Angular speed that breaks a spinning body apart with inertial stress

  • #1
olgerm
Gold Member
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How to find the angular speed, on which a spinning hollow cylindrical body breaks due to inertial stress(force)?
I found 2 sources(http://www.roymech.co.uk/Useful_Tables/Cams_Springs/Flywheels.html (last 2 equations) , https://www.engineersedge.com/mechanics_machines/solid_disk_flywheel_design_14642.htm (eq. 4) ) that offer different formulas to calculate tangential and radial stresses. One of them claims that maximum radial stress is at ##r=\sqrt{r_1*r_2}## and other one that it occurs at ## r=0##. Which one of these is correct?
Is it that the body breaks if
##\sigma_{tangential}>\sigma_{ultimate\ stress}\ or\ \sigma_{radial}>\sigma_{ultimate\ stress}##
or if
##(\sigma_{tangential}^2+\sigma_{radial}^2)>\sigma_{ultimate\ stress}^2##
 
Last edited:

Answers and Replies

  • #2
olgerm
Gold Member
472
26
More generally how determine if a body breaks if I know stress tensor appllyied on that body and mechanical propetis of that body?
 
  • #4
olgerm
Gold Member
472
26
I heard that it has something to do with principal stresses. Can someone explain that to me with more details how to determine whether body breaks based on principal stresses applied on the body?
 
  • #5
olgerm
Gold Member
472
26
More generally how determine if a body breaks if I know stress tensor appllyied on that body and mechanical propetis of that body?
What about simple case when it pushed from 2 sides so that the stress tensor is:
##\begin{bmatrix}
\sigma_{xx}&0 &0 \\
0&\sigma_{yy}&0\\
0&0&0
\end{bmatrix}##
How to know if a body breaks under this stress?
 
  • #6
2,320
664
You will need to know something about the material properties (is it brittle or will it deform plastically?) and you will need a failure theory. The inputs to most failure theories are the principal stresses, so you are part way there.
 
  • #7
olgerm
Gold Member
472
26
you will need a failure theory.
Which criterion should In use to determine whether a metal body breaks into pieces or not?

Is one of these good approximation?
body breaks if
##\sigma_{tangential}>\sigma_{ultimate\ stress}\ or\ \sigma_{radial}>\sigma_{ultimate\ stress}##
or if
##(\sigma_{tangential}^2+\sigma_{radial}^2)>\sigma_{ultimate\ stress}^2##
 
  • #8
2,320
664
The question is too broad. You have to specify what the metal is and what its state is (annealed, hardened, drawn, etc.). This is not a simple question, and not the sort of thing that can be adequately answered on PF.
 

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