# Strain gauge - determination of x and y strains

## Homework Statement

Determine x and y strains in order to construct a Mohr's circle of strain.

A 2-gauge Wheatstone (the third/middle gauge was not working), with gauges 90-degrees apart, was attached to a specimen steel plate 15-degrees offset from the x and y axes. An axial load was applied to the plate on an Olsen tensile testing machine.

http://img39.imageshack.us/img39/8294/straingaugeplate.png [Broken]

## Homework Equations

Strain 1 = ((strain-x + strain-y)/2) + ((strain-x - strain-y)/2) cos (2theta) + ((shear strain-xy)/2) sin (2theta) = -65 micro strain

Strain 2 = ((strain-x + strain-y)/2) + ((strain-x - strain-y)/2) cos (2theta) + ((shear strain-xy)/2) sin (2theta) = 278 micro strain

These equations are usually used when a three-gauge rosette is used. The lecturer who set this assignment has moved to another university, and I am unable to reach him at the moment. The lecturer who took his place told me, over the telephone, that these equations only apply to a 3-gauge rosette and cannot be used for this problem. The new lecturer uses all three gauges for his experiment.

There is nothing in my notes explaining how to determine x and y strains where only two gauges of a rosette were used. Please could you help me to work out the x and y strains?

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nvn
Homework Helper
Presumably, E = 200 GPa, and nu = 0.30. Hint: epsx = (sigmax - nu*sigmay)/E, and epsy = (sigmay - nu*sigmax)/E. But by inspection, what is the value of sigmay? Now substitute into your given relevant equations, and solve for the unknowns.

Thanks for your reply. Unfortunately, one of the aims of this assignment is to use the strain gauge data in order to determine Poisson's and Young's. I am unable to use them to calculate for strain.

nvn
Homework Helper
OK. Hint: gammaxy = (epsx - epsy)*tan(2*theta1).

I read that gamma xy cannot be determined with fewer than three gauges. I am thinking this is incorrect.

I am afraid that I am unable to find epsx and epsy from your hint.

nvn
Homework Helper
epsx, epsy, and theta1 are given in post 1. Hint 3: epsx = -65 microstrain. Hint 4: theta1 = 75 deg. See hint 2 in post 4.

epsx and epsy are what I am trying to calculate, so I do not understand how they can be the same as the values in post 1, which are offset 15 degrees from their respective axes.

I have since been able to speak with the original lecturer who set this experiment. He told me that I should have all three sets of data from all three strain gauges of the rosette. I arrived in the lab for this experiment several minutes late, and group had started without me. They assured me that we only needed to work with the two gauges (1 and 3). Even the lab technician told me that this lecturer only used the two gauges and never all three! So I do not know what was going on!

Anyway, the current lecturer has given me three strain values with which I am to construct a strain circle (to save me from repeating the experiment). This means I am no longer in need of the x and y values which I started this thread in order to find. However, after reading that a 2-gauge 90 degree strain gauge - known as a tee rosette - needs to be precisely mounted on the x and y axes, and after being told by two lecturers that I definitely do need the three strain gauge values in order to draw the Mohr's circle of strain, I am interested to see if there actually is a way of determining epsx and epsy from the values given in post 1.

Thanks, nvn.

nvn