Buckling of shrunk in bushing

Buckling of shrunk in bushing

Roarks, 7th Ed, pages 711 and 712 (Chapter 15.2, Buckling of bars) lists a formula to check for buckling of shrunk-in shells (e.g., bushings): P0/AE =2.67(k/r)^1.2.

P0 is labeled as “pre-buckling hoop compressive force”
A is listed as hoop cross-sectional area
k is the radius of gyration of the cross-section

Unfortunately, there is no sketch explaining these variables. As non-native english speaker, I am not certain what the pysical meaning of those variables is. I would greatly appreciate if somebody could post an explanation. I would also like to know how P0/A relates to the interference pressure.

Thank you in advance.

Chapter 15 in the 7th Edition. Looks like I got to get myself a new copy. I use this book from time to time it is very helpful. The 6th Edition does not have a section on bearings.

Now to answer your questions.

PO – pre-buckling hoop compressive force – This is the force holding the bearing into the hole due to its being press fit or forced into its mounting hole. If it is excessive the walls will hoop that makes up the bearing cross section will actually buckle.

A – Hoop cross section – This is the area of material that makes the bearing the calculation for that number would be

A = (R^2-r^2)*pi

R= outside Radius
r = inside radius

k – Radius of gyration of the cross-section – see the link below I would be r as show in those equations from Wikipedia.

Niel Leon
Community Developer – Engineering.com