Find the principal stresses in a shaft with torque applied

  • #1

Homework Statement


8tgqJGX.jpg


Homework Equations


M = Fd
σ/y = M/I
T/J = τ/r
σalternating (σa) = σmax - σmin / 2
σmean (σm) = σmax + σmin / 2
soderberg: σa/σ'e + σm/σy = 1/FoS

The Attempt at a Solution


I am still unsure whether my progress so far is correct but..
I have calculated J to be 38.35e-9 m4 and I to be 19.17e-9 m4. I then use these values in the shear stress and normal stress equations to find that:

σ = 82.16 MPa
τ = 41.07 MPa

I apply these values to a loading element diagram (am I right in thinking there is no force in the y direction??) and then used Mohrs circle to find that the maximum and minimum principal stresses are:

σmax = 99.17 MPa
σmin = -17.01 MPa

When applying these values to the σalternating and σmean equations, I am not sure whether it is expressed as:

σa = σmax - σmin / 2
σa = 99.17 - (-17.01) / 2 OR
σa = 99.17 - 17.01 / 2

After I get the correct σa and σm values and I need to find a suitable factor of safety, I'll have σa, σm, σy but im not sure how im to find the σ'e, or is there a different method to finding a suitable factor of safety?
 

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Last edited:

Answers and Replies

  • #2
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I'm not sure whether they really intended for you to be considering the bending of the shaft in addition to the torque. What do you think?
 
  • #3
I'm not sure whether they really intended for you to be considering the bending of the shaft in addition to the torque. What do you think?
I see what you're saying, I guess when I saw 'principal stresses' I thought about what we had learnt in class and to draw mohrs circle. Im not sure how I would go about finding the maximum and minimum principal stresses without applying a bending stress? I have drawn the following loading element:

gNiNW9p.jpg


Im just unsure as to whether im on the right track with this..
 

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