I am a novice at stress analysis. For my competition, I need to calculate the stress on a torus in vacuum filled with air at pressure P.(adsbygoogle = window.adsbygoogle || []).push({});

Here's is what I have managed to do. I have attached an image below.

The torus section is an angular section of a curved cylinder. Its angular dimensions are [tex]d\psi[/tex] in reference to the torus cross section at an angle [tex]\psi[/tex] to the horizontal and [tex]d\theta[/tex] in reference to the center of the torus. The major radius of the torus is R and the minor Radius is r.

Summing the forces in the radial direction

[tex]

\displaystyle\frac{1}{2}(r+dr)d\psi[R-rcos(\psi+d\psi)+R-rcos\psi]d\theta*\sigma_r - \displaystyle\frac{1}{2}dr[R-rcos(\psi+d\psi)+R+drcos\psi-rcos(\psi+d\psi)]d\theta*\sigma_{t1}+\displaystyle\frac{1}{2}\pi[(r+dr)^2-r^2]d\theta*\sigma_{t2}=0

[/tex]

Here [tex]\sigma_{t1}[/tex] is the tangential stress with reference to the cross section of the torus and [tex]\sigma_{t2}[/tex] is the tangential stress with reference to the center of the torus and [tex]\sigma_r[/tex] is the radial stress.

[tex]

\displaystyle\frac{1}{2}(r+dr)d\psi[R-rcos(\psi+d\psi)+R-rcos\psi]d\theta[/tex] is the area between [tex]R_{rt}[/tex] and [tex]R_{rb}[/tex](See figure)

[tex]

\displaystyle\frac{1}{2}dr[R-rcos(\psi+d\psi)+R+drcos\psi-rcos(\psi+d\psi)]d\theta[/tex] is the area between [tex]R_{rt}[/tex] and [tex]R_{lt}[/tex]

Am I correct upto this point? If I am, how do I process further?

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# Homework Help: Torus pressure vessel stress

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