Changing Catamaran Beams from Wood to Composite.

That is a lot of boat to assemble sans crane. My boat is half as big and needs a crane.

 

Coming late into this thread – haven’t been looking at Boat Design Forum for a few weeks.

I take it that it is now agreed that an all composite construction is the only acceptable alternative to the original epoxy sheathed mahogany construction and that any composite construction must closely follow the dimensions and functionality of the wood construction.
Your diagram showing the four piece mould looks a bit strange to me. I wonder what would be the sequence of laminating and assembly – I am not sure this is practical.

I would suggest an alternative as described in the attached pdf file - the calculations could probably do with checking - I included the data used and assumptions to make that possible.

Interesting that you mention a Wharram catamaran flexing by 150mm but this doesn't mean much without knowing what the measurement refers to - do you know how the measurment was made?

The AYRS is now holding monthly Zoom meetings to discuss projects, if you like we could discuss your project there. details at ayrs.org.

 

Looks well done - did anyone build one to this design?

 

John
The I-beam you cite is an open cell and very poor in torsion, and thus not recommended.

 

These beams are loaded in bending so torsional strength and stiffness are largely irrelevant. Indeed, for this particular type of craft a degree of torsional flexibility in the beams may well be desireable since if the beams are torsionally stiff then when the craft is in a quartering sea the ends of the beams will tend to rotate in the beam lashings causing chaffing and possibly loosening the lashings. I note that Mark o Hara mentioned wear between the lashings and the wood/epoxy beams.

 

It is not just bending loads that are occurring...you're missing the point of a raft structure's purpose. .

That is not correct. The two hulls are rotating in opposite directions, and thus generating large torsional moment:



The ends of the raft structure experience the greatest torsional moment and cause the ends to deform into the classical "S" shape.

 

The torsional moment on the hulls does increase towards the ends of the craft but we are considering the cross beams. Assuming that the hulls are reasonably rigid, the angle of twist along the length of each cross beam is the same for each beam so if each beam is built the same way the torsional moment will be the same for each beam. If the beams vary in structural details the more torsionally stiff ones will have greater torsional moment. It is the bending deflection in the beams, and hence the bending moment, not the torsional moment, that increases towards the ends of the craft - this is clearly shown by your FEA output. This is of course considering only relative rotation of the hulls about an athwartships axis, as caused by quartering waves or by inadequate support of the craft on shore. It is also necessary to superimpose loading from the rig etc.

It seems to be a common misconception that the cross beams of a multihull need to be torsionally stiff! For the type of mulithull that has hulls connected by two or more individual cross beams it is pretty well inevitable that the hulls will be torsionally much stiffer than the cross beams because the cross section dimensions for the hulls are much greater than for the cross beams. Basically the hulls are fat tubes, in the case of a Wharram design triangular section tubes but still tubes, so torsionally stiff. Even if the cross beams are also tubular, which they often are, they will be torsionally less stiff than the hulls because, for any normal craft, they are slimmer. We are not considering here the type of mutihull that has a large cabin structure connecting the hulls - that is quite different.

Given that the hulls are torsionally much stiffer than the cross beams, when the craft is subjected to the kind of wracking distortion shown so clearly in your pictures, the cross beams bend into 'S' shapes and this will set up bending moments in the cross beams and it is the stress in the cross beams due to these bending moments that provides the main resistance to this kind of distortion, not the stress that is due to the torsional moment. So to resist this distortion the cross beams need to be made stiff in bending. Any attempt to make them also stiff in torsion will do relatively little to resist this kind of distortion.

The S shape of the deflected beams means that for this kind of loading there is actually no bending moment at the mid point of the beam (i.e. on the centreline of the craft). Perhaps this is the reason that the James Wharram design office has made the cross beams of this craft reduce in depth towards the craft centreline, or maybe there are also aesthetic or other considerations behind that. Of course, when rigging loads are superimposed then there may well be bending moment all along a cross beam and in the case of a main cross beam carrying the downforce from a mast the maximum bending moment is likely to be at the mid point - hence the use of 'dolphin strikers' etc.

