Finding the correct angle for stress transformation equations

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stpmmaths
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Homework Statement



5712887080_d9cf167096.jpg


Homework Equations



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The Attempt at a Solution



I'm in doubt the angle that I should be using to solve σx' and Tx'y'. Is 60 degree or -30 degree?
Ps: I know how to determine the principal stresses and max shear. Just the angle that I'm in doubt at.

60
5712325543_d432b6f6cb.jpg


-30
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Discussion

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B u m p!

I just want to know the angle. Thanks.
 
60 deg
 
nvn said:
60 deg

Why is it 60 deg but not -30 deg?

And how you see whether the line a-a is going to be the new x or y-axis?
 
Last edited:
stpmmaths: A plane is defined by its normal vector. The axis normal to the new plane is always x'. We see +x' is +60 deg from the +x axis. Theta is the angle measured from the +x axis to the +x' axis. The y' axis is parallel to line a-a. The +y' axis is +150 deg from the +x axis.
 
nvn said:
stpmmaths: A plane is defined by its normal vector. The axis normal to the new plane is always x'. We see +x' is +60 deg from the +x axis. Theta is the angle measured from the +x axis to the +x' axis. The y' axis is parallel to line a-a. The +y' axis is +150 deg from the +x axis.

So if the question is
5716044984_cdee889e42.jpg


The angle I will be using is 120 or -60 deg, right?
 
stpmmaths: Yes, 120 deg. Also try -60 deg, and see if it gives the same answer. If it gives the same answer, you can use either 120 deg or -60 deg.
 
nvn said:
stpmmaths: Yes, 120 deg. Also try -60 deg, and see if it gives the same answer. If it gives the same answer, you can use either 120 deg or -60 deg.

Thanks a lot! :D

Yup it gives the same answers.