Strain gauge - determination of x and y strains

[Aerstz]

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

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?

 

[nvn]

Presumably, E = 200 GPa, and nu = 0.30. Hint: eps_x = (sigma_x - nu*sigma_y)/E, and eps_y = (sigma_y - nu*sigma_x)/E. But by inspection, what is the value of sigma_y? Now substitute into your given relevant equations, and solve for the unknowns.

 

[Aerstz]

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]

OK. Hint: gamma_xy = (eps_x - eps_y)*tan(2*theta₁).

 

[Aerstz]

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]

eps_x, eps_y, and theta₁ are given in post 1. Hint 3: eps_x = -65 microstrain. Hint 4: theta₁ = 75 deg. See hint 2 in post 4.

 

[Aerstz]

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]

Aerstz: The people who said you need only two gauges to solve this problem are correct. Those people who said you need three gauges appear to be incorrect. You only need two gauges as given in post 1.

Some confusion is caused by somewhat confusing nomenclature; therefore, I will try to clarify. In your relevant equations in post 1, you called the strain gauge coordinate system the x and y axes. However, the problem statement in post 1 also seems to imply that the steel bar orthogonal axes are also called the x and y axes. You used the same name for both coordinate systems, so I tried to use your nomenclature. It might be more clear to you to call the steel bar orthogonal coordinate system the x' and y' axes. Therefore, change each x and y in the first two and last two sentences of post 1 to x' and y'; but leave all other x and y subscripts, in your relevant equations and in all my posts, as x and y.

Rewrite your relevant equations in post 1 using the correct 1 or 2 subscript on each theta. Also, remove the second right-hand side of your relevant equations in post 1, which is wrong. See hint 3. Now compute the equations to obtain the answer. No third gauge needed.

Aerstz wrote: "epsx and epsy are what I am trying to calculate, so I do not ..."

No, you are now trying to calculate eps_x' and eps_y'. Strains eps_x and eps_y are already given in post 1.