Calculating the stiffness of a cored deck?

[Pylasteki]

Hi guys,

I'm refitting a 1961 Pearson Triton, she needs a deck recore. The top fiberglass skin needs to be replaced as well... So I am contemplating building a thicker deck for better insulating properties and stiffening up the hull so she flexes less under sail.

The original balsawood was 3/8ths thick.

I'm wondering about the calculations involved with composite decks. From what I've read the two skins are in tension, and the core is in shear trying to keep the skins from moving separate from one another... The farther apart the skins, the stiffer the structure. Do I have that right?

My understanding of hull stiffness is that the deck contributes a lot to the structure, like boxing the C-channel. The stiffer the deck, the less the hull pinches together due to rigging loads... is that a true statement?

Thanks,

Zach

[marshmat]

Hi Zach,

You have the basic concepts right, albeit with a few things not quite right.

Picture, in two dimensions, a solid laminate, the same thickness as both skins of your sandwich together. Let's assume that it's sitting there with no load on it except its own self-weight, which we will neglect in this example. The panel is simply supported at each end (can't slide, but is free to pivot).

When we put a load on this panel, it bends into a U-shape (or a C-shape, if it's sideways). The side being loaded- the concave side- is in compression. The side away from the load- the convex side- is in tension. Somewhere in between, there is a "neutral axis" which is in neither tension nor compression. At that point in the structure, the stress is purely shear.

Now, the stiffness of our panel is determined partly by its mechanical properties (Young's modulus, E) and partly by its geometry (area moment of inertia in the direction under study, I). The area moment of inertia is proportional to the cube of the thickness. If we make our panel twice as thick, it will be eight times as stiff.

Our twice-as-thick panel, though, is also twice as heavy. And that's not usually a good thing if we want a light, fast boat. But remember how the moment of inertia goes with the cube of the thickness? That means that most of the stiffness is due to the little bit of material that's farthest away from the neutral axis. Everything in the middle is just bulk, to distribute the shear stresses.

So by taking that same amount of fibreglass laminate (thus keeping similar tensile strength), but splitting it into two skins separated by a lightweight core that's worthless for handling anything except shear, we have a much thicker, much stiffer panel of about the same weight. This is why we have cored-hull boats. It's also why we have such things as I-beams, web trusses, corrugated steel roof deck, and drywall. And it's also why your deck is structural, as you describe- the deck itself forms one flange of a much larger box girder structure, the hull itself.

But there's a nasty engineering problem that comes up in the process. Originally we had a solid laminate. It could fail in tension, it could buckle in compression, it could snap in bending, or it could simply deflect too far. Generally it wouldn't do much else. But add a core and you have a lot of new failure modes to consider, plus it's a non-linear, non-isotropic material. I treat deflection in whole-panel bending and deflection from core shear separately. There's also the tensile and compressive stress in both skins to consider. There's the shear stress in the core- quite often this is the predicted failure mode. You can get wrinkling of the compression skin before the rest of the panel fails; this failure mode, too, is calculated separately. With honeycomb cores, you can get intra-cell buckling on the compression skin if the skin is too thin for the core type. Most commonly, you get spontaneous, unpredictable shear or peel failure of the bond between core and skin due to poor compatibility of materials, poor preparation, or sloppy workmanship. (Of all the above, this is the only one that scares me, because there are well proven equations for all the rest- but not for crappy core/skin bond failure.)

So as to your original question about a thicker, stiffer deck- well, it depends on what loads the deck was originally designed to take. Stiffening the deck could be a very good thing, noticeably improving the boat's structural performance. On the other hand, stiffening the deck could cause loads to be transferred into the deck that should have been transferred through other members- possibly overloading it and causing failures. Without a lot more engineering data on the boat it's impossible to say exactly what will happen.

[tom28571]

I think Matt is correct in all the engineering problems that can cause grief in deck structures.

However, if you come close to duplicating the original deck structure, you can't go too far wrong. After all, the boat has lasted almost 50 years with that old deck.

