Calculating Spherical Contact Stress 

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. 

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Calculating Spherical Contact Stress
by u/mgreminger in EngineeringPaperXYZ