Keel and factor of safety

[DUCRUY Jacques]

Hello,

In the book of Larsson and Eliasson (Principles of yacht design), I find an example of keel calculation (90° heeled and grounding, i.e. load case 1 and 4 of ISO 12215 part 9).

I am surprise par the factor of safety used : 5 for the first case, and only one for the second.

What do you think about it ?

Thank you in advance

Best regards


Jacques

[daiquiri]

Yes, in fact it is not well-explained in the book.

By comparing the PYD formula for the bending moment loads due to heeled hull with the ISO 12215-9 (still a draft) formulas, it can be seen that ISO uses an overall safety factor of 3.7 for the calculation of keel bolts, so PYD is more conservative.
It is even more conservative when it comes to the calculation of the floor bending moment due to heel. PYD uses an overall safety factor of 5, while the draft ISO rule uses just 1.83 (from the reverse analysis of the formula) for the calculation of maximum bending moment and no safety factors for the calculation of section modulus.

It is hard to say beyond any doubt which one is right and which is not. However, considering that bending moments due to heel are ordinary, repetitive and cyclic loads, it makes much more sense to use a more beefy safety factor in order to include material fatigue effects and ensure a long life of the structure.

The case of longitudinal grounding is more difficult to compare, because PYD ignores the inertial relief due to hull rotation, while ISO 12215-9 apparently accounts for it (through the incluson of a factor proportional to LWL/T). So even in this case it turns out that PYD is more conservative than the draft ISO 12215-9 rule. However, in the case of grounding, the concept of "conservative" is imho debatable. What is better - a relatively thin and flexible structure or a thick and rigid one? I'm thinking about that thin plastic disposable glass in front of me. I can deform it quite a lots before it breaks and suffers a permanent damage. If it was made of a thicker plastics it could withstand a bigger force but would break in a much brittle-like way (with a much smaller elastic deformation). But, once you have reinforced and thickened the structure for the heeled-hull loads, you have no other choice than to go the same way for the longitudinal grounding case.
Fatigue in this case doesn't play a role in this case because longitudinal grounding is load case which will hopefully not be repeated many times in the lifetime of the boat.

Cheers

[DUCRUY Jacques]

Thank you for your answer.

But can you explain me how you calculate a "global safety factor" of 3.7 in the heeling case ?

Have a nice day


Jacques

[daiquiri]

Correction: the safety factor in ISO is not 3.66 but half that value, 1.83. There was a multiplier 2 that I have forgotten to account for.

How did I get that number:
The equation (1) in 6.2.1 of the ISO 12215-9 gives a bending moment due to heel as Mhqd = 18 Kdca Q a - where Kdca=1 for cat. A & B vessels, Q is the ballast mass, in kilograms.
It means that the multiplier 18 is 9.81 times a safety factor for Mhqd - let's call it FOS1. And hence the value of the first safety factor is FOS1 = 18/9.81 = 1.83
Why was the value 1.83 chosen - well, that's the first mystery here to me.

Then you have the equation (18) in 9.1.1 of the ISO 12215-9, which gives a bolt diameter and should contain a second safety factor FOS2. If you elaborate the equation (and, in particular, analyze the multiplier 1273 which appears in the equation), you'll discover that FOS2=1.
I would have expected to see at least a value of 2.0-2.5 instead... And that's the second mystery.

The overall safety factor is then the product of the two:
FOS = FOS1 * FOS2 = 1.83
Should they (folks who wrote the ISO 12215-9) have used a value of 2.5 for the FOS2, then the overall FOS would be a more comfortable 4.5 and that would be pretty close to what Larsson and Eliasson use in their book.

Hope I have explained my calculations in a clear enough way.

Cheers

[DUCRUY Jacques]

Hello,

Thank you for your answer ; can I to do few observations :

1) It seems that you use an old version of 12215-09 (2005 ?) ; in the more recent version (2009 and 2011), the moment for heeling case is :
M = Q * a * 9.81 (Nm) ;

2) for the section modulus calculation, the FOS is 3 for GRP (for heeling and grounding cases);

3) for bolt calculation, I agree with you about the multiplier of 1273 ; but the
admissible stress is 0.5 * yield stress, so the FOS is 2 (for grounding case, the FOS is only 1.33).

I admit that all the formulas and the choice of FOS is not alwaws clear in ISO; for example, in case of grounding, the calculation of "impact force" is very different of ABS ORY.

Have a nice day


Jacques

[daiquiri]

Yes, my ISO 12215-9 is ver. 2005. I haven't updated it yet as I haven't been working with sailboats recently.

Back to the FOS issue - actually a 90 deg. heel is not a cyclic and very repetitive situation. A 30 deg. heel would be a more ordinary case, on which fatigue should be considered. In that situation there's an additional safety factor on keel bending moment, equal to 1/sin(30) = 2. If the keel was scantled for 90 deg, it gives an overall safety margin (at 30 deg heel) equal to 3*2=6. Which is not so bad imho.
Cheers

[DUCRUY Jacques]

Hello,

I agree with you about the FOS for fatigue ; but note please that :
sin 90° / sin 30° = 2 !!!

But it seems that, in ISO rules, the FOS is not the same for floors and for bolts.

Best regards


Jacques

[daiquiri]

Originally Posted by DUCRUY Jacques

but note please that :
sin 90° / sin 30° = 2 !!!

Well, that's exactly what I wrote: 1/sin(30)=2

[daiquiri]

Oh yes, I forgot to add that the number 3 in the equation 3*2=6 is a FOS given by you for the load case n.2 (section modulus for grp floors, post#5). It would become 2 for the calculation of bolts (and the overall FOS would be 4 in the latter case, for a 30 deg heel).
Hope it's more clear now.

[DUCRUY Jacques]

Thank you, this is very clear.

Excume me for "sin 90/sin 30 =2", I had read your answer too quickly !

Have a nice afternoon



Jacques