How to Conclude -23.7 Corresponds to SigmaX' in Plane Stress Transformation?

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SUMMARY

The discussion centers on the application of the plane stress transformation equations to determine the principal stresses SigmaX' and SigmaY' at an angle of -23.7 degrees. Substituting this angle into the equations yields SigmaX' as -46.42 MPa and SigmaY' as 116.4 MPa. The key question raised is how to definitively associate the angle -23.7 with SigmaX' instead of SigmaY'. Understanding the relationship between the rotation angle θ and the transformed axes is crucial for clarity in this context.

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influx
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When one substitutes the angle -23.7 into the plane stress transformation equation for SigmaX' you indeed get -46.42 MPa (as shown in the images). However, if you substitute this same angle into the plane stress transformation equation for SigmaY', you yield the other principal stress of 116.4 MPa. My question is how can you conclude the angle -23.7 corresponds to SigmaX' rather than SigmaY' ?
 
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influx said:
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When one substitutes the angle -23.7 into the plane stress transformation equation for SigmaX' you indeed get -46.42 MPa (as shown in the images). However, if you substitute this same angle into the plane stress transformation equation for SigmaY', you yield the other principal stress of 116.4 MPa. My question is how can you conclude the angle -23.7 corresponds to SigmaX' rather than SigmaY' ?
The angle θ is the angle that you have to rotate the x-axis to get the x' axis.

Chet
 
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what the difference between angles of theta p and theta which it used to find sigma theta?
 

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