Catamaran crossbeam design

Hello boat enthusiasts!

I am refitting a 47ft cat, 11 ton strip planked.

she has a crossbeam at the stern that supports the rear deck and davits. It’s about 1.5 meters from the transom of the bridgedeck. It was an aluminum mast section with a white oak timber on top of it. The white oak was rotted and the aluminum is corroded; I desire to replace both with a single wooden beam. The rudder cables pass through the beam.

I am looking for some second opinions about design of the replacement beam.

My approach was to make a beam of wood that has the same flexural rigidity as the aluminum beam it is replacing.

If my understanding is correct;

EI = EI

or

Aluminum modulus of elasticity * Moment of inertia of aluminum cross section = selected wood modulus of elasticity * moment of inertia of the new beam cross section

The aluminum beam’s cross section is an ellipse, its longer centroid axis is 170mm and the shorter is 120. Wall thickness is 4mm, with thicker walls maybe 6mm at the ends of the longer centroid. The span between the hulls is 4.35 meters.

I am unsure how to calculate the moment of inertia of the aluminum given it’s non uniform wall thickness; but if a uniform wall thickness of 5mm is used it is;
1.2625 x 10^6
And it’s modulus of elasticity is 69 Gpa.

So I have a value for flexural rigidity that I am trying to match.

I have on-hand 12mm okume plywood. I had imagined building a scarfed plywood box beam with bulkheads every 60 cm and dimensions of 200x120mm.
That would give a moment of inertia (not considering the bulkheads) of 33.846 x 10^6.

I am not sure of the modulus of elasticity of the plywood. According to the Gougeons, okume timber has a modulus of 7.86 gpa; how that translates to plywood, I am not sure and can’t find much info…

Unless the wood in plywood form has a dramatically lower modulus of elasticity it would seem the plywood box beam would come out at least twice as strong… able to replace both the aluminum and the white oak.

What do ye experienced designers and builders think about my approach? Would there be significant advantage in strip planking the beam rather than plywood?

I am only considering loading in one dimension; however I know it’s also holding the hulls apart/together… thoughts?

I am essentially a laymen and not an engineer… thanks in advance, photos in next post.

Here I have some photos that hopefully illustrate the position of the beam relative to the structure of the boat.

Jagarwal said:

.....… thoughts?....

Click to expand...

So much easier with a sketch/diagram of the sections you are proposing and comparing against - to avoid any misunderstanding.

Jagarwal said:

....If my understanding is correct;

EI = EI

....

Click to expand...

That is basically correct.
It is about "equivalence"....But it is about the axis of bending and thus the equivalent width of material.

So, for example if you have material A with a square shaped cross section that is 3cm wide by 2cm deep and has an Youngs Modulus, E(1)of say 10 (whatever units).
Then a material with an E of say 15 (that 50% more) the same 'block' would then become width = ratio of E's, so E(2)/E(1)= 15/10 = 1.5 then x by the original width of 3cm = 4.5cm.
So the material of E(2) is then 4.5cm wide by 2cm deep.
It is about an equivalent cross sectional area parallel to the axis of bending.

Would the calculations also need to account for the white oak beak that was removed? What are its cross-section dims? Was the beam fastened to the aluminum at intervals or resting on top?

Thanks for the responses Ad Hoc and Tops.

I’ve attached a crude sketch of the two cross sections I am imagining. I hope it is interpretable.

you mention the axis of bending. I am not sure how to estimate where this will be; it’s more or less a simply supported beam so I assume if the cross section is symmetrical then the axis of bending will lie in the middle.

in regard to the example calculation; I had understood that a larger E (modulus of elasticity) implies that the material is stiffer, and therefor the cross section need not be as large/have the same moment of inertia… in order to achieve the same flexural rigidity. If those things are true I would think in your example you need to flip the ratio, and the resultant dimension for E(2) would be less than 3 cm, some dimension that would produce a moment of inertia that was 2/3 of the original beam.

Tops,

You are correct I have not yet considered it. It was 4cm wide by 6.5 cm deep. It was sitting on top and attached with some variation of a sika sealant. I am not sure how to combined two modulus’ of elasticity into one flexural rigidity calculation.

I would like the proposed beam to be well stronger than both original beams.

I have realized that a plywood box beam would only allow me to fillet two of the joined corners. I would plan to use a rabbit joint and bulkheads; if someone who has built a similar beam could chime in on method that would be great.

there is also the option to go timber lamination; but I don’t trust the dryness or cut of the local wood and am concerned about warping. I don’t have experience with strip planking.

Jagarwal said:

I would like the proposed beam to be well stronger than both original beams.

Click to expand...

You have a beam that has performed well with no failure. What is the reason to make it stronger? Also, as you are changing materials, the tensile and compressive strengths vs weight are going to change. Further, the attachment points need to take into account the difference of materials too. Plywood is not the best for a beam because half the wood grain in perpendicular to the length.

Jagarwal said:

I had understood that a larger E (modulus of elasticity) implies that the material is stiffer, and therefor the cross section need not be as large/have the same moment of inertia…

Click to expand...

The same stiffness in not the same strength. All the properties of the materials have to be taken into consideration at the same time.

Hello again,

Replying with an update after the fact for anyone who finds this thread with similar questions.
I ended up building a hollow timber box beam with plywood webs. The upper and lower parts of the beam were laminated out of smaller strips and I added bulkheads across the whole length before closing the beam with the final web. I then added unidirectional glass on the top and bottom, lightweight glass on the webs for protection.

The hull opening was modified to accommodate the rectangular shape, and the beam was epoxied in place and then glassed to the hull from the outside using biax. Deck was then rebuilt over the new beam.

Took a while but I learned a lot and am overall happy with the result. Update to follow when the boat has been sailed.