- What is your measured value?
- Choose which number you have. If the amplifier already shows a strain in µm/m (micrometres per metre; 1000 µm/m = 0.1 % change of length), choose strain. If it only shows the raw Wheatstone-bridge signal in mV/V (millivolts of output per volt of excitation), choose signal; gauge factor and bridge circuit are then needed for the conversion.
- Measured outer-fibre strain ε_b [µm/m]
- The longitudinal strain shown by a gauge bonded on the beam surface along the beam. On the stretched side it is positive, on the compressed side negative – in bending both of equal magnitude. For half or full bridges enter the strain of one single gauge, not the sum. Source: the amplifier reading after zero balancing with the beam unloaded.
- Bridge signal U_M/U_B [mV/V]
- The raw bridge signal: Wheatstone-bridge output divided by the excitation, in mV/V. Keil's bending spring gives 3.44 mV/V at limit load. Source: the amplifier reading in mV/V mode after zero balancing.
- Gauge factor k
- The gauge factor is the sensitivity of the strain gauge: it states how much the electrical resistance changes when the gauge is stretched (ΔR/R = k·ε). Without it no strain can be computed from an electrical signal. Source: printed on every gauge package or in the manufacturer datasheet, typically 2.0 to 2.1 for constantan foil gauges; valid at room temperature. The same value must be set in the amplifier.
- Bridge circuit
- How the gauges are wired – this sets the bridge factor B, i.e. how many times the outer-fibre strain is contained in the signal. One gauge: B = 1. One gauge top and one bottom in adjacent arms: the opposite strains add, B = 2. Two top and two bottom (Keil's bending spring, Fig. 10.10): B = 4, plus temperature and axial load compensated. Source: your own wiring or datasheet.
- Cross-section
- How the section modulus W_b is determined – the geometry figure linking bending stress and bending moment. Rectangle from width and height, circle from the diameter, or directly from a section table (e.g. for I-beams or tubes). Only the section exactly at the gauge position counts.
- Width b [mm]
- The width of the rectangular section across the bending direction – the dimension of the face the gauge is bonded on (Keil's spring: 10 mm). Enters linearly. Source: calliper or drawing.
- Height h [mm]
- The height of the rectangular section in the bending direction, i.e. the distance from the tension to the compression side (Keil's spring: 1 mm). It enters squared – a 1 % error in h is a 2 % error in the moment. Source: calliper or drawing.
- Diameter d [mm]
- The diameter of a round beam (axle, shaft journal, round bar) at the gauge location. It enters to the third power – a 1 % error in diameter is a 3 % error in the moment. Source: calliper or drawing.
- Section modulus W_b [mm³]
- The section modulus in bending in mm³, entered directly – only when ‘enter directly’ is selected. For rolled sections it is listed in section tables (often called W_y or W_el), for tubes π/32·(d_o⁴−d_i⁴)/d_o. It must belong to the axis about which bending actually occurs.
- Young's modulus E [N/mm²]
- Young's modulus describes how stiff the part's material is – how much stress it takes to produce a given strain (σ = E·ε). It is needed to turn measured or computed strains into stresses and vice versa. Source: material tables or datasheet; steel ≈ 210 000 N/mm², aluminium ≈ 70 000 N/mm², titanium ≈ 110 000 N/mm². E drops at elevated temperature.
- Lever arm x (0 = moment only) [mm]
- The distance from the centre of the gauge grid to the point where the force acts perpendicular to the beam – 18 mm for Keil's spring. The bending moment at the gauge is force times this distance, so x turns the moment into the force. Enter 0 if you only need the moment or the load point is unknown. Source: measurement on the part or drawing.