ± (1/2)√[(εA-εC)² + (2εB-εA-εC)²]
Principal angle:
tan(2θ_p) = (2εB - εA - εC) / (εA - εC)
Principal stresses (biaxial):
σ₁ = E/(1-ν²) × (ε₁ + ν ε₂)
σ₂ = E/(1-ν²) × (ε₂ + ν ε₁)
Maximum shear strain:
γ_max = ε₁ - ε₂
Signal Conditioning
Excitation voltage: typically 1–10 V DC or AC carrier
Higher V_ex → larger signal; but self-heating of gauge (limit: ΔT < 2°C in gauge)
Power density limit: P/A_gauge ≤ 2–8 W/cm² (for metal specimen)
Amplification: bridge output ≈ 0.5–10 mV for 1000 με at 5V excitation
Instrumentation amplifier (INA): high CMRR (>80 dB); gain 100–1000×
Filtering:
Anti-aliasing low-pass filter at < f_sampling / 2
Dynamic measurements: f_s ≥ 10× highest signal frequency
Residual Stress Measurement (Hole Drilling)
ASTM E837 standard method:
Drill blind hole (1.6–2.0 mm diameter) in center of 3-gauge rosette
Relieve residual stress → measure released strains
Calculate residual σ₁, σ₂, θ from calibration coefficients (a_bar, b_bar from E837)
Depth: typically 0.05–0.2 mm increments to 1.0 mm total
Limitation: ≤ 60% of yield strength (otherwise data invalid)
Digital Image Correlation (DIC) — Comparison
Full-field alternative to point gauges
Tracks speckle pattern on surface; measures displacement field
Strain = ∂u/∂x, ∂v/∂y — full strain field without bonded gauges
Installation Best Practices
Surface prep: grit blast or abrade; solvent clean; pH-neutral surface
Adhesive: M-Bond 200 (cyanoacrylate, fast); M-Bond 610 (epoxy, 260°C)
Leadwire: avoid bending near gauge; use solder tabs; strain relief
Waterproofing: M-Coat D (urethane); Gagekote for hostile environments
Check: zero strain output before loading; verify resistance 120±0.5Ω
Output
Provide: gauge selection (GF, R, STC), bridge configuration, V_out/V_ex per με [mV/V], rosette analysis (principal strains, principal angle, σ₁ and σ₂ [MPa]), temperature compensation method, signal conditioning gain required, sampling rate recommendation.
