A strain gage is a device for measuring small movements. Figure 12.12 shows a st

Question

A strain gage is a device for measuring small movements. Figure 12.12 shows a strain gage attached to a block that is being pulled in tension. The strain gage consists of a small wire that is bonded to the block [Figure 12.12(a)]. As the block stretches, it lengthens the strain gage wire and narrows its cross-sectional area. (Note: The volume of the strain gage wire is the same regardless of how far it is stretched.) (a) The strain gage wire is constructed from Monel metal. Calculate its resistance in the normal, unstretched geometry. (b) The block is stretched so the strain gage wire increases its length by 0.5%. What is the new resistance of the strain gage wire? (c) Seven strain gage wires can be mounted in parallel [Figure 12.12(b)] or series [Figure 12.12(c)] onto the block. In each case, calculate the resistance before being stretched and after being stretched to a 0.50% increase in length. To get the most precise measurement of the amount of stretching, which arrangement (parallel or series) would you recommend?

Explanation / Answer

(a) I found an electrical resistivity of 5.47 E-5 Ohm cm. This is 5.47 E-4 Ohm m. If we multiply this by the length of the wire and divide by the cross sectional area, we will get the resistance in Ohms R = 5.47E-4Ohm m*0.050m/(0.002m*0.00050m) = 27.4 Ohms (b) now it is 0.5% longer with the same volume, so the cross sectional area is smaller. Let's find the new cross sectional area. Volume divided by length equals area. Volume is 0.05*0.002*0.0005 = 5 E -8 m^3 V/l = A if the length grows by 0.5%, it is 100% + 0.5% as long as it was. So we multiply by 100.5% or by 1.005 5 E -8m^2/(1.005*0.050m) = 9.95025E-07 R = 5.47E-4Ohm m*0.05025m/(9.95025E-07m^2) = 27.6 Ohms (c) In parallel 1/Rtotal = 7/Rindividual or 1/Ri +1/Ri + 1/Ri + 1/Ri +1/Ri + 1/Ri +1/Ri 1/R totalnormal = 7/27.4Ohm R total normal = 3.91 Ohms 1/R total stretched = 7/27.6 Ohms R total stretched = 3.95 Ohms In series we add them up R total = 7*Rindividual R total normal = 191 Ohms R total stretched = 193 Ohms Recommendation is tough (3.95 - 3.91)/3.95 = (193-191)/193 so the percentage change is the same. I would go with the series, since it is easier to measure the same percentage change in a large resistance due to things like contact resistance, which add noise to the measurement.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.