Trimaran crossbeam calculations

Discussion in 'Multihulls' started by langdon2, Jun 5, 2011.

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rxcompositeSenior Member

Thanks Ad Hoc, that was quick. Why did I not think of that. I was already thinking along the lines of a "submarine".

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DCockeySenior Member

Interesting and informative thread. One question - how significant can torsion be as a design factor for trimaran beams? The first part of the discussion seemed to focus on bending of the beams.

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daiquiriEngineering and Design

Since there are two beams for each ama (from the opening post: "The usual crossbeam layout, that is two beams per side, one fwd one aft.") the torsion will be balanced mostly by the differential bending of the two beams. If it was a single large beam, then the torsional loads of it's cross-section would have to be adressed too.
Cheers!

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rxcompositeSenior Member

When you get hit by a quartering wave, the front end of one of the amas will rise first causing torsion for the crossbeam.

This can be quite significant. I fed Catbuilders catamaran basic particulars in my software and I am getting 3.5 g's of vertical acceleration at 18 knots. His boat is a high performance sailboat.

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DCockeySenior Member

Understand that. I was wondering about torsional stresses in the beams resulting from the twisting of the beams as the amas twist (in sideview) relative to the center hull.

If the connections of the beams to the amas are sufficiently compliant in torsion then the torsional stress the beams will be low since the torsional moments on the beams will be low. An interesting example of where making joints stiffer can lead to problems.

Another approach would be to use a beam section which is sufficiently flexible in torsion within allowable stresses compared to bending stiffness. An "I-beam" section may be a better choice than a circular tube. (Someone commented earlier that a circular tube was not a particularly good choice.) Increasing stiffness in the wrong way may lead to higher stresses.

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Richard WoodsWoods Designs

You are right. In simple terms a beam has to have some width as well as depth. In just vertical loading a beam could be, say, 300mm deep and only 30mm wide. Stiff enough to resist the static bending. Even if there were two of them, properly spaced beams with this proportion would twist. For more "properly spaced" comments see the FAQs page of my website

Fortunately practicalities come into play. On an open deck trimaran the beams act as the walkways so have to have a sensible width. On the boat under discussion probably 100mm wide min, plus fairing (which helps control twist)

The Wolfson Unit did a lot of work on the beams of GB3 (the 80ft trimaran forerunner to GB4). They decided that the fore/aft loads were about 1/3rd the plain vertical bending loads.

Again fortunately that means that for "normal" proportioned beams these loads are safely supported. So beam torsion isn't usually a problem with trimaran beams. Providing they are correctly positioned along the hulls.

Richard Woods of Woods Designs

www.sailingcatamarans.com

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rxcompositeSenior Member

Circular section is better in torsion but the amas primary load is tension/compression so a rectangular section (or I beam) is better. The crossbeam fore and aft works in unison. When the front crossbeam twist, the aft beam tend to rotate in the same direction because it is mechanically connected to the front beam thru the hull and the ama.

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DCockeySenior Member

Another thought about torsional stiffness of the beams. Assuming the torsional stiffness of the structure as a whole is dominated by the bending stiffness of the beams (as discussed by daiquiri with the beams sufficiently spaced), then as the torsional stiffness of the beams is decreased the torsional moments at the connections of the beams to the amas and center hull would decrease. Presumably lower torsional moments at the connections is usually a good thing.

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DCockeySenior Member

What I'm trying to suggest is that torsional stiffness of the beams in a trimaran may not always be desirable to minimize stresses in the beams for a given overall system stiffness. So a beam section which is generally considered "better in torsion" may not be better for this application. A catamarn is a different situation. I realize this concept is counter-intuitive at first glance.

As daiqiri said above:
Consider a trimaram with two beams which are rigidly connected to the center hull, but the connections to the amas are sleeves which can rotate. The boat as a whole will be stiff in torsion as long as the beams are sufficently stiff in vertical bending (assuming the center hull is stiff in longitudinal torsion). Due to the sleeves being able to rotate there is no torsional moment acting on the beams so the torsional stiffness of the beams does not affect the stiffness of the whole system. Rather the vertical bending stiffness of the beams and the spacing of the beams determines the torsional stiffness of the system.

Replace the sleeves with fixed connections. Now the beams will twist when the amas twist. The system will be stiffer, but how much stiffer depends on the ratio of torsional stiffness of the beams to the vertical bending stiffness of the beams multiplied by the beam spacing. If the ratio is low then the added system stiffness will be small. Depending on the sectional propoerties of the beams stresses may go up due to the torsional distortion of the beams.

I'm not suggesting a particular design solution. Rather just that this may be a case where for same overall system stiffness a design with "stiffer" components may have higher stresses than one with components with selectively reduced stiffnesses.

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daiquiriEngineering and Design

Yes, what you're saying is theoretically correct, but (for a typically proportioned tri) the beam-root stresses due to torsional loads will be around 1/10th of the stresses due to bending moment. So in practice the torsion will play just a minor role in the design of a multi-beam multihull.

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DCockeySenior Member

.... with "typical" proportions, beam section shape and load assumptions which the "torsional loads will be around 1/10th of the stresses due to bending moment" statement is based on.

Vary substantially from those proportions or beam section shape, or a design which has different loads and the torsional stresses may become significant.

The other reason for considering torsional moments and stresses is the connections of the beams to the amas and center hull.

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Richard WoodsWoods Designs

You may like to look at the Gougeon's Adrenalin F40 trimaran from 1988 which I think used the flexible attachment/stiff beam approach

Richard Woods of Woods Designs

www.sailingcatamarans.com

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DCockeySenior Member

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daiquiriEngineering and Design

A picture says more than thousands of words, so consider this trimaran by Michael Waters:
http://www.smalltridesign.com/W17/study-profile.html
I have choosen this one because it states all the most important dimensions and it's proportions can be considered typical. Differently from the Waters' design, i have assumed crossbeams made of aluminum circular bars, to simplify the calculations.

Imagine a moment in which the ama is twisted upwards (passing through a wave crest, for example), while the rest of the boat is leveled (that's a conservative situation).
The explanation of my previous post then is given in the following attachment, made upon dimensions of the above tri:

The resulting torsion stress is 15% of the bending-moment stress. So, while one could take the torsional stress into consideration for a detailed design of the crossbeams, in reality the exact value of the real forces acting on a seaway-going trimaran are unknown to us, so the actual significance of results which include that additional 10-15% stress is questionable. 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).
Cheers

Last edited: Jun 13, 2011

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DCockeySenior Member

Thanks for the example.

Based on the photos it appears that the Buccaneer 24 has a lashed connection between the amas and the beams which may allow some relative twisting motion between the beams and amas, particularly for large pitch angles of the amas relative to the center hull. If so the torsional stress in the beams will be significantly reduced compared to a fixed connection with twist in the beams equalling the "pitch" angle of the ama relative to the center hull.

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