What the D Over d Ratio Does to a Sling

Why this matters

Every correction in rigging except this one is about the load. Angle is about where the hook is. Hitch is about how you wrapped it. Share is about the centre of gravity. Bend severity is about a piece of hardware you picked off a rack because it was the one that was there, and it is the only derate on the list that a rigger can inflict on a perfectly planned lift by grabbing the wrong shackle.

It is also the one nobody measures. A crew will tape a leg length to the inch and then thread a sling eye over whatever pin fits, and the pin is very often the smallest bend anywhere in the rig. The damage it does is not visible while the load is in the air. It is visible afterwards, in the sling, and by then the lift has already been made at a design factor nobody chose.

Nobody stands under the load or in the arc a released leg swings through, and everything below that involves handling a sling happens with the load landed and the sling slack, in gloves, because a broken wire at the throat of an eye punctures a hand before you feel it.

What D and d actually are

D is the diameter of the thing the sling bends over. A shackle pin, a hook saddle, a master link, the load's own edge or rail. d is the diameter of the sling body. The ratio of the two is the whole measure of how hard the sling is being bent.

Bending a sling around something takes capacity away because the outer wires or fibres at the bend travel further than the inner ones, so they pick up more than their share of the tension before the sling is anywhere near its rating. Tighten the bend and that unevenness gets worse. The relationship is one-directional and there is no argument about which way it runs: efficiency falls as D over d falls.

     sling body, diameter d
          ||     ||
          ||     ||
           \     /
            \   /
     pin, diameter D
             ---

   D over d = pin diameter divided by
   sling body diameter, at the bearing

The published rating for a wire rope sling already contains a bend assumption. Basket ratings for wire rope slings are commonly based on a D over d of 25 to 1, stated in the sling manufacturer's tables and in ASME B30.9 in the edition your authority having jurisdiction, contract or employer programme has adopted. So applying an efficiency factor for a smaller bend is a re-basing of the published number onto your geometry, not extra margin added to a raw strength.

Where the smallest D usually is

Walk every bend in the load path, not the obvious one. In a common two-leg pick there are four or five:

• The crane hook saddle. Usually generous, and usually fine.
• The master link. Usually fine, but it is a bend and it gets counted.
• The shackle pin at each leg. This is the one. A shackle chosen for its rated capacity rather than its pin diameter can be entirely adequate on strength and still be the tightest bend in the rig by a factor of five.
• The load's own edge, rail or padeye hole. Sometimes the tightest of all, and if it is sharp it is not a bend problem at all, it is a cutting problem, and the answer is corner protection or a different sling rather than a percentage.
• The bight of a choker, where the sling bends around its own body at a ratio of roughly 1. That one is already inside the published choker rating, so do not charge it twice; the choker card owns it.

The governing D is the smallest one, because the sling is only as good as its worst bend. Averaging them is not a thing.

The shape of the relationship, and why it matters where you sit on it

The efficiency curve for a wire rope sling bent over a round pin is steep at the bottom and flat at the top. Between a ratio of about 1 and about 4 you gain a great deal for a small increase in pin size. Above about 8 the curve has mostly flattened and the remaining climb to the 25 to 1 publishing basis is small. The exact percentages belong to the sling manufacturer's table for the sling in your hand, and they are the only numbers to use.

The practical reading is that being slightly undersized is cheap and being badly undersized is ruinous, and the difference between those two states is a fraction of an inch of pin. That is also why "it fit through the eye" is not a check: a sling eye will pass over a pin far smaller than the sling can tolerate.

This relationship is for a round wire rope body bent over a round pin, holding rope construction constant. It does not transfer as written to other families. A flat web sling bends flat and its concern is edge radius and the width of the bearing surface. A roundsling has its own minimum diameters from its manufacturer. Alloy steel chain is not governed by a D over d in this form at all, and its bearing rules come from the chain manufacturer along with the requirement that only that manufacturer's components go into the assembly.

The lift, and what the sling showed afterwards

A crew set a machine base with a small mobile crane. The pick was a two-leg wire rope bridle, sling body 1/2 in diameter, legs measured at 60 degrees from horizontal, load 6,000 lb from the equipment nameplate, hook over the centre of gravity, legs equal. Both eyes went over the crane hook at the top and both bottom eyes were shackled to the machine's padeyes.

The shackles came off the truck because they were the ones on the truck. Their rated capacity was comfortably above the leg tension. Their pin diameter was 5/8 in.

The lift was uneventful. The sling was not. On the post-use inspection, done with the sling off the load and slack and in gloves, the throat of both bottom eyes showed the wires flattened where they had lain on the pin, and one strand carried a cluster of broken wires at that exact bearing point rather than scattered along the lay. Clustering at a single point is a bend or crush signature and it says where the damage came from, which the wire rope failure card in this group covers in full.

