ABS Offshore Racing Yacht, definition of Section Modulus?

[JesperW]

I am in the process of assesing my aluminium yacht design according to the ABS ORY Specification.

Section 8 deals with scantling determination. My scantling cross sections are typically I-shaped with the hull plating as one of the beams of the I.

Calculating the Moment of Inertia Lxx [length^4] of the cross section is straight forward, but the ABSORY specifies Section Modulus Ixx [length^3].

What makes sense to me is to take the Section Modulus from either the top or the bottom of the cross section, thus Ixx = Lxx / Yc where Yc is the Y distance from the cross section centroid to the top or bottom.

I cannot find any directions in the ABSORY as to what origin of the section modulus is calculated from. Using the plating side as the origin gives me much higher SM values since the plating is much wider than the stiffner beams.

Anyone here who knows what would be the correct SM origin?

/j

[Stephen Ditmore]

Isn't there something about how much plate width to include? If that's settled, then I think you set up one of those transfer of axis tables, calculate the combined "I" about the combined centroid, then divide by the distance from the new axis to the farthest fiber c (or calculate both ways, using tensile strength for the inside and compressive for the outside).

It shouldn't matter what axis you use as a baseline if you follow the transfer of axis procedure correctly. But it's been a long time since I've done this...

Stephen

[JesperW]

Yes you either take plating thickness x 100 or smallest stiffner spacing, whichever is less. That's not the issue.

The issue is that the section modulus of a asymetric beam is dependent on the direction you are trying to bend it in, inwards into the hull or outwards, and the spec doesn't say as far as I can tell... I'm not familiar with "transfer of axis tables", maybe due to english not being my engineering language :-). Will try to look it up...

[Stephen Ditmore]

I would assume inwards, into the hull, putting the outside in compression and the inside in tension.

[JesperW]

Originally Posted by Stephen Ditmore

I would assume inwards, into the hull, putting the outside in compression and the inside in tension.

??? Now that did come out backwards somehow, didn't it?

[Stephen Ditmore]

Perhaps I'm misunderstanding the question. I assume we're looking primarily at pressure loads from outside the hull...? So the pressure is inward... perhaps you're saying the reaction forces are outward?

[JesperW]

No no, I was just thinking that if you were bending inwards the inside would be in compression and the outside in tension, no?

It's the ABSORY Spec that doesn't say what forces I am to look at, thats my problem. I would assume like what you did, outside forces, but that's just speculation. There must be a true answer somewhere...

Of course in real life most forces are from the outside, but for example in way of the keel and chainplates the mast compression forces actually are acting to bend the hull sides outwards (as the force wants to pull the gunwale up and push the bottom down, thus "straightening out" the sides).

Also a real life outside point load would bend parts of the beam inwards and part outwards.

[SailDesign]

I believe that if you look hard in the definitions, the Section Mod is specified as the least LEAST secttion mod. That is standard practice in most rules. You cannot pick one side or the other as being the "correct" one due to loading, since the stringer/frame will be flexed one way in the middle of the panel, and the other way near intersections with other structure.
Steve

[sorenfdk]

SailDesign is right!
According to section 8.1.3 of the Guide, the section modulus "...is to be not less than given by the following equation."
As an asymmetric section has two different moduli, it's the smallest that counts.

[JesperW]

Well I'm glad we all agree then, I need to go back and increase a few dimensions... Thanks all for help sorting out!

Allthough I must say that the long chord length of the aftmost transverse frames on a beamy transom design give an awfully high SM requirement there. That does not seem necessary, given that there aren't much load back there...

(Due to chord length squared increasing much quicker than design head decreases going aft)
/j

[SailDesign]

Originally Posted by soren

SailDesign is right!

Don't sound so surprised, Soren!
It was bound to happen sometime.....

[sorenfdk]

Originally Posted by SailDesign

Don't sound so surprised, Soren!
It was bound to happen sometime.....

I wrote that message just before my holidays, so i really had my mind on other things. That's probably why I forgot the "again"...

[DaveB]

Unless stated otherwise you should assume that the moment of intertia or moment of area (in this case) is calculated about the neutral axis. The neutral axis is the middle of the section when distribution of area is taken into account.

The moment of area is first calculated from some arbitrary reference point (typically the baseline) and then shifted to the neutral axis using the parallel axis theorem.

I think you are interested in moment of area (m^2 x m = m^3) [represents distribution of area... you're looking at a section and a section doesn't have volume... it's just a slice], not moment of inertia (m^3 x m = m^4) [represents distribution of volume].

Just to complicate things the best reference that I could find is for the second moment of area... you might be more interested in the first moment of area, but a little time with google should straighten you out.

It sounds a lot more complicated than it is... once you set up a spreadsheet it's pretty straightforward... the only hitch is that with small boats that have round bilges the modulus of the hull can be a little tricky and is often approximated initially.

If you're still working on it and having a hard time messenge me n' I'll send you a spreadsheet (not in the office now).

All the best,

Dave

[CDBarry]

Buy "Design of Welded Structures" from the Lincoln Foundation, under the educational section of www.lincolnelectric.com

This book (and the others in the list) cover most of the important issues in structural calculation that will come up, including the SM issue (which is right at the beginning), and the books are very inexpensive.