2million pound stteel roller, a flate steel plate, & hertzian stress

[brmech]

I'm looking for good reference literature on hertzian stress theory and empirical data that I can apply to the following cylinder slow rolling on flat plate configuration.

Cylinder:
Diameter = 100"
Length = 40"
Load on cylinder = 2 million pounds

Plate:

width = 40"
thickness = 3"

Material of both Plate and Cylinder
Nickle Chrome cast steel with .40% carbon
Ultimate Strength 102000 psi
Elastic Limit 52000 psi
Elongation 14%
Reduction 17%

In addition, I would like to find a way of measuring the contact area and load so a more accurate contact stress can be calculated.

 

[butelja]

Formulas for Stress and Strain by Roark & Young covers this in chapter 13. In my 5th edition, the answer can be found in case 2a of table 33.

For plate and cylinder of same material, the following formulae apply:

b = 2.5 * sqrt(p*Kd/E)

Sigma_c = 0.591 * sqrt(p*E/Kd)

Tau =~ Sigma_c at depth of 0.4*b

Where
b = width of contact zone
E = Elastic modulus of material
Kd = Roller diameter
p = Roller load per unit length
Sigma_c = maximum compressive stress
Tau = maximum shearing stress

For your case, I calculated:
p=50,000 lbf/in
Kd = 100 in
E = 29*10^6 psi
b = 0.893 in
Sigma_c = 71,170 psi
Tau = 23,700 psi at 0.357 in deep

Since the maximum calculated compressive stress is above the yield stress, the results cannot be completely accurate. To keep the compressive stress in the elastic range would require either reducing the load, increasing the roller diameter, or increasing the roller width.