Question

3. Two different types of strain gauges with a nominal resistance of 120 2 are both used to measure an axial strain in Figure 3. They are connected to a Wheatstone bridge (the lead wire effect is negligible) at R1 and R3 R3 is a nickel wire strain gauge with a gauge factor -12.1 and R1 is a nicrome wire strain gauge with a gauge factor 2.1. The bridge has a supply voltage of 4.5V and two fixed resistors R2 and R4 are 6022 and 24092, respectively. The strain gauges are attached to the surface of an aluminium cantilever beam. The Young's modulus of aluminium is 6.89 x 1010 N/m² and Poisson's ratio is 0.32. The bridge is initially balanced. What will be the bridge output (in mV) when the structure is axially strained by 500 ustrain (tensile), assuming that tensile strain is positive?. (Answers must match to 2 decimal places) [20 marks] R3 Figure 3

Answer 1

Given,

Two different types of strain gauges with a nominal resistance of 120 Ω are both used to measure an axial strain in given figures

Here R1 refers to tensile stress and

R2 refers to compressive stress

Answer :- Consider two different types of strain gauges with nominal resistance of 1200 are both used to measure an arial strain in the yolu'ng figures: DO Lent BAN In the diagram eve observed that Ro/R Luulere Rg geefers to ensile fires and R, refers to compressive stress

We need to calculate the Gauge factor for RIER from the giun decra, R: 120 Strain = 500 i strain Gauge factor - -122 for Ri Gauge factor (AR/R) 시지 ARIR strain -AR. Gauge factor x Strain and for AR · Gauge factor x Hrain AR: 421) X(-900 XI0G ) x 120 . ..-12.1 x -0.0005 X120 -1.91 X-006 = 0.726 ohm To R, is compressive strain] Strain must be ove /

Similarly, Arg · (21) X (600x106) X120 = 2.1% 0.0005 X 120 = :1 X0:06 : :0.126 cohm) Now the have to calculate output voltage Vo No Tel R3 )-C + Rx)] «VO a cluat otoue Rand R, que conhechd budge (elle lead wire effect is negligible) by B2 Strain gauges. (+12040126 ) - ( 130 20-126 4130 )pes 1120 120 +0426 -0.0088519 v [:10 = 100 mv .-8.8515 mV tem -8.8615 m