What the calculation gives you
A padeye is a plate with a hole, welded to the item to be lifted, that takes a shackle. It is a small part that carries the whole load, and it is checked in several ways at once: bearing of the pin on the hole, tear-out of the material above the hole, shear and tension across the plate, bending at the base from the sling angle and from any out-of-plane pull, and the weld to the structure. The calculation gives each stress and compares it with the allowable, so that the lug, the shackle and the slings can be matched.
The design load
The load used is not the weight. It is the maximum gross weight multiplied by design factors that cover dynamics, uneven sharing between slings and the sling angle:
F = MGW · g · DF
MGW maximum gross weight of the item · DF the design factor; DNV 2.7-3 for offshore units gives DF = 1.4 + 0.8 √(50 t / MGW) for its R60 class, so lighter items carry a larger factor
RSF = 1.2 · SKL · PL · F / cos ν
RSF resultant sling force on one padeye · 1.2 a consolidation factor for the padeye · SKL skew load factor, 1.1 to 1.25 for the unequal sharing of a four-leg lift · PL the proportion of the load on this padeye, 0.5 for two slings · ν sling angle from vertical, 45° at most for a horizontal lift
The sling force rises with the angle: at 45° from vertical each sling carries 1.41 times its vertical share, at 60° twice. Other standards (ASME BTH-1, DNV-ST-N001, the lifting-lug rules in AISC) use different factors on the same structure of calculation; the stresses below are the same whichever factors feed them.
The checks at the hole
Bearing: σb = RSF / (Dpin t) when the pin nearly fills the hole; with clearance, a Hertz contact form σb = 0.18 √[RSF · E (1/Dpin − 1/Dhole) / t]
t plate thickness at the hole, including any cheek plates welded on · the Hertz form is what DNV uses when the pin-to-hole ratio is below about 0.95
Tear-out: σto = 2 RSF / [(2 R − Dhole) t]
R radius of the rounded top of the padeye; the two shear planes above the hole each see half the force
The hole should be only a little larger than the pin (6% is a usual limit) so that the load spreads over the pin surface rather than concentrating at a line, and the material above the hole should be at least as thick as the hole diameter.
The checks at the base
At the weld line the padeye is a short cantilever of width w and thickness t, loaded at the hole centre, a height h above the base. The sling force is split into its vertical and horizontal parts, and a force of 3 to 5% of RSF is added perpendicular to the plate for out-of-plane loading, which a thin plate resists poorly:
Tension σt = RSF cos ν / (t w) · Shear τ = RSF sin ν / (t w) · In-plane bending σxx = RSF sin ν · h / Wxx · Out-of-plane bending σyy = Fop h / Wyy
Wxx = t w2 / 6 and Wyy = w t2 / 6, the section moduli of the base in the strong and weak directions
σvm = √[(σt + σxx + σyy)2 + 3 (τxx2 + τyy2)] ≤ 0.85 Sy
the von Mises combination against the allowable, 85% of yield in DNV 2.7-3 for the padeye body
The same set of checks is repeated for a vertical lift (ν = 0), which loads the base in tension and the weak-axis bending from the out-of-plane force, and the governing case is kept. The weld is checked separately for the same forces, with its own throat and allowable.
Worked example
The worksheet below checks the padeyes of a riser for a mobile offshore unit against DNV-GL 2.7-3. It sets the material (S355, yield 345 MPa), the gross weight of 4.15 t, computes the design factor for the R30, R45 and R60 classes and keeps R60, and applies the skew and proportion factors to get the resultant sling force at a 45° sling angle. With the pin and hole diameters, plate thickness, hole height and padeye radius it computes the bearing stress by the Hertz form, the tear-out stress, the tension, shear and the two bendings at the base, combines them into the von Mises stress and marks each check Accepted or Unaccepted against 85% of yield, for the horizontal lift and again for the vertical one. Change the sling angle to 60° or the plate thickness to 20 mm and see which check fails first.
Common mistakes
- Weight instead of design load. The dynamic and skew factors double or triple the force; a lug checked against the bare weight is not checked.
- Sling angle ignored. The side pull from an angled sling bends the lug about its strong axis and is often the largest term; it also decides the shackle size.
- No out-of-plane allowance. A padeye loaded a few degrees off its plane bends about the weak axis, where its capacity is lower by the ratio w / t. Thick lugs or cheek plates, and lugs aligned with the sling, both help.
- Oversized hole. A hole much larger than the pin turns bearing into a line contact; the Hertz form shows the stress climbing fast.
- Shackle not matched. The shackle's working load limit must cover RSF, and its pin must fit the hole; a bow shackle allows the angled pull a D-shackle does not.
- Weld checked to the plate's allowable. Welds have their own allowable stress and need full penetration or a sized fillet on both sides; the weld, not the plate, is where lugs usually fail.
Questions
- Which standard applies?
- Offshore containers and portable units follow DNV 2.7-1 and 2.7-3; general lifting in the US often follows ASME BTH-1 for below-the-hook devices; structural lugs on buildings and plant follow the local steel code. The factors differ; the geometry checks are the same.
- How thick should the padeye be?
- Thick enough that bearing and out-of-plane bending pass with the pin of the shackle you intend to use: a rule of thumb is a plate at least 0.5 to 0.6 of the pin diameter, with cheek plates where that is not practical.
- Does the padeye need testing?
- DNV requires a proof load test of the unit after fabrication, typically 2.5 times the maximum gross weight for the lifting set, and a visual and magnetic-particle inspection of the padeye welds.
