Plane Stress Analysis Homework: Determining σx' and Tx'y' Angle with Equations

[stpmmaths]

Homework Statement

Homework Equations

The Attempt at a Solution

I'm in doubt the angle that I should be using to solve σ_x' and T_x'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

-30

 

[stpmmaths]

B u m p!

 

[stpmmaths]

B u m p!

I just want to know the angle. Thanks.

 

[nvn]

60 deg

 

[stpmmaths]

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?

 

[nvn]

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.

 

[stpmmaths]

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

The angle I will be using is 120 or -60 deg, right?

 

[nvn]

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.

 

[stpmmaths]

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.