# Moment of Inertia of a hollow beam inside a rubber shell

1. Nov 22, 2012

### MaxOtis

Hello guys,

I am calculating Bending and Shear stresses in hollow beams. We have a particular kind of shell that we use for impact loading, so we put rubber discs around the steel shell.

So my question is, how will it affect the moment of inertia ? Since I know that the rubber discs will resist to the stress, can I consider only the steel shell in my calculations ?

What do you guys think ?

Thanks.

2. Nov 22, 2012

### Studiot

You need to provide considerably more information for anyone to make a sensible comment.

In particular why do you think the disks act compositely with the steel?

3. Nov 22, 2012

### MaxOtis

I attached a pdf of an impact roller.

The roller is use in conveyor to carry ore/material. More specifically, we use it where we drop the material on the belt.

The reason why we use rubber is to make the load more uniform on the steel shell, without it, their would be huge concentrations of load on small area on the shell and it wouldn't resist a day.

Even with the rubber, the quantity of load supported by the steel shell is obviously the same, and if we make a Free Body Diagram of only the steel shell, I could take the Moment of Inertia of the shell without rubber. Am I right?

EDIT: After consideration, it doesn't really make sense to consider the load only on the steel shell. I am out of idea. The minimum Inertia would be in between 2 rubber discs, but since the load are applied on the top of the discs, I am not sure whether it is assumption to use this value of Inertia for my calculations.

#### Attached Files:

• ###### Impact Roller.pdf
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135.1 KB
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Last edited: Nov 23, 2012
4. Nov 25, 2012

### MaxOtis

Any Idea ? :uhh:

5. Nov 26, 2012

### Studiot

OK I think you are talking about rotational inertia.

My earlier comment was directed on the assumption of structural bending of the roller.

For rotational inertia the rubber will add significant mass at a significant radius to greatly increase the rotational inertia about the shaft axis.

I assume there is no slip on rotation.

In terms of adding to the shaft stiffness against bending I doubt that even if the rubber was sufficiently shrunk on to the steel to act compositely it would attract much stress, despite its position) simply because of the huge difference in elastic moduli.

Is this making progress?