Calculating beam scantlings for catamarans

Farjoe,

Yes, your beams are under-designed. Basically, your math is correct. In addition, you are using a high number for tensile yield strength, 276 MPa, whereas my handbooks show 241 MPa (35,000 psi). Also, you do not have any safety factor. You are comparing a live load against a failure strength (yield). Factor of safety should be at least 3 and possibly 4 for such a critical element of the craft.

Let's use FS = 3, required SM would be about 197,500 mm^3 based on 241 MPa yield strength. So the section will be knocking on the door of about 300 mm dia. x 6 mm wall thickness. Check the math. This is pretty heavy tubing. You can see why carbon fiber becomes so attractive as it would be about twice as strong with only about half the weight for the same size section, and you could reduce the size of the section for further weight savings.

Eric

 

Eric,
Thanks for your fast reply.

I got the tensile strength figure from www.matweb.com which gives the following figures for 6061-T6:

Ultimate yield strength : 310 MPa
Tensile yield strength : 276 MPa

With my limited knowledge of Mechanical Engineering I understand the former to stand for the strength at which the metal actually fractures while the latter is the point at which the metal goes beyond the elastic limit.

With reference to the size you proposed I think I have seen this installed on much larger cats and therefore wonder whether the cantilever method is already conservative. Perhaps the effect of the windward shroud may be helping to reduce the purely cantilever bending moments!!!

regards

 

Nice site
And it confirms that laminated spruce or pine may be a good alternative.
http://www.matweb.com/search/SpecificMaterial.asp?bassnum=PTSE550
http://www.matweb.com/search/SpecificMaterial.asp?bassnum=PTSE560

 

Farjoe,

You may be right. The math for the proposed model gives a result that may seem heavy and/or too conservative. So is the model correct? Is everything included? Golly gee, maybe you should include the windward shroud. Anything that you can come up with to make the model closer to reality all works toward getting a more accurate and realistic model. That's the whole point of engineering.

Eric

 

Hi Farjoe,

I did some checking on my own handbook about the yield strength of 6061-T6 aluminium.

I have two references in French, the first one is
"Des Materiaux" (materials) from the engineering school Montreal Polytechnique:

6061-T6 = Yield = 275 MPa, ult = 310MPa

I also looked at Russel Metals handbook and they give me:

6061-T6 Yield = 40 ksi Ultimate = 45 ksi

40 ksi = 275,9 Mpa
45 ksi = 310,3 Mpa

35 ksi is more in the range of the 6063-T6

One last thing:

According to my Russel Metal handbook, the strength of 6061-T6 after welding is:

6061-T6 welded with 5356 alloy: Yield = 20 ksi Ultimate = 30 ksi.
6061-T6 welded with 5356 alloy: Yield = 137,9 MPa Ultimate = 206,9 MPa.

I still have not received my copy of "Designing Power and Sail " from Arthur Edmunds and I am still waiting for a copy of "A Method for Estimating Loads on Catamaran Cross-Structure", by A.L. Dinsenbacher even if I already have purchased the Sname Small craft papers compilation cd :-(

However, please note that : SCANTLING RULES WILL OFTEN ASK YOU TO USE THE YIELD STRENGTH AFTER WELDING. Before performing any calculation, make sure that you read carefully all of the requirement.

 

My mechanical properties came from The Aluminum Associatioin Handbook, "Engineering Data for Aluminum Structures":

6061-T6 aluminum drawn tube and pipe, minimum strengths, suitable for design, unwelded:
Ultimate tensile strength: 42,000 psi, 290 MPa
Yield tensile strength: 35,000 psi, 241 MPa

The typical tensile properties, BUT NOT SUITABLE FOR DESIGN, are:
Ultimate tensile strength: 45,000 psi, 310 MPa
Yield tensile strength: 40,000 psi, 276 MPa

Minimum expected welded tensile properties for drawn tube and pipe (less than 3/8" wall thickness, 10 mm) are:
Ultimate tensile strength: 24,000 psi, 166 MPa
Yield tensile strength: 20,000 psi, 138 MPa

In this design situation, there may not be any welding on the crossbeam tubes, so you can use the minimum mechanical properties, unwelded.

