“Toroidal” shell is basically a fancy name for a *donut*-shaped shell. Yes! Donut-shaped shell:

The procedure for analysing the stresses in these shells is exactly the same as the one in Chapter 1.1,
but we need to define our σ_{θ}, σ_{Φ} and r_{θ}, r_{Φ}.

“Toroidal” shell is basically a fancy name for a *donut*-shaped shell. Yes! Donut-shaped shell:

The procedure for analysing the stresses in these shells is exactly the same as the one in Chapter 1.1,
but we need to define our σ_{θ}, σ_{Φ} and r_{θ}, r_{Φ}.

It might be hard to imagine how σ_{θ}, σ_{Φ} and r_{θ}, r_{Φ}
are defined for a toroidal shell, but as long as you follow the convention shown in the picture below you should be able to answer toroidal shell problems.

For toroidal shell problems you might be asked to find the stress in any of the 4 quadrants:

Using the same rules, we can work out the signs of r_{Φ} and p for quadrants III and IV:

For the force due to pressure in the y-direction, we take the segment of the shell from the *point of interest* to where it ends at the *minor-axis*:

For σ_{Φ}, it acts on the thickness along the circumference with r = r_{o}.
Since r >> t, we can approximate the area σ_{Φ} acts on as 2πr_{o}t:

Let’s look at an example now.

It might be hard to imagine how σ_{θ}, σ_{Φ} and r_{θ}, r_{Φ}
are defined for a toroidal shell, but as long as you follow the convention shown in the picture below you should be able to answer toroidal shell problems.

For toroidal shell problems you might be asked to find the stress in any of the 4 quadrants:

Using the same rules, we can work out the signs of r_{Φ} and p for quadrants III and IV:

For the force due to pressure in the y-direction, we take the segment of the shell from the *point of interest* to where it ends at the *minor-axis*:

For σ_{Φ}, it acts on the thickness along the circumference with r = r_{o}.
Since r >> t, we can approximate the area σ_{Φ} acts on as 2πr_{o}t:

Let’s look at an example now.