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

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Discussion Overview

The discussion revolves around determining the correct angle to use for calculating σx' and Tx'y' in a plane stress analysis homework problem. Participants explore different angle measurements and their implications for the analysis.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses uncertainty about whether to use a 60-degree or -30-degree angle for the calculations.
  • Another participant confirms that the angle should be 60 degrees.
  • A question is raised about how to determine whether line a-a will be the new x or y-axis.
  • One participant explains that the angle is measured from the +x axis to the +x' axis, indicating that the y' axis is parallel to line a-a.
  • There is a suggestion to also consider 120 degrees or -60 degrees as potential angles, with a note that both should yield the same results.
  • Participants confirm that using either 120 degrees or -60 degrees produces the same answers.

Areas of Agreement / Disagreement

There is no clear consensus on the angle to use, as participants propose different angles (60 degrees, -30 degrees, 120 degrees, -60 degrees) and discuss their validity without reaching a definitive agreement.

Contextual Notes

Participants rely on definitions of angles in relation to the x and y axes, but there are unresolved aspects regarding the implications of choosing different angles for the calculations.

stpmmaths
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Homework Statement



5712887080_d9cf167096.jpg


Homework Equations



5712325509_c275e8a59f.jpg


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
5712887164_15f0099237.jpg
 
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B u m p!
 
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.
 

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