 

The hull is out-of-plane from the transverse moment. The hulls are infinitely stiffer than the traverse members... unless it is made of Switz cheese rubber, or a very long thin slender member itself.

As noted above, one always assumes the hull is infinitely stiffer than the transverse members. ...however.



Place an I-beam at the centre/midships and another at the ends of the hull, as shown.

The I-beam on the port hull rotates in an equal and opposite angle to the one on the stbd hull. The angle of twist is created because the I-beam has displaced vertically relative to its original position. Now either the I-beam remains plane as it it is displaced vertically, i.e no twist, and the hull simply moves under it....or it remain plane with the deck it is attached too...in which case it is forced to twist, as shown.

At the centre of rotation, there is no vertical displacement, the I-beam attached to the deck does not displace, it remains in the same position as its original position, prior to the applied load on the hulls, therefore there is no angle of twist experienced by the I-beam.

If, instead of an I-beam... you had an RHS, of same scantlings at the end... the torsional resistance of the RHS to the applied angle of twist is roughly 400 times greater than the I-beam....

Open cell structures are very weak at resisting torsion.

Nope...only a misconception that they do not need to be! They must be closed cell structures, NOT open cells structures.

What you cite as "distortion"... is an angle of twist...i.e torsion....like this image...as also noted above.

It is because the deflection at the centreline is zero.

 

If all you did was accept Wharram's design criteria for the beams; you'd need to meet that standard; not less.

It is not right to delve into polemics or a great debate about reducing the beam properties to build in composite.

If you feel Wharram over designed his beams; that is a different discussion.

I would enjoy seeing a side by side, line by line comparison of a cored composite beam versus the Wharram spec, mostly because I am incapable of doing it, but darn curious. This would or could include Perry's beam if it is deficient.

I realize it is not necessarily an easy task and I apologize in advance. Some of this is done already.

My curiousity lies in my own concerns over rotational forces acting on my boat and some prior ado on that subject.

of course, beam size must be constant in the compare..

 

There are a few points in AdHoc's recent posts that I could comment on but I think the main thing he is saying is that cross beams for multihulls must be 'closed cell' structures (e.g. tubes) and that 'open cell' structures (e.g. I beams) are unsuitable for this purpose.

I think that the word 'must' is far too strong here. I would say that cross beams for multihulls can perfectly well be either closed cell or open cell structures but for structural efficiency (i.e. minimum weight of material) in this application the bending properties are more important than the torsional properties - to put it in rather loose terms - a bit of bending stiffness is worth a rather larger measure of torsional stiffness.

Just to try to make this clear I have run a comparative pair of simple FEA studies. I would not usually go to so much trouble in answering a post on a boating forum but I think this could be of interest to quite a few people and perhaps it might also be the basis for a short article for the AYRS magazine.

So, I have considered two structures that represent, in very simplified form, the structures of two catamarans. The only difference between the two structures is that one has round tube cross beams and the other has I beam cross beams. And the tubular and I beam cross beams are alike in all but the form of the cross sections - they are the same cross sectional areas, and hence weight, the same material and the same height as viewed from the end of the craft, so given that they are both bluff bodies they won't be a lot different aerodynamically. Having said that, for a performance sailing craft, both types of cross beam could perhaps do with some non-structural fairings being added.

The dimensions for both catamarans are:
Hull length 8000mm, cross beam fore and aft spacing 5000mm (centre line to centre line), hull depth 300mm, hull beam 300mm, length of cross beams (i.e. gap between hulls) 3000mm. The hulls are solid cuboids and as such have much greater torsional and bending stiffness than either type of cross beam. The material for the whole structure of both craft was chosen to be aluminium 6061 T6, but this is arbritrary, any solid material could have been selected for comparative purposes. The loading used is self weight and because the solid metal hulls are so heavy (this craft would never float!) I reduced the value of the acceleration of gravity from 9.81 to 1.0 m/s2 for both cases. This was simply to keep the stress levels within the strength of the material, so as to avoid the software stopping with an unwanted warning message. For both cases the craft was supported on points at the bow of one hull and the stern of the opposite hull, to simulate loading from a quartering sea, albeit in a rather exagerated manner.