What the pin cost

Every correction gets its own line.

• Load weight, from the nameplate: 6,000 lb.
• Legs counted: 2, hook over the centre of gravity, legs equal.
• Vertical share per leg: 6,000 / 2 = 3,000 lb.
• Angle factor, from horizontal: sine 60 degrees = 0.866. Leg tension = 3,000 / 0.866 = 3,464 lb.
• Hitch: vertical at each leg, factor 1.00.
• Bend severity, the governing bend: pin 0.625 in over body 0.500 in gives D over d = 1.25. Say the sling manufacturer's table gives 0.65 at that ratio for this product. That figure is illustrative and belongs to the table, not to this card. Required rated capacity = 3,464 / 0.65 = 5,329 lb.
• Design factor: not applied again. The 5,329 lb is already a rated-capacity number and gets compared straight against the tag.

The same rig with a shackle whose pin diameter met the sling manufacturer's stated minimum carries a bend factor of 1.00 and needs a rated capacity of 3,464 lb. The wrong shackle therefore demanded 5,329 / 3,464 = 1.54 times the sling, about half again, on a lift where nothing about the load changed.

Read from the direction the crew was actually in, they had selected a sling against 3,464 lb. Its effective capacity over that pin was rated x 0.65, so a sling rated 3,500 lb was worth 2,275 lb at the eye against 3,464 lb applied. That is 3,464 / 2,275 = 1.52 times its capacity in that geometry, and against the 5 to 1 design factor commonly inside a wire rope sling rating, per the sling manufacturer's rating and ASME B30.9 in the adopted edition, the lift ran at 5 / 1.52 = about 3.3 to 1. It held. The flattened wires are what 3.3 to 1 looks like when you get to see it afterwards.

The fix that costs nothing: bow, not pin

There is a free improvement available on almost every shackled connection, and it is a habit rather than a purchase. Put the sling eye in the bow of the shackle and put the pin through the padeye, not the other way round.

Two reasons, both real. The bow is a larger diameter than the pin, so the sling gets a better bend for no change of hardware. And a sling bearing directly on a pin can rotate that pin as the load settles or swings, which backs a screw pin out over a series of picks. A shackle used the other way round, pin through the fixed padeye and sling in the bow, cannot do that.

Beyond the habit, the actual fixes for a bad ratio are to select a shackle by pin diameter against the sling manufacturer's minimum rather than by rated capacity alone, to use a thimbled eye where the sling manufacturer supplies one, or to change the connection so the sling never bends that tightly.

What flips the answer

• The sling is web or roundsling rather than wire rope. Different family, different rules, and the numbers on a wire rope efficiency curve do not transfer. Route to that manufacturer's minimums.
• The bend point is sharp rather than round. A ratio describes a curve. An edge cuts, and no efficiency factor covers a cut. Corner protection or a different sling.
• The pick is a choker. The bight bend is already inside the published choker rating, so charging a D over d factor on top of the choker column double-counts it. The choke-angle factor is the correction that applies there.
• The load is being turned or rolled rather than lifted. The bearing point moves during the operation, so the governing D changes mid-lift, and that is a lift-plan question for the qualified person your employer designated rather than a single factor.

How to verify you got this right

Measure the pin, do not eye it. Take the shackle out of the rig and put a rule or a caliper across the pin's bearing face on the bench, with nothing loaded, then compare that dimension to the sling manufacturer's stated minimum for that sling body. Comparing to another shackle's pin proves nothing.

Then confirm you took the smallest bend in the rig and not the first one you noticed. Walk the load path end to end and write each D down. If your governing bend turned out to be the crane hook, look again, because it very rarely is.

Check the direction of the correction. A smaller bend must produce a larger required rating. If your number came out smaller, you multiplied by the efficiency where you should have divided by it.

Last, inspect the eyes after the pick rather than only before it. Flattening at the throat, or broken wires clustered at one bearing point rather than scattered along the lay, is the sling telling you what the geometry was, and it is the only feedback this correction ever gives you.

References

• 29 CFR 1910.184, slings, for general industry, and 29 CFR 1926.251, rigging equipment for material handling, for construction. Say which Part governs the work before quoting a requirement from either.
• ASME B30.9 for slings and ASME B30.26 for rigging hardware such as shackles and links, in the editions your authority having jurisdiction, contract or employer programme has adopted; a consensus standard binds through one of those routes and not on its own.
• The sling manufacturer's efficiency table and stated minimum bearing diameters, and the shackle manufacturer's markings, which own every figure this card routes to.
• See related: How a Wire Rope Sling Fails and What You See First; Why a Choker Derates and by How Much; What a Rated Capacity Actually Refers To.