The information presented in this blog post is for educational purposes only. It should not be used for engineering design or relied upon as engineering advice.
Contact stresses are import for predicting surface failure due to excessive static loading or due to repeated loading, which may lead to fatigue failure. It turns out that for some geometries, these stresses can be predicted analytically. These contact stresses are often referred to as Hertzian stresses, named after Heinrich Hertz, who originally derived the equations for the contact stress between curved surfaces. The EngineeringPaper.xyz sheet below shows how to calculate the contact stresses for the case of two spherical surfaces in contact. As described in the sheet, the case of a sphere in contact with a planar surface can also accounted for by setting the radius of the second sphere to infinity.
Important Note: This sheet relies on features in the latest version of EngineeringPaper.xyz, if you see a green refresh icon in the title bar of the sheet and there are errors in the sheet, you'll need to close all of your open EngineeringPaper.xyz tabs and re-open this page to get the latest version of EngineeringPaper.xyz. You'll know that the upgrade is complete when the green refresh icon disappears.
This spherical contact stress example sheet may also be opened in a separate tab.