The tube cross beams are 100mm OD, 90mm ID. The I beam cross beams are 100mm overal height, 50mm width, 11mm flange thickness, 5mm web thickness. The dimensions of this I beam were not particularly optimised for the application, they were just chosen to make the cross sectional areas, and hence weight, the same as the tube within close limits, actually the I beam is marginally lighter than the tube.

The attached pictures from the FEA analysis show the deflections with the colors indicative of the Von Mises stresses. Note that both beams bend into S shapes, just as with the FEA analysis that AdHoc shows us.

These are the numerical results:

Tube cross beam:
Cross sectional area of beam 1492.26 mm2
Moment of area of beam - Ixx - 1.688e6 mm4
Maximum deflection of whole structure 39.5mm
Maximum Von Mises stress in whole structure 62.4 MPa

I beam cross beam:
Cross sectional area of beam 1490 mm2
Moment of area of beam - Ixx 2.387e6 mm4
Maximum deflection of whole structure 36.6mm
Maximum Von Mises stress in whole structure 51.4 MPa

So, as one would expect, the I beam has the greater value for Ixx. Of course, nothing beats a round tube in pure torsional loading so the round tube will be much stiffer and stronger than the I beam in torsion but for this application that advantage does not quite make up for the better bending properties of the I beam, it does end up quite close though.

Everything else being held the same, the I section cross beam offers slightly less deflection and slightly lower stress levels than the round tube. So there you have it.

-------

I would add that I am quite capable of making silly mistakes! - while using a software function to check the Ixx value for these cross beams today I realised that when I used the same software function the other day to work out the Ixx for Mark o Hara's real catamaran beams I may well have picked out the wrong numbers from the rather small print displayed on my screen. I think I would have made the same error for both Mike's existing wood beam and the possible alternative composite beam so the conclusion probably remains but the numbers may change. I will check and make a correction if necessary but havent time for that right now.

 

Thinking over the beams, I came up with the idea that torsion is not vital in many cat beams.

In the pics above, the hulls are twisting, that I get. But twisting only happens because the beams allow deflection. If the beams are stiff, then there would be little twisting of the structure, and hence little need for torsion resistance in the beams. Torsion occurs IF the beams are flexible, as shown in the exaggerated deflection diagrams.

This is born out in my folding cats. The mechanism is like a folding book and the mechanism components have little torsional resistance. They are thin flat panels. But the boat is incredibly stiff and under load, the lack of beam torsion resistance is never needed because the hulls cannot twist, because the beams are deep and therefore the structure is very stiff. The folding cat is stiffer than a same size three beam cat - or any cat of the same size.

So the composite beams could be fine as drawn. Torsion only occurs to a large degree IF the beams are flexible. And even if the beams were flexible, torsional resistance would not reduce twisting of the structure greatly because turning torsion into beam bending resistance is not efficient. Just make the beams deep and ensure the compression edges do not Euler buckle and all should be right. Torsion is a second order issue for forward and aft beams. (Mast beams will require torsion resistance to cater for loads when sailing).

In trimarans designers sometimes try to reduce the size of the panel between the two beams, to reduce the size and deflection of the torsion box in the main hull. Nigel Irens used this approach sometimes. Fleury Michon was one example. But that is in the main hull of a tri and torsion resistance allows the hulls to stay in a similar plane.

The worst cat I ever sailed for torsion resistance was a 3 beamed Tennant Bladerunner. As the CG was way in front of the chainplates, flying the hull led to the windward hull torquing bow down by about 10 degrees. The owner fitted a spectra line from the hounds to the bows which loaded up when a bow depressed. We blew an 8mm line once. The beams were mast sections and had good torsion numbers, they were just too flexible to stop wracking. Still the boats were damn fast. You can twist and sail really quickly.