Eric

 

Eric,

Any idea why one would give figures which ARE NOT SUITABLE FOR DESIGN?

I don't see the need for numbers for any other reason.

regards

 

i like Grainger Design chamfer bevel joint, efunda may be of help calculating

 

Reverse engineering Seawind 24

Hello all,

We had terrible weather here yesterday so sailing was called off. I jumped into the kayak and measured a Seawind 24 that lives nearby. The Seawind 24 is the most numerous large cat in Australia with over a hundred built and it was exported as well. They a reputation for robustness and structural integrity even if they are regarded as dated nowadays. They have to be a good example of safe engineering practice. Best of all the load path must be through the beams so it is a useful cat to reverse engineer. Most are 20 years old so they have proven themselves safe from fatigue.

LOA - 7.6m
Beam c-c - 3.8m
Displacement - 800kg
Crew - usually two - if they are fat say 200kg

The Seawind has three beams connecting the hulls. The forebeam is set back about 700mm from the bow and has a good 500mm of bury on the deck. The rear beam has about 700mm bury on deck but the mast beam has no bury. The mast carrying beam ends in a casting with one bolt holding the beam in the casting. The casting itself is bolted to the side of the hull. The mast beam can be assumed to be pin jointed and therefore take no cantilever stress but does act as a simple beam. As the loading of the beam is on the inside of the hulls it sets up a moment for both hulls to rotate deck inwards which must be opposed by the other two beams. Let's forget this for now.

The beams are mast sections approx 190x128 with 4mm wall. All beams are identical in section. I as I calculate it is 4x10-6m4
Moment of Seawind 24 = 800/2 +200 x3.9mx9.8ms-2
=23400Nm

Stress in beam = My/I
=23400.x 0.065/4 x10-6
=380Mpa for one beam
If we assume that the mast beam does no work then this stress will be fed through two beams so stress
= 190Mpa
SF = 241/190 = 1.26 assuming the mast beam does nothing

The mast beam is under stress due to rig tension. The boat I measured doen't have a dolphin striker so deflection shows load. Measured deflection is 8mm on 2.8m long pin jointed simply supported beam.

W = 48EIa/l3
=48x72x10 to 9 x 4 x 10 to -6 x 0.008/2.8 cubed
= 5038N or 514 kg

So mast beam is already highly loaded and can't take much more stress. Stress in mast beam at mooring is

Stress = Moment x OD/2 divided by I
= 7196 x 0.065 divided by 4 x 10 to 6
-116 Mpa close to half allowable stress of alloy.

When boat flies a hull mast beam will be stressed more as rig loads up and mast compression increases.

So

As the Seawind is a very safe boat I think the model from the edmunds book is conservative. The Seawind is a demonstrably safe boat that has proven iteslf time and time again with many offshore passages along the coast and even across oceans. There was a vastly overloaded version that sailed parts of the Pacific.

Probably it would be good practice to accumulate a wealth of data of proven three or two beam cats and reverse engineer the good ones but especially the ones that broke - British Oxygen for example. If my calculations are correct then the Edmunds example needs a very small safety factor and may be over engineered with no safety factor.

As for me I will be trying to get a sail on the Seawind and measure the mast beam deflection to work out mast compression loading (a little thing I am interested in)

The next cat I will measure will be a Hobie 18. The 16 has issues with the beam castings but the 18 has proven itself strong and safe. People use it in the surf and give it hell which is great testing. Two beams and a dolphin striker but it is pretty easy to see the load paths.

Cheers

Phil Thompson

 

For a standards lab to say a value is suitable for design, requires an incredibly high degree of confidence in the test results. Variations in the material quality are important too. Say I'm a lab techie, and I measure 50 samples of the same grade of aluminum from 10 different makers. On average, they're good to 275 MPa. But let's say five samples, probably not all from the same supplier, are in the 240 MPa bracket. I can say that most of this grade of alloy will handle 275 MPa, but since there's a very real possibility that a given random piece will be lower, I have to quote 240 MPa as the value to design to. You design with the lower value (and, in the case of Al, you will often use the fatigue value which is lower again), but the average is there to give you some idea how much more than design load will actually damage things.

