Thread: Strain Gauge Mechanics

I have some strain gauge calculations to complete to produce a mohr-coloumn circle for rock mechanics, but I seem to be missing a trick with completing the initial calculations.

To be honest, the application probably doesn't matter as the bit I'm stuck on is more a rearrangement of equations.

Q is the radius of the circle which is what I am trying to find, along with E1 and E2 to produce the circle.

The example I have runs through as follows:

Q.Cos 2θ = -363
Q.Sin 2θ = -90.64
Q2 = Q2.Sin2 2θ+ Q2Cos2 2θ = 131769+8215.61
Q = 374.15

The 2's in green are to represent squared symbols as I can't produce an elevated 2 in the message composition box.

I have calculated Q.Cos 2θ and Q.Sin 2θ for my problem, but can't figure out how to get Q2.Sin2 2θ+ Q2Cos2 2θ as eveything is squared apart from 2θ. Am I missing something obvious?!

All help would be greatly appreciated.

I found a way of solving the above using the following, but I still don't get how the example sorts things through.

tan2θ = 0.249
2θ = tan-1 0.249 = 13.98
θ = 7

Q.cos13.98 = -363
Q.0.970 = -363
Q= -374.2