Also the thickening of the beams at the outer edges could be because of building rather than load. The beam sockets are flat - parallel to the water but the beam aims slightly upwards, so the beam has its lower edge run down to the inner gunwale, more for ease of building than engineering. Many boats are designed to be easy to build and this may seem silly from a strictly engineering viewpoint. But it can make sense if you have to build it.

 

Correct.

Numbers and theory do not lie.. it is elementary structural theory.

In my sketch above, if the I-beam is moved to the centre of rotation as shown - what occurs?... can the I-beam do the job. No. ..why?
Because this moment no longer has a displacement, ergo it is a pure torque. And by definition a pure toque has no axial or bending. It is governed by a state of pure shear.

The ideal shape to resist pure shear in torsion is... yup.. a solid shaft.

So, if you used the I-beam, it would do very little to resist the torque. But if you used a solid shaft...aahh.. that's a different matter.
Because a shaft remains radial and plane in cross section after the twisting.

So, now for the beam, or structural member located at the end of the hull... in the case of the sketch it is an I-beam. And as shown, the ends have twisted against each other. There exist an angle, causing the warp, thus:-


the angle of twist which in terms of a shaft is the angle of strain. Thus there is a simple formulae for the torsion, viz:



So, we can now investigate the difference in sectional shape resistance to this torsion, by simple theory.
Given that everything remains constant save for the 'J' the polar moment of inertia. And we can relate this to the shape of the section being used in terms of K.

Lets take the values of your:

And I shall add one more to it... changing the I-beam to an RHS... simply by halving the web and pushing to the edges to create the box section. Thus your common themes of area, weight etc remain the same.
It does create a very weirded shaped RHS, but this is purely an illustrative exercise for now....so the exact shape for production etc, is not so relevant.

Tube:


The value for K = 337.6cm^4

I-beam:


The value for K = 4.8cm^4

The RHS:


The value for K = 89.5cm^4

The tube is 70 times greater at resisting the same torsion, given all things remaining equal, and the RHS is 19 times greater than the I-beam.

So there you have it. It is not rocket since... and the I-beam is always , always the worse section to choose, because it is an open section and has very little shear flow area.

You need to understand what is shear flow and how it is influenced in shapes and it subsequent effects.

 

In a 4 stay situation such as the A class uses, could a lot of the twisting of the hulls be prevented by simply fitting additional front stays to each hull from the mast ?

 

How is this of value to the original question?

Seriously asking. The original beams were designed in wood. If you are simply suggesting beams with lower engineering attributes are suitable, I have a follow on idiot question.

What builder or boat owner would reduce the engineering attributes of a key structural component of his/her vessel? It is rhetorical. None or nearly none.

What is of interest is the raw comparison of moments of inertia/other of the original Wharram beam and a beam constructed not of wood.

For me, unqualified that I may be, I am curious because if my beams ever had a problem; I wondered if they could be made of glass or core or wood or some combination. My beams are a mast extrusion, subject to the whims and fancies of the manufacturer. Just so people understand the nature of my lurking/inquisition (sorry in advance). The concern is if a beam is damaged somehow, must I A, purchase an entire 18 meter aluminum mast or B, could I replace it with composite as Mark has inquired.

Kindest regards.

 

The simple answer is - yes.

But it is not just a stress driven solution, it is deflection.
Using composites, you can have a design allowable stress limit ranging from 25MPa to around 250MPa, or higher, depending upon the combination of resins and reinforcement selection.
If you opt for a high spec, then you can of course save weight.
However...

With composites being around 1/3rd of the 'E', the Young's modulus compared to aluminium, it shall flex more. In other words, it is easy enough to satisfy the "stress" part of the solution, as an equivalence. But the deflection side is not so easy. Since in order to obtain - approximately - the same deflection, you end up with either a thicker section (which begs the obvious - why go higher spec then..), or a large cross-sectional shape (to increase the 2nd moment of area), or a combination of the two.

Thus, as I noted several pages ago... it can be done, but it requires many compromises to be made, in order for it to work and be a suitable alternative.