Scantlings in real word

There is a small boat that I have designed with FreeShip. (attached)
I know it is small and does not really needs scantling, but I want to obtain the skills necessary. I will have a lot of questions, I will number them.
So I have looked up the GL scantling rules (I-3-3, yachts < 24m), and started to do the calculations. (attached, alongside with the library I am using for mechanics. It uses sympy)

First, I am using plywood. GL do not seem to like this material, I could not meaningfully derive the rule for shell thickness.

1. I reckon I could pretend that I am using steel, and use an appropriate k material constant to multiply the shell thickness (GL quotes 12 and 16 depending on wood type).
Is it true?

I have choosen the "hard way", because I want to obtain the necessary skills in applied mechanics. Calculated the design load in a conservative way by the formulae.
Now to derive shell thickness, first I tried to calculate the maximum flextural stress based on the maximum moment of a beam.
The first thing to overcome was that I did not really planned frame. I can pretend that the two bulkheads at 0.6m and 2.4m are frames, and even that the one in midship is one.
I pretended it for a moment, and approximated the plate between the frames as a supported beam of 1.8m length (you will find a = 0.3m in the attached file).

2. As the plate is convex from the side of the load (outside) I guess it is a conservative estimation. Is it true?

3. What if I did not pretend having frames? Doing the same approximation using Loa as frame length would work? (based on the reasoning that one half of the boat supports the other half at their joint at the end)

4. Beam computations as I have learned them use s beam with a width. But I eliminated the beam width (or used 1m, if you like). Is it correct? (One reason for using dimensioned calculations to check it for myself. But I want to be sure.)

Well, I am just learning mechanics as yet. From that point on I used instinct rather than knowledge.

5. I used the equation
fbmax = M * c / I
to derive c, which is half the shell thickness. Used the formula for rectangular cross-section beam
I = b * h^3 /12
where h is the shell thickness, so it is 2*c
b is the beam width which is eliminated as of question 4.
the above two equations merged constitue eq2 in the calculations
eq2 = maxmoment*c/((2*c)**3)*12 - fbmax
Is the above logic okay?

6. I had a real problem to determine fbmax. There are a lot of constants for various types of wood in the GL rules (I-3-3, annex C, table C.7), but these are timber and not plywood. Now I tried to look up the numbers and found this.
Now we have 6 numbers in 3 names in GL rules, and 7 numbers in 5 names in matweb.
I picked 30MN/m^2, as a conservative value, thinking of breaking strength and ultimate tensile strength.
What name should I look up for fbmax, and what number should I use?

I came up with 4.5 cm as a shell thickness for a 3m kayak, using 1.8m as frame spacing. I have a feeling that 4mm is enought though... I know that I used very conservative estimates everywhere, but this result still seems a bit too high.

7. for the design load
- I simply used the maximum of all design loads as a design load.
- For speed factor, I also used the greatest
Now the design load is 12627 N/m^2: more than a ton for each square meter.
Is it an okay number?

8. is the beam estimation I describet before question 2 too conservative?

9. I started to get values in the vicinity of 4 mm when modified frame spacing to 0.3m
what is the truth? do I really need frames, or the calculation is so mch off?

Thank you for any insight.

 

Gotta admit I did not fully understand all that, but if you're using yacht formulae to calculate scantlings for a kayak you are likely to end up on the high side of normal practice. The following is practical experience rather than theory.

A 3m kayak is a very small boat and IMHO it shouldn't need more than 3 mm thickness assuming you are using the good stuff, marine plywood that is, and do not plan on assaulting well-defended rocky beaches or using it for white water rapids

Although my ultralight canoes do not have the benefit of decks to stiffen them, I can use 3 mm ply for canoes up to 4 m length, and I do not glass either side, to keep them light, because I am getting old and I want to be able to cartop for a few more years. This works for me. However, I paddle in slow water where there are no rocks to hit.

Ply thickness of 4 mm is more common, and the norm for kayak kits, Also most folk glass one or both surfaces, which increases the strength of ply by several times, expecially puncture resistance.

The use of frames varies in practice: I use none for canoes. A frame used to make a decked space into a closed box greatly increases resistance to twisting forces as you are obviously aware, even if the frame has an opening for storage. So does the use of side decks; usual practice is to provide knees under the side decks, partly for stiffening but mainly to prevent damage if the paddler sits on them! Other than this, extra frames do more to provide emergency buoyancy volume than stiffness, at least in kayaks, except for a skin on frame boat.

Seam joint construction is a factor that affects required skin thickness. Most folk use glass tape and epoxy which makes for a fairly flexible joint, even after adding an epoxy fillet. I use chine logs to reinforce the seams, which results in a stiffer joint, allowing me to drop down a notch on skin thickness and still have a sufficiently stiff hull.

All bets are off for other boat types. However, I recently completed a 3 m sailing dinghy which was constructed like my canoes but using 4 mm ply for the sheers. It has built-in torque tubes which double as buoyancy volume. It seems adequately robust FOR MY PURPOSES, puttering around small lakes. 6 mm would have been appropriate for a boat intended for harder use.

LOL

 

Thank you, it is a bunch of very useful information.
I hope someone can shed some light on the theoretical part of it either.

 

I did some additional research.
Using shell thickness scantling rule for steel gives some 0.3 mm for steel, and 1.28 mm for wood. Now this looks like a bit undersized, but there is also a rule for minimum thickness which gives 1.5mm for steel and 6mm for wood.
The wood rule starts the table with scantling number 7, at shell thickness of 11mm, and frame spacing of 120cm.
The scantling number for my boat is 1.36, which would give somewhere around that 4mm considering nonlinearity of the table.

I did the above for a "normal" size yacht Loa=10.0m, Boa=2.5m, Dd=1.5m, Lwl=9.2m, etc.
Now steel rule gives 0.6mm for steel, 2.8mm for wood, with minimums 2.8mm for steel and 11.15 for wood.
Wood rule (scantling number is 32.32) gives 26-27 mm shell thickness at 270-280 cm shell spacing.
These numbers look like something around normal, are they?
Also my computation gives 58mm at 1.8m spacing, which is gets nearer to the range if we consider that it uses rather conservative means. But I would still like to know if the flow of my computation is correct, and what the heck fbmax should be?

I do not know what to think about the design loads. They are in the range of 1.5 ton per square meter (or more than 300 lb/square feet for you americans) for the 3m vessel, and 4 tons range for the 10m one. Is it a reasonable value or exorbitant?

Another thought: I guess I could make the beam computation more precise by using an I which considers the bending of the panel. But how?