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Strength of Ropes, Shackles, Pulleys, Wire and Chain

QUESTION: How can I estimate how strong a rope, shackle, pulley is, so that I can use the right size for the job ?

ANSWER: I can empathize with this question, as one is sometimes away from the internet and cannot access the prime choice; that is, checking data in suppliers catalogues!

First, let me say that strength for ALL these items is primarily related to 2 factors … their Material & Diameter.

So I hope the following empirical* formula will help. It’s easy to remember as all you need is just one Factor Number (F) for each item. These are all based on the fact that strength is approximately proportional to the sectional area … or diameter2 .. and to the material.

*Empirical Formulae are approximations created more from experience, though they can still be science based. (I’ve always loved them, as with essential safety factors applied, we really don’t need ‘precise’ figures that can seldom, if ever, be 100% correct anyway).

For SHACKLES and PINS, I use this rough formula and it also works well enough for other boat fittings having pins also working in shear (like pulleys etc). It's close enough to test results to be useful and it’s also safe, being slightly conservative. Please keep in mind, that ALL these values should always be used with appropriate safety factors … see below for guidance on these.

For the SWL or Safe Working Load in kgs, measure the Pin Size (D) in mm, square the figure, and then multiply by 15. ie: D2 x 15 for SWL

And for the Proof load, take D2 x 35 ...  (proof load is the point at which the pin starts to deform). Multiply either of the above by 2.2 to convert to lbs.

This is for decent alloy-steel shackles, and includes S/S.    But note that really cheap steel shackles can be up to 30% LOWER in strength .., so allow for this if in doubt or use one size larger. Sharp edges, corners and poor threads, visually indicate a cheap shackle.

Example of using above formula D2 x 15. Check for 5/16" shackle.  That's 8mm. So, 8 squared = 64,  and then, 64 x 15 = 960 kg (2112 lbs) SWL or 64 x 35 = 2240 kg (4928 lbs) Proof load. (so use 5/16” shackle with 1/4" dia wire rope with breaking strength of about 5000 lbs)

The same formula will generally apply (close enough), to the pins used on pulleys, as both shackle pins and pulley pins are in double shear.

ROPES and WIRES

We can now consider wires and ropes in the same way, as they also show strengths with a fairly direct relationship to their (diameter)2. So for quick reference, the following FACTORS are given for comparison and a quick way to estimate strength when new.

Today, there’s a HUGE range of rope strengths, as seen by these Factors that show the latest modern synthetics can be up to 30 times stronger than our old cotton ropes!

For wire ropes, the rough formula is :

Breaking Load of Rope in kg = F (factor) x Dia.(mm) squared. [BL = F x D2]

For Safety when humans are involved, divide this by 5 for a working load for wire and divide by 10 for a working load with rope (fibers are less consistent than wire). The very minimum Safety Factor (SF) under other uses, should be 2.5 for steel wire and 4 for soft rope.

So, as for shackles etc, the ‘guestimate’ Rope Formula is F x D2 (mm) = breaking load (BL) in kg. D is easy to measure and here is a list of factors for F. (SWR = steel wire rope). The two numbers given, refer to the construction, ie: the no. of strands and the no. of wires in each strand. The more small wires there are, the more flexible the wire rope will be, at a small loss in strength and durability. These F values work acceptably well for wires up to 3/8” (9.5) in diameter and ropes up to ½” (12.5) in diameter. For stainless steel, deduct 5% in strength, due partly to less malleability in nested wire bundles.

WIRE ROPE

SWR (6 x 19)F = 60
SWR (7 x 19)F = 72
SWR ( 7 x 7)F = 74
SWR (1 x 19)F = 76 so a 6mm 1 x 19 SWR will have a Break Load of [D2 x F] = 36 x 76 or approx 2736 kg.
SWR (1 x 7)F = 78

Note: Always keep in mind that 1 x 19 wire absolutely requires 2 compression sleeves for an eye, as it tends to slip slightly more easily that other wires that have 6 protruding strands.

ROPES

Now, let’s look at the many soft, woven ropes out there. The D2 x F formula will work the same. (Remember, D is in millimeters and the result is in kilograms).

Note that braided ropes average about 30% less in strength than 3-strand (when new), but better handling of the braided usually justifies their choice, other than for mooring lines.