 

Alu beam sections?

Illuminating!

I own a number of 12m extrusions, made by Proctor Metal Masts for a 60' racing tri mast project some years ago ( see attached .jpg file ) - Proctor Section 10080. These are 250 x 200mm x 5mm min wall thickness, and in - I believe - 6061 T6 alu.

I'm considering using these as catamaran cross beams, perhaps joining pairs of tubes into 'flat-back-to-flat-back' oval sections by bonding and - using strip alu inserts in the 5mm corner 'lands' - blind fastening. I am trying to determine what working loads this configuration would reliably support, in a cantilever configuration, with a load-bearing 'central' mast beam and a load-bearing rear beam.

The cat I'm looking to 'glue' together has 13.5m ply/epoxy elliptical hulls, weighing in at 765kg each, with a planned loaded AUW of 5 tonnes, and a c/l to c/l beam of about 7m. I'm trying to avoid the need for a 'dolphin striker', and may need to consider a biplane rig, with spars buried in the two hulls.

I'd welcome thoughts from those forum members with better facility in eng math than I.

 

Marshmat is correct in his description of why some values are labelled "not suitable for design." They are listed in the catalog as "Typical Values". Design values would have to be somewhat lower. Sometimes you see references to the use of standard deviation. All data points as a group have a standard deviation, and a safe design value from a test group is the average value of the total of data points, less two standard deviations. Then you are pretty sure that your actual stress will not reach the maximum breaking stress, or yield stress, whichever you are designing to.

Phil Thompson's reverse engineering is precisely what classification societies do--they look at the history of both successful and broken designs to come up with a reasonable guideline for design somewhere in between. I think it is very interesting that he finds Art Edmond's guideline to be conservative without a safety factor. So this is very good information. Here is a good example of an easy-to-use analysis method verified by an actual boat design. More examples should, one way or another, solidify this method.

Eric

 

What do you think about this folding cat?
http://www.sailingscuttlebutt.com/media/06/0626/
(Has it been discussed before?)

 

I haven't seen it before.
It loooks neat.
More details on
http://www.cat2fold.com

 

folding cat beams

The beams on Rafael Francke's cat are examples of a highly engineered beam system. The video shows how the boat can be winched in and out quite successully.

Putting hinges into the middle of a beam is problematic as the highest stresses in a beam are in the top and bottom flange at the middle point of the beam. You really have to engineer the system well. Cat2fold has very well made beams.

Having the beam work well when it is fully extended is the easy bit, getting it to do its job whilst it is folding is the hard part.

If you draw a free body diagram of the forces on the hulls of a cat one that tends to be forgotten is the torque on the hulls when looked at from in front (or behind). The hulls want to rotate deck inward due to all the weight of the beams, mast and rigging and bridgedeck. If you were to quickly cut the beams in the middle both hulls and beams would fall inwards.

When folding this force is really hard to deal with as the beams are not good at resisting this force when half folded. This torque tends to bind the hinges up and seize the system.

Rafael Francke originally used a single mast but has gone to a twin rig set up. He doesn't explain why on his web site but I guess that he found the torque hard to cope with with the weight of the mast on the beams so the mast was removed. What I like about Rafael's approach is that he has done the experiment, modified it and proven it when building and trialling the boat. Design and experiment followed by vindication.

In my own folding cat I use a different (also patented) system to Francke that seems to cope with the torque reasonably well. The lessons I think both Rafael and I have learnt are that you have to do lots of homework and then be ready to do lots of modifying when the boat is launched.

If anyone out there is thinking of doing their own folding (or original concept) cat I would suggest doing a small (say 16ft ) prototype that can use Hobie 16 or similar gear. This would allow cheap and easy modification and give good data for the builder. Better to spend less on the software and get out there building and learning. The real world always includes the things you can forget.

cheers

Phil Thompson

www.foldingcats.com