MethodWhat is calculated?
On a cantilever the bending moment grows linearly towards the clamp; gauges are installed close to the clamp on top and bottom where tensile and compressive strains are equal in magnitude. Four alternately wired gauges add all individual signals (U_M/U_B = k·ε) and reject axial force and temperature. Keil's spring-tongue example: 32.6 N at a 30 mm lever arm gives ±1676 µm/m and 1.68 mm deflection.
Equations
σ_b = ±M_b/W_b = ±F·x/W_b (Keil Gl. 10.6)
W_b = b·h²/6 (Gl. 10.7)
ε = ±F·x/(E·W_b) (Gl. 10.11)
f = F·l³/(3EI), I = b·h³/12 (Gl. 10.10)
U_M/U_B = k·ε (Vollbrücke, Gl. 10.14) bzw. k·B·ε/4
ProcedureStep by step
- Enter beam geometry, force and the gauge distance from the load point.
- Check that σ_b stays below roughly 50 % of the yield strength (Keil).
- Choose the circuit and compare the signal with the amplifier range.
Typical mistake
Using the gauge distance instead of the free length for deflection, or swapping h and b (ε depends on h²).
PracticeApplication and limits
Bending-beam load cells, spring tongues as force or displacement transducers, stress measurement on cantilevers and booms.
Bernoulli beam with rectangular section, gauge grid centred at x, no shear deformation, no notch effect at the clamp.
SourceTechnical basis
Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 10.2.2.2 cantilever beam, eqs. (10.6)–(10.14); sec. 4.5, eqs. (4.13), (4.16).
The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.
FAQFrequently asked questions
Why not measure right at the clamp?
Notch effects and clamp reactions disturb the field there; Keil recommends a small offset, accounted for in the lever arm x.
What changes with a half bridge?
The signal halves relative to the full bridge; axial force and temperature remain compensated.
Does it apply to simply supported beams?
Only for the cantilever moment distribution; for other supports determine M_b at the gauge separately (Keil 10.2.2.3/10.2.2.4).
In the same cluster
All strain-gauge calculators