5. (20) Consider the cantilever beam setup from the lab, strain gauge where a qu

Question

5. (20) Consider the cantilever beam setup from the lab, strain gauge where a quarter-bridge circuit was implemented with a strain gauge as shown. Suppose VcH was measured at 0.10 [mV] under no loading, and then-1.00 [mV] was measured under an unknown constant loading of P [N]. The excitation voltage was 5 [VI i) Assuming Ru is negligible, the nominal gauge resistance R is 120(Q)+0.3%, and the gauge factor is 2.1±0.5%, what is the calculated strain? Ru Ri A)-3.4×104, B) 4.2x104, C) 8.4-1r', D) 1.3x10, E) 3.8x10, F) other value (specify: ii) Given the strain from (i), we want to solve for the loading p, based on the theoretical equation, where we have the following data: /-/00t0.1 [mm], w-20+0.1 [mm], ,-3±0.1 [mm], E-700 5 [GPa]. What is the loading and propagated uncertainty? Assumptions: the uncertainty ofl, w, and t may be random but certainly not independent:; the uncertainty of E is random and independent from other parameters; the uncertainty of the calculated strain from (i) is 3% and considered random and independent. Loading: A) 7.1[N], B) 8.8]NI, C) 18]NI, D) 27[NI, E) 8NI. F) other value (specify: ) Uncertainty: A) 1%, B) 2%, C) 4%, D) 8%, E) 16%, F) other value (specify: Ri Ry = Ewt2

Explanation / Answer

Under No loading Vch= 0.10 mV

Under Unknown const loading Vch= -1.00 mV

Excitation voltage 5V

i) RL tends to zero

R4= 120+-0.3%

Gauge factor = 2.1+-0.5%

We know that , Gauge Factor= (deltaR/R)/strain

                          2.1=( 0.3/120)/strain

                         strain =0.0013

Answer. D)

Delta strain = delta R/ delta GF = 0.5-0.3= 0.2……………..eq 1

ii) strain= 6tp/(Ewt*t)

0.0013= (6*100*p*0.001)/(70*20*3*3)

           =27.3 N

Answer. D)

Uncertainity in propagation

Delta strain = Delta l+ Delta p- Delta E – Delta w – 2*Delta t

From eq 1 we have Delta strain as 0.2 ,

Therefore,

0.2= 0.1*100/100 + delta p – 0.5*100/70 -0.1/20*100 -2*0.1*100/3

Delta p= 7.9%

Answer. D)

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