Trimaran crossbeam calculations

[daiquiri]

Wrong link in my previous post, I'm sorry. The tri in the calculations above is the W17, from the same designer: http://www.smalltridesign.com/W17/study-profile.html
Just for correct info.

[Richard Woods]

Daiquiri

Unless I misunderstood your attachment, you say 150mm dia beams are insufficiently strong for a 17ft trimaran

Reverse engineering is always useful.

My Strike 18 trimaran is very similar to the W17. My design uses 100mm (4in) OD tubes which I feel are oversize.

150mm OD tubes are what I use on my Strider 24 catamaran. Typical displacement 1T, CL spacing 4.2m. None have broken in 25 years.

Clearly the practical design of crossbeams is not matched by theory. There was a similar thread a couple of years ago regarding catamaran beams. The "theoretical" calculations given by others were also massively over spec compared to reality.

Richard Woods of Woods Designs

www.sailingcatamarans.com

[Ad Hoc]

Originally Posted by daiquiri

It makes much more sense, imho, to consider just the bending moment stress in this case, since it is by far the biggest factor, and then apply a guesstimated safety factor (which you'd have to apply in any case).

Daquiri, et al

You’ve got the main elements correct. However, it appears no one has mentioned or even realises the most obvious aspect that has yet to be mentioned, when designed these beams. Deflections (and rotation).

The bending and more importantly the torsional loads, are related to the amount of deflection, since both ends are fixed. This is exacerbated by the material in question. When using aluminium, all calculations are deflection driven, very rarely stress driven. When using composites, even more so, owing to the lower Youngs modulus.

The successful method of designing these beams is by looking at how much deflection you expect or wish to experience, and design to that value, not the direct in-plane bending stress. You’ll find that the deflection always predominates, unless you have a very odd arrangement (which does occur).

Then when you factor in fatigue, the stress values you obtain, from your deflection calc’s, suddenly appear somewhat too high!...and off you go.

As you say, a picture is a thousand words.

Here are 2 very different examples.

Earth Race, you can see those very stiff beams and root connections to prevent excessive deflections and slope, at the ends, but mainly the angle of twist and the shear flow from ama to main hull. The longer the connection (long.ty), helps to prevent rotation and hence excessive deflections longitudinally of the ama, relative to the main hull.



In B&Q, the beams are deep and spreading the load over a wider bases (less couple), and a similar type of connection. The shear flow requires more “area” which is why those connects to the main hull are so large. Which also assists in reducing the angle of twist, which is the objective for these. It does appear that the method used here is having the ends of the ama’s almost “pin ended”, as much as a possible to reduce the fixity of bending to pure reaction loads too.



Final note. If you take a simple open channel and compare the amount of twist, under a given load, to a closed cell, like a box, the open cell has an angle of twist 15,424 times greater and a shear stress 257 times greater, than the closed cell (box)!

Food for though

PS...you should also check the buckling too...if your beam is too long and slender, buckling may become the dominate mode of failure.

[daiquiri]

Richard, no - you have missed the point of that example. The calculation shown serves as a numerical example which shows the ratio of stresses due to bending moment and torsion. It serves to illustrate the point that the torsional stress is generally much lower than the axial stress due to bending.

The numbers you see come from two input assumptions:

1) that the structure is thin-walled. That allows me to perform a simplified analysis, because I can't waste my day in making useless calculations. I have a life to live, jobs to finish and the drawing I've attached is already over the top, considering the purpose of the discussion. But it's ok, I did it anyways.

2) that the loads on the beam arise from an assumed 3 cm upwards flexing of the forward beam. Again, the point is not the actual number, but the need to have some initial data for the calculation. A diam. 150 mm, 1.7 meters long beam requires a big load (with the consequent huge material stress) to flex 3 cm. I could have said, for example, that it flexes only 1 cm and all the numbers would shrink down to a perfect fit. And perhaps even less than diam. 100 mm tube would suffice then.

If you want to make a comparison between the theoretical scantling and the reverse-engineered one, you give me the correct loads and I'll give you the structure.
Cheers

P.S.:
Ad Hoc was faster this time.

[Ad Hoc]

Originally Posted by Richard Woods

Clearly the practical design of crossbeams is not matched by theory. [/url]

Im with D here, you’re missing the point.

Beams of cat’s and tri’s are based upon assumptions. Assumptions of what the expected loads are, then the material of choice and the finally the arrangement. The theory is sound, the assumptions, ie the applied loads, is not so, this is a massive variable and generally we are unable to obtain this “absolute” figure to use for a design to compare to theory. Thus we guess, or assume, as our starting position, just as D did in his example, to provide “real figures” to an abstract example.

There is no disconnect with sound engineering theory and the design, just the final result, which is the difference between a good design and bad design, knowing what assumptions to use and what not to use, and how to use them correctly.

[langdon2]

So...we're back at the starting point again, are we not? Defining loads? Except that it's not quite the same starting point. The assumptions are better informed and the methods of assessment, measurement, design and construction have been discussed. Next step - choose an assumption, build to it and see what happens. Which, of course may or may not be conclusive.

I'm learning a great deal from you all. Thank you.

[Ad Hoc]

Originally Posted by langdon2

So...we're back at the starting point again, are we not? Defining loads? Except that it's not quite the same starting point. The assumptions are better informed and the methods of assessment, measurement, design and construction have been discussed. Next step - choose an assumption, build to it and see what happens.

Correct.

The load scenarios and assumptions you make, shall dictate the final result and its success or failure.

[Ad Hoc]

Originally Posted by daiquiri

P.S.:
Ad Hoc was faster this time.

Only by virtue of timing. I had just recently woken up and was going through my emails as the coffee downstairs was filtering it way through and filling the house with its aroma

[Richard Woods]

My apologies

Like you I also have to earn a living so tend to scan read most posts. I re read yours more carefully and now see what you were saying

I also should have put the word "simple" before Theory in the quote below.

Originally Posted by Richard Woods

Clearly the practical design of crossbeams is not matched by theory.
[/url]

Having said all that I think this is a very useful thread for everyone.

Richard Woods of Woods Designs

www.sailingcatamarans.com