Lifting Lug Bearing Stress 1

[bobsaw]

Can anyone advise an accepted method of determining bearing stress between a lifting Lug and a shackle pin ? I cannot seem to find any standards or literature on the subject which I would have thought was quite important.
If you have a Lifting Lug with a hole diameter, 'D' and a shackle with a pin diameter,'d' then the bearing stress between them will be dependent on the contact angle between pin and hole which will be dependent on the ratio of d/D ? ie if d/D is small then you will get a very small contact area and high bearing pressure or if d/D is very close to 1 then contact angle will be approaching 180^ with a low/minimum bearing pressure. The problem I have is how do you work out contact area for values of d/D between 0 & 1 ?

 

[prex]

This is an Hertzian contact problem.
The formula you are looking for is
sigma=0.418 * sqrt(P*E*(1/R₁-1/R₂)/l)
where:
P is the applied load
E is Young's modulus (the formula is calculated for Poisson=0.3)
R₁ and R₂ are the radii of cylinders (R₂ is of course the hole)
l is the width of contact
0.418 is adimensional, so use consistent units
sigma is the maximum contact pressure.
The allowable value for sigma is of course much higher than the normal allowable stress and is determined by fatigue considerations: if you take 2 times the yield stress, you are still on the safe side.

Please note also that this contact stress is normally not the limiting factor for the lug-shear pin assembly, also because they are used only occasionally.

You will also see that of course this formula is not valid for R₁=R₂, as it gives zero. In that case the average bearing pressure on an area l*D is used and normally limited to 2.5 times the allowable stress in tension.
prex
motori@xcalcsREMOVE.com

http://www.xcalcs.com

Online tools for structural design

 

[Rich2001]

PDF File showing Calculations

http://pntbeldyk.wirefire.com/Lug/Lift Lug.pdf

REFERENCE " Ropark's Formulas for Stress and Strain" Warren C. Young, Chapter 13 Table 33 Case 2c