Calculating the bending modulus of a cored beam can either be a pain or fairly easy to approximate. Just calculate the the result for a solid beam of the same dimensions as the total structure and make-up of the skin material. Then do the same thing for a beam of the dimensions of the core. Subtract the second from the first and there you have it. Close enough.

[Pylasteki]

Thanks for your thoughts guys!

Matt, Well said! Makes a lot of sense, thanks for the clarification on the theory.

Tom, thats about what I'm thinking. Replicate the performance of the old deck... What I've been mulling over is the difference in weight vs strength between balsa and foam. Give up a little in compressive strength, and for the same weight make something thicker. Go to far and its a thought process that leads to "if its gonna break, it'll do so in spectacular fashion."

Any thoughts on the hull thicknesses of boats with deck cores thicker than 3/8ths? The hull on Tritons are mighty thick so I doubt it would be the weak link. The only gel coat crazing on the hull is along side the chain plates, and under the counter... I believe the adjustable back stay is the cause, and the hull not being stiff enough to keep the fore stay bar taught the reason. I think a stiffer deck would go a long way to keep her from bending like a banana. (Particularly since the core is potting soil at the moment...)

It appears that most of the hull stiffness on my old Pearson comes from the deck and hull being glassed together. Not a whole lot in the way of stringers, and most of the bulkheads aren't really structural: loosely tabbed in, or only tabbed on one side. Only the main bulkhead is heavily tabbed in, but really only because the mast sits directly on top of it, and the chain plates bolt to it. The mast load goes 4 2x4's to the hull, and the tabbing is a 1/4 inch thick on each side with the chain plates through bolted. My mast beam has a crack, so it'll get built back bigger.

Speaking of such things... are foam core/fiberglass bulkheads done under masts on the more modern boats? I'm curious as I have to replace the bulkhead due to rot... I'm a big fan of repairs that never need to be done again... for the same reason. (Grin!)

While I've got your ear, Tritons have a plywood "spine" running down the center of the fore deck in front of the cabin top up to the bow. Is this a common feature on other boats?

Thanks again guys!

Zach

[tom28571]

Zach,

My first keelboat was a 1963 Alberg 30 which is a big brother to the Pearson Triton. These boat are tanks compared to those built today. They were built before designer/builders knew how much less they could get away with. When my 13 year old boat was sold, there were zero blisters and zero gelcoat cracks.

I would get some NA advice before making the main bulkhead in foam cored material though. That bulkhead needs a lot of tensile and compressive strength. This boat will have little benefit from such small amounts of reduced weight anyway.

[Pylasteki]

Hi Tom,

Yup, she's a tank.

I'm planning on going cruising next spring, and want to take along a bunch of tools... so whatever weight I can keep off her while empty, the extra load won't hurt as bad. At the moment she's floating about four inches higher than what I started with after being mostly gutted... if I remember correctly Tritons take around 550lbs for every inch of submersion. Still has a full water tank, and the deck is full of water... but I'm getting there. She feels a lot more spry when you step on her from the dock too... but i think thats mainly lost form stability from floating high in the stern.

Thanks for your thoughts.

Zach

[Pylasteki]

Thanks again guys.

I've decided to go back with 3/8ths balsa. Simple, works... and lasted the first 47 years. Otherwise I'll keep on plugging in calculations and not sailing... (Grin)

What do you guys think about dividing the deck with internal ribs glassed inside. I believe Allan Vaitses talks about it in his book about fiberglass repair, basically creating a scarf joint between two sections of core. (I'd like to stop whatever water that ends up in the deck from turning the whole thing to mush again...)

I haven't thought through whether or not the divisions should go athwartship as though they are internal deck beams... or along her length.

[tom28571]

Divisions in cored decks is common practice. I do it myself in wood boat deck construction with common waterproof insulating foam. Gougeon's book shows this somewhere, I think. I use transverse internal beams on a crowned deck and think they would be stronger although the main stiffness is provided by the skin. In my case, the foam is not very structural so I need the beams to do the job of a structural core.