Polyester BraidedF = 10Nylon 3-strandF = 15
Polyester 3-StrandF = 14Nylon braidedF = 11
Polypropylene 3-strF = 10Manilla 3-strandF = 7
Cotton 3-strandF = 5Cotton BraidedF = 3.5
Braided (high density polyethylene) Spectra (and Dyneema SK-78 HTS)F = 110

Note: For ropes (as for shackles) higher breaking loads may be quoted by manufacturers, but as you may not know the true source of your material, these figures are conservatively safe.

Note that Spectra has a very low melting point <300F and is also very slippery, making knots a concern. So it’s now often woven inside a jacket of nylon or polyester to reduce the slip.

Kevlar is not listed as it fatigues and abraids internally and then fails without warning, so should only be used a few times before replacement, especially when a failure would be considered catastrophic. (ie: for rescue operations etc)

Vectran - has less creep than Spectra, but poor UV resistance, so also needs to be enclosed.


While on the subject of ShortCuts for Quick estimates, the younger generations are often stumped when they find themselves ‘in the field’ without a calculator ... so perhaps this will help when figuring the above ‘quick estimates’.

Mathematical shortcuts.

To multiply by 15, add ‘0’ to your base no. and increase total by 50%.
So 36 x 15 = 360 + 180 = 540 (Useful for shackle SWL)

To convert inch-fractions to mm, multiply by 25.4. So for ¼”, 25.4 x ¼ = 25.4/4 = 6.35 mm If you work in decimals, you can also get a close approximation by multiplying by 100 and dividing by 4. [0.25” x 100 = 25. 25/4 = 6.25 mm]

To convert kgs to lbs. Multiply by 2 and add 1/10th of total. So for 70kg. 70 x 2 = 140 and 1/10th = +14, so total is 154 lbs.

CHAINS

When sometimes asked, ‘how strong is this chain?’ .… it’s hard to know where to start! The more you look into chains the more complex the issue can become, as there are not only different link sizes and constructions, but there must also be a dozen grades of material options! What IS interesting, is that the Grade number (often punched into a link about every 3 feet (or meter), is claimed to be a direct function of its ultimate strength. So a Grade 90 is rated as 3 times the strength of a commercial Grade 30.

So in this case, the Grade No. would be directly related to my ‘F’ factor if we check chain strength by the same formula of F x D2. But although I say ‘directly related’ it would not be identical as it needs a correction factor because the “Grade No. x 10”, refers to its strength in the metric system .. ie: in newtons per mm2 (with a newton approx. = 0.225 lbs) and my D2 is also not exactly the true X-sectional area (3.14 x R2) that’s needed – but it can be directly related. In fact, multiply D2 by 0.785 (ie: π/4) and you have the area !

As each side of the link provides strength, we also need to multiply the area by 2.

So with all this … we can now state that the ultimate tensile chain strength is equal to:

D2 x Grade No. x 10 x 2 x 0.785 x 0.225 / 2.2 kgs. (or just forget the 2.2 for strength in lbs)

This formula readily simplifies to:

Estimated Ult. Tensile strength in lbs = Grade No. x 3.53 x D(mm)2

(So my ‘F’ factor effectively becomes 3.53 x Grade No. in the case of chain strength).

So for 5/16” chain (8mm), the tensile strength of a good Grade 40 chain, would be indicated as: 40 x 3.53 x 82 = 9037 lbs. and will often test out well over 5 tons.

In practice, actual chain tests show a large range of results, with some above this and some below. The low figures are typically more to do with poor link welding rather than actual steel quality and even a good visual inspection will often show hints of incomplete welding that looks more like ‘a glue-job’ than a proper weld with good penetration. So, use your eyes first ;)

Your best bet for critical use anchor chain is to buy from a company that will issue you a certificate of proof loading for the chain you buy (like Peerless will) or at least, buy chain that has links that are stamped. Avoid any cheap chain where the joints ‘look glued’ and line up poorly, or plan to cut their load rating at least in half!

Here’s an excellent YouTube on Anchor chain testing by Yachting Monthly 2012.

https://www.youtube.com/watch?v=3TK-hkoFSGc

And if you still want to learn more … here’s a collection of interesting anchor chain info. from an online book available called: ‘Anchoring Made Easy’

https://www.morganscloud.com/2011/05/11/things-to-know-about-anchor-chain/


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mjw ... Nov 2015



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