Two different types of strain gauges with a nominal resistance of 120 are both u

Question

Two different types of strain gauges with a nominal resistance of 120 are both used to measure the longitudinal strain of a prismatic cantilever beam as shown in Figure 2. They are connected to a Wheatstone bridge (the lead wire effect is negligible) at R and R3. R is a nickel wire strain gauge with a gauge factor -12.1 and R3 is a nicrome wire strain gauge with a gauge factor 2.1. The bridge has a supply voltage of 5V and two fixed resistors R2 and R4 are both 1202. The strain gauges are attached longitudinally to the top/bottom surfaces of the aluminium cantilever beam whose 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 linearised output (in mV) when the top surface of the structure is stretched by 500 ustrain (tensile) under the load as shown in Figure 2, assuming symmetrical deformation with positive tensile strain and negative compression strain? Answers must match to 3 decimal places. [5 marks] R3 0 3 R1 Figure 2 Strain gauge measurements.

Explanation / Answer

Q2)

From the given figure R3 is under tensile stress and R1 is under compressive stress

Gauge Factor = (delta R / R) / (delta l / l ) = (delta R / R) / strain

delta R = ( Gauge Factor )*strain*R

delta R1 = ( Gauge Factor )*strain*R1

delta R1 = (-12.1)*(-500*10-6)*120

( R1 is under compressive strain hence strain value is negative )

delta R1 = (-12.1)*(-5*10-3)*12

delta R1 = 0.726 ohm                    ..........1

delta R3 = ( Gauge Factor )*strain*R3

delta R3 = (2.1)*(500*10-6)*120

( R3 is under tensile strain hence strain value is positive )

delta R3 = (2.1)*(5*10-3)*12

delta R3 = 0.126 ohm                    ..........2

Let Vo ne bridge output voltage

Vo= [(R2/R2 + R3) - (R1/R1 + R4)]*Vs

Vo= [(120 /120 + 120 + 0.126) - (120 + 0.726)/(120+0.726 + 120)]*5

Vo = [ (120/240.126) - (120.726)/(240.726) ]*5

Vo = [ 0.4997376 -0.5015079 ]*5

Vo = -0.0088515 V

Vo = -8.8515 V mV                     .............3

This is the required bridge output voltage in mV

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