How Do You Calculate Strain in a Faulty T-Delta Rosette Configuration?

AI Thread Summary
To calculate the strain recorded by gauge A in a faulty T-delta rosette configuration, the relationship between the strains measured by gauges B, C, and D must be carefully analyzed. The measured strains are eB = -135x10^-6, eC = 227x10^-6, and eD = -63x10^-6. It is essential to recognize that gauges B and C are not mutually perpendicular, which complicates the calculations. The correct approach involves adjusting the equations to account for the angles between the gauges, specifically noting that gauge A is perpendicular to gauge D. Ultimately, the solution hinges on correctly applying strain transformation equations to derive the missing strain value for gauge A.
jcurtis
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Homework Statement

For experimental validation of a design based on FEA, a prototype was tested using strain gauge rosettes at critical locations in a typical t-delta configurations, consisting of 3 gauges: A, B, C and fourth (extra) gauge D. D normally serves as a check on the strains recorded by the rosette arms. In this instance due to a fault in the measuring circuit, the strain response in gauge A could not be recorded the measured strains in the other three gauges were: eB = (-)135x10-6, eC=227x10-6 and eD= (-)63 x 10-6.
What would have been the strain recorded by gauge A?

Homework Equations


I found that J=eXX + eYY = eA + eC = eB + eD


The Attempt at a Solution

I've looked in my notes that my lecturers put online and I've been searching on google all day and I can't find anything. I know it has something to do with the fourth gauge, but there's no information on the web about it that I could find. The equation I found seemed too simple as the question is worth 8 marks. Or is it more simple than I'm making out? Can anyone help please?
 
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jcurtis: As I currently see it, you have four equations and four unknowns. Your relevant equation is currently incorrect; eB and eD are not mutually perpendicular. Try it again. And, you need to list three more equations, for strain in a strain gauge leg. You must list relevant equations yourself. The angle from gauge A to gauge D is 90 deg; but I think you knew that, right? Hint: thetaA = 0 deg.
 
Thanks for replying. So you're saying I should swap eB and eA around because a and d are perpendicular?
I can't find any other strain equations that aren't to do with resistance. other than principle strain equations which I need the value of A for, however I know it has to just do with the values of B, C and D as that's all they've given me.. Sorry I'm being a bit dense here, I'm just very confused.
 
Yes, swap eB and eA, then omit eB + eC from your above equation, because gauges B and C are not mutually perpendicular.
 
Hint 2: thetaYY = 90 deg. Do you have anything else at 90 deg? What does that tell you about the value of eYY?
 

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