# Formula for the tensile stress on a spinning ring

• boab
In summary, the conversation discussed a problem involving finding an equation for the tensile stress on a spinning ring and determining its maximum spinning speed before breaking apart. The solution involved looking in Roark's Formulas for Stress and Strain and using the equations for a ring's stress in terms of its outer and inner radius, mass density, Poisson's ratio, and angular velocity. The maximum stress occurs at the square root of the product of the outer and inner radius. The person expressing the problem was grateful for the quick response and assistance.
boab
I'm having a problem finding and equation that will give me the tensile stress acting on a spinning ring, like the rim of a flywheel, that is trying to "pull itself apart". The ring has no spokes or disc, but is just a ring spinning on its axis. I need to know how fast the ring can spin before it separates from the tensile stress acting on the material it is made of.
I seem to have stepped in over my head.

Go to the library and look in Roark's Formulas for Stress and Strain.

For a ring:

$$\sigma_r = \frac{3+\nu}{8} \rho \omega^2 \left(a^2+b^2-\frac{a^2b^2}{r^2}-r^2\right)$$

$$\sigma_{\theta} = \frac{3+\nu}{8} \rho \omega^2 \left(a^2+b^2+\frac{a^2b^2}{r^2}-\frac{1+3\nu}{3+\nu}r^2\right)$$

where:
$$a$$ = outer radius
$$b$$ = inner radius
$$\rho$$ = mass density
$$\nu$$ = Poisson's ratio
$$\omega$$ = angular velocity

The maximum value of $$\sigma_r$$ happens at $$r=\sqrt{ab}$$

Well I thank you very much for the quick reply, and the effort! You have saved the day, and advanced the project.
Cliff

I used to be Cliff, now its "boab: as something got lost in my previous registration.

## 1. What is the formula for calculating the tensile stress on a spinning ring?

The formula for calculating the tensile stress on a spinning ring is σ = ρω²r, where σ is the tensile stress, ρ is the material density, ω is the angular velocity, and r is the radius of the ring.

## 2. How is the tensile stress affected by the spinning speed of the ring?

The tensile stress on a spinning ring is directly proportional to the square of the angular velocity. This means that as the spinning speed increases, the tensile stress also increases.

## 3. Does the material density of the ring affect the tensile stress?

Yes, the material density plays a significant role in determining the tensile stress on a spinning ring. A material with a higher density will experience a higher tensile stress compared to a material with a lower density, given the same spinning speed and ring radius.

## 4. Can the radius of the ring impact the tensile stress?

Yes, the radius of the ring also affects the tensile stress. A larger radius will result in a higher tensile stress, while a smaller radius will result in a lower tensile stress, given the same material density and spinning speed.

## 5. Are there any limitations to the formula for the tensile stress on a spinning ring?

Yes, the formula assumes that the ring is spinning at a constant speed and that the material has uniform density. In reality, there may be variations in spinning speed and density, which can affect the accuracy of the calculated tensile stress.

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