## Moment of Inertia of Rounded Hollow Rectangle

## Moment of Inertia of Rounded Hollow Rectangle

(OP)

Hello,

I can't seem to find how to calculate the second moment of inertia (Ixx and Iyy) of a rectangle WITH rounded corners.

The below link is great for hollow rectangles, but does anyone know how to calculate it if the corners have radii?

http://www.amesweb.info/SectionalPropertiesTabs/Se...

I can't seem to find how to calculate the second moment of inertia (Ixx and Iyy) of a rectangle WITH rounded corners.

The below link is great for hollow rectangles, but does anyone know how to calculate it if the corners have radii?

http://www.amesweb.info/SectionalPropertiesTabs/Se...

## RE: Moment of Inertia of Rounded Hollow Rectangle

Get out your strength of materials textbook. Calculate the centroid and MOI of each segment about

its owncentroid. Then calculate the centroid and MOI of thecomposite shapeper the parallel axis theorem.Or, if it is a standard shape, you may be able to just

look it up.Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

## RE: Moment of Inertia of Rounded Hollow Rectangle

Also note that tabulated values may not show the same section properties that you'd get using tabulated radii. I think on beams, they use the largest radius for clearance reasons and the smaller radius or some average radius for area properties, etc., so they don't always correspond.

## RE: Moment of Inertia of Rounded Hollow Rectangle

## RE: Moment of Inertia of Rounded Hollow Rectangle

https://newtonexcelbach.wordpress.com/2015/07/08/s...

It is from "our own" ids

http://www.eng-tips.com/userinfo.cfm?member=IDS

=====================================

(2B)+(2B)' ?

## RE: Moment of Inertia of Rounded Hollow Rectangle

another day in paradise, or is paradise one day closer ?

## RE: Moment of Inertia of Rounded Hollow Rectangle

I've done enough parallel axis theorem calculations over the years to know the approach, and yes it could be done this way, but it would be slow and painful.

## RE: Moment of Inertia of Rounded Hollow Rectangle

calculateit...Regards,

Mike

The problem with sloppy work is that the supply FAR EXCEEDS the demand

## RE: Moment of Inertia of Rounded Hollow Rectangle

See sample spreadsheet attached. I have split the section into two vertical rectangles, two horizontal rectangles and two semi-annuli for the corners. The section properties for the semi-annulus come from my spreadsheet previously linked by Pete (https://newtonexcelbach.wordpress.com/2014/11/02/s...).

As always, please assume that both spreadsheets give incorrect results, until proved otherwise.

Doug Jenkins

Interactive Design Services

http://newtonexcelbach.wordpress.com/

## RE: Moment of Inertia of Rounded Hollow Rectangle

another day in paradise, or is paradise one day closer ?

## RE: Moment of Inertia of Rounded Hollow Rectangle