Determine the bridge factor B and output signal for Keil's nine elementary strain-gauge bridge circuits from strain, gauge factor and Poisson's ratio.
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Whether a gauge is wired as quarter, half or full bridge determines the signal size and which loads and disturbances cancel. The bridge factor summarises how often the active strain appears in the signal: in bending full bridge VII all four gauges add (B = 4), in longitudinal/transverse layouts the transverse gauge contributes only ν-fold.
U_M/U_B = k·B·ε/4
B = 1 (I, II), 1+ν (III), 2 (IV, VI), 4 (VII, IX), 2(1+ν) (VIII) (Keil Gl. 4.10–4.18)
Applying the bridge factor twice (many amplifiers already include B) or using longitudinal strain instead of 45° strain for torsion.
Choosing the wiring for stress analysis and transducer design, converting the amplifier reading into strain via 'strain per mV/V', and checking whether a circuit rejects temperature or axial components.
Linearised relation; assumes equal gauge factors, ideal alignment and, for III/VIII, a uniaxial stress state. Circuit V (2 active, no compensation) is temperature-sensitive and not included.
Keil, Dehnungsmessstreifen, 2nd ed. 2017, sec. 4.5 elementary bridge circuits, eqs. (4.10)–(4.18), figs. 4.8–4.16.
The source supports the equation structure and worked examples; this calculator does not replace calibration of the measuring chain.
Half bridge IV and full bridge VII (top/bottom) reject axial force and temperature response and measure pure bending.
The transverse gauge sees only ν times the longitudinal strain with opposite sign.
The conversion factor for the amplifier reading: 4/(k·B); with k = 2, B = 1 that is 2000 µm/m per mV/V.