Axial force transducer: strain, stress and bridge signal

What is calculated?

For a slender, axially loaded body the axial direction is principal direction 1. Two longitudinal and two transverse gauges wired alternately into a full bridge give the largest signal (B = 2(1+ν)) and cancel temperature and bending. Keil's force-transducer example: ν = 0.29 gives B = 2.58; with k = 2.1 and ε_l = 956 µm/m the sensitivity is 1.295 mV/V at 10 kN.

Equations

σ = F/A, ε_l = σ/E, ε_q = −ν·ε_l

U_M/U_B = k/4·(ε_l + νε_l + ε_l + νε_l) = k/4·ε_l·(2+2ν) (Keil Gl. 10.1, 10.2)

allgemein U_M/U_B = k·B·ε_l/4

Step by step

1. Enter rated force and measuring section; strain at rated load should be about 500–1500 µm/m.
2. Choose material data and circuit.
3. Match the sensitivity to the amplifier input range (typically 2 mV/V) and adjust the section if needed.

Typical mistake

Adding the transverse strain as a magnitude instead of through B, or entering A in cm².

Application and limits

Designing self-built force transducers and tie rods, assessing signal yield in rod or anchor force measurements and converting amplifier signals into forces.

Homogeneous uniaxial stress without notches; superimposed bending is compensated only in the full bridges, torsion does not affect longitudinal gauges.

Technical basis

Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 10.2.1 axially loaded objects, eqs. (10.1)–(10.5); sec. 4.5, eq. (4.17).

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
• Basic strain-gauge bridge equation: signal from four strains

All strain-gauge calculators