hoistinglifting eye

huangyhg

hoisting/lifting eye
here's one for you...
what would be the most straightforward way to determine the stress in a lifting eye made of plate w/o fea?
the lifting eye in question is made from a piece of a36 plate, essentially a 4" x 4" square with a 2" diameter hole through the center of it.  it stands on edge and is fillet welded all of the way around the base.  the "upper" corners are chamfered, but likely wouldn't change the stress, i see these corners as "dead zones".
the eye is intended to have a hook inserted through it which will induce a "point load".  the load is only about 2kip.
i would check two planes of shear, each 1" times the plate thickness in area.  this should control over a tension failure across the plate, parallel to the weld.  as far as the weld goes, its entire length should be effective.
daveatkins
on
regarding the stresses in the plate, a simple curved beam analysis assuming a 1-inch thick constant section could be in order.  look it up in a "mechanics of materials" book, the calculations are pretty simple once you have the section properties and this would give you a good approximation of the bending stresses in the eye.  not as accurate as fea, but may suit your purposes.
one of the guys i used to work with did his masters thesis and washington state university on using curved beam analysis for analyzing lifting lugs (padeyes).  our shipyard provided the lugs and he strain gaged them and pull tested them to failure.  he checked the data against his predictions from curved beam analysis.
what he found was that the predicted failure from curved beam analysis was ultra conservative (a factor of 2 or 3 over actual).  he developed a table of conversion factors to adopt the curved beam analysis to the test data and published his thesis.
we read his results and then did our own normal shear pull out calculations (similar to those talked about in the pdh online course) and found our failure predictions were very close to his test data.  what do you know.  many years of designing lifting lugs by guys with slide rules was not too far off.
i believe the problem with the curved beam analysis is that it tells you when the first element fails.  in reality on these "short tightly curved beams" as the first elements start to fail under the concentrated load there is a redistribution which continues until you finally do get an "average shear stress" across the lifting lug and it can't redistribute it any more and it fails.  the tighter the curve relative to its depth the farther off curved beam analysis results are to actual failure.
if you design a lifting lug by curved beam analysis you end up with a monster.  i have been forced to do it in the past by managers who believed a professor teaching us an advanced mechanics of materials class.  the professor thought curved beam was the correct way to design a lifting lug. after a period of creating rediculously large lifting lugs at great expense, some common sense prevailed and we returned to the more correct standard method that has been used for many years successfully.