Calculate the bridge factor B and output signal for Keil's nine elementary strain-gauge bridge circuits from strain, gauge factor and Poisson's ratio.
Enter values and run the calculation.
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)
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.
Applying the bridge factor twice (many amplifiers already include B) or using longitudinal strain instead of 45° strain for torsion.
One card per selectable circuit, in the order of the selector above: first, where the grids sit on the part and in which direction they are strained, then the Wheatstone bridge with Keil's arm occupancy – strains in opposite arms add, strains in adjacent arms cancel.
The general bridge equation is U_M/U_B = k/4·(ε₁ − ε₂ + ε₃ − ε₄): strains in opposite arms count positive, in adjacent arms negative. Expressing every active strain as a multiple of one reference strain ε, B is exactly that signed sum of multiples – e.g. B = 2 for two adding contributions, B = 4 for four. U_M/U_B = k·B·ε/4 summarises this.
To assess it: B is a pure gain of the circuit, not a statement about temperature compensation or which load type is in the signal – that is covered by “Use” and the response chips below. A larger B gives a larger, more easily measured signal U_M for the same mechanical strain; this calculator inserts B into the calculation automatically once you pick a circuit, so you never enter it yourself.
Layout: One longitudinal gauge on the part; the other three bridge arms are fixed resistors in the instrument.
Use: Only at constant temperature and for a known uniaxial stress state along the principal direction.
Keil Abb. 4.8, Gl. 4.10
Layout: Active longitudinal gauge on the part; the compensation gauge in the adjacent arm sits on an unloaded piece of the same material at the same temperature.
Use: The circuit used most often in stress analysis: measures the mechanical strain at one point with temperature compensation.
Keil Abb. 4.9, Gl. 4.11
Layout: Two gauges at the same spot, one along and one across the bar axis, in adjacent bridge arms. The transverse gauge measures −ν·ε.
Use: When a separate compensation gauge is inconvenient or impossible; uniaxial stress only.
Keil Abb. 4.10, Gl. 4.12
Layout: One longitudinal gauge each on the top and bottom face of the beam, in adjacent bridge arms (top +ε, bottom −ε).
Use: The ideal half bridge for bending measurements on bars.
Keil Abb. 4.11, Gl. 4.13
Layout: Active longitudinal gauges on top and bottom in opposite arms; the two adjacent arms carry compensation gauges on unloaded blocks.
Use: Measuring axial force when bending is superimposed and transverse gauges cannot be used.
Keil Abb. 4.13, Gl. 4.15
Layout: Two longitudinal gauges each on top and bottom, wired alternately: gauges strained alike sit in opposite arms, oppositely strained ones in adjacent arms.
Use: Ideal for bending-loaded measuring elements and transducers (bending-beam load cells).
Keil Abb. 4.14, Gl. 4.16
Layout: One longitudinal and one transverse gauge each on top and bottom; the longitudinal gauges sit in opposite bridge arms.
Use: The typical circuit of axially loaded force-measuring elements and simple force transducers.
Keil Abb. 4.15, Gl. 4.17
Layout: Two perpendicular gauge pairs at 45° to the shaft axis, 180° apart around the circumference; the two gauges of a pair sit in adjacent arms.
Use: The ideal arrangement for measuring torque.
Keil Abb. 4.16, Gl. 4.18; Abschn. 10.2.3
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.
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.