Load Paths in a Catamaran

Discussion in 'Multihulls' started by AndrewK, Feb 24, 2009.

  1. Guest625101138

    Guest625101138 Previous Member

    Stefano
    It looked like there was no obvious torque carrying section. I can see it would certainly load up the window frames.

    Car designers even have trouble resolving torque in car bodies and these are more compact structures than a boat. I had one car that creaked each time it was driven at an angle through a spoon drain. I was told that a particularly ford model would pop the front windscreen if driven with a bit of speed at an angle across a drain.

    I have had experience with a planing monohull splitting along the keel line due to poorly resolved torsional loads from quartering seas so it is something I am sensitive about. A split along the keel is not very obvious but it will let in lots of water.

    I have also seen many problems in steel machine structures that are poorly designed to resolve torsion.

    A good test is to support the stern of one hull and the bow of the other and see how far the two hulls rotate relative to each other. Also listen for any obvious stress relieving.

    From numbers I have done on small cats I find you only need a single cross brace if it is adequate for the torsional loads. Might need minor cross beams to support tramps or deck but a single major beam will carry all the primary loads. Needs to be well fixed to the hulls of course. A bridge with lots of big openings is not very good for resolving the torsion.

    Rick W
     
  2. Ad Hoc
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    Ad Hoc Naval Architect

    "...I have done on small cats I find you only need a single cross brace if it is adequate for the torsional loads..."

    The two hulls will move independently. As such one single beam is insufficient, unless of course the beam is the entire raft/bridge structure.

    For example. If one designs an I-Beam at midships, or even a very torsionally stiff RHS, the ends of the hull (bow or stern) will still displace vertically relative to each other. The midships beam wont help in that regard. If you place the single beam at one end, it doesn't alter the relative displacement between the two "free" ends either, since one is stiffened, and the other is not.
    Unless of course if the single beam at the end is so stiff it can absorb the loads from the far end effectively to reduce the displacement. This requires a stiff hull to accomplish this. However, to do this single beam approach requires a significant bit of structure, ie heavy!

    one beam fwd and one beam aft is far superior. Just look at racing cats.
     
  3. AndrewK
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    AndrewK Senior Member

    Stefano
    Thanks for the link to the photos, nice boat.

    My roof top is only 4.3 x 4.3m and 20mm 80kg foam, sounds like 600g DB laminates will do nicely.
    The photo of your outboard location and setup appears to be the same as what I had in mind, would you do the same again?

    Your reply to Rick's question regarding the connecting beams; I imagine the rear and mast connecting bulkheads were in effect boxed sections. Behind the mast in most bridgedeck cats the saloon seating and back rest makes it into a boxed section, similar for the rear beam. Although the amount of UD glass (32x20mm) seems low. Mine is not incorporated into the web, it is a solid glass flange roughly 200x10mm. This makes the mast bulkhead an I beam and the rear beam is box section. At a guess this is roughly 2.5 times more UD.
     
  4. Guest625101138

    Guest625101138 Previous Member

    An "I" beam has little to no moment carrying capacity hence is an inefficient section for a cross beam.

    Fore and aft beams do not provide better torsional rigidity than a single beam having the same sectional area of the two beams. So with a single beam you can reduce the weight as you can enclose greater area for less surface.

    Rick W
     
  5. Ad Hoc
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    Ad Hoc Naval Architect

    Rick

    "..An "I" beam has little to no moment carrying capacity .." can you explain what you mean by this?

    "..Fore and aft beams do not provide better torsional rigidity than a single beam having the same sectional area of the two beams..."
    This is in correct. It is not a case of calculating the required modulus and saying oh, i'll make one beam and place it at one end.

    It is simple maths. The lever from the free end (at one end) to the beam (at the other end) is much greater with a single beam placed at the opposite end. With a given displacement the hulls will still experience the same vertical force no matter how many beams one designs into the vessel, it is an external force. This force, times the now large lever from the free end to the single beam at the opposite end, creates a very large moment.

    Since you will experience greater displacement at the unstiffened 'free' end of the unstiffened hull, be it bow or stern. This increase in displacement will affect the structure and requires additional load paths (ie structure) to sherk the increase in local loads. Again this is assuming the hulls are stiff enough to do this without flexing locally themselves. Unless of course you're happy to have the hull ends moving up and down with relative ease, while the opposite end does not, but creeks owing to the movement of the free ends and light structure which is unable to transfer the loads properly.
     
  6. Guest625101138

    Guest625101138 Previous Member

    If the maths is so simple then show me.

    Take an example of a 4T catamaran that is 12m long and 8m beam. The boat is supported on dry land for repairs. The port hull is supported at the very stern on blocks and the starboard hull is supported at the very bow also on blocks. There is no support for the bow of the port hull or stern of the starboard hull. This is the same case of the cat operating in a quarter sea - arguably more severe but there would be dynamic loads when operating.

    Show me how your two "I" beams will resolve the tendency of the port hull to droop at the bow and the starboard hull to droop at the stern. Give me the stresses in the cross beams. Make them as big as you need to control deflection less than 0.1m bow to stern on each hull.

    Rick W
     
  7. sigurd
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    sigurd Pompuous Pangolin

    Hello Rick...

    "Fore and aft beams do not provide better torsional rigidity than a single beam having the same sectional area of the two beams. So with a single beam you can reduce the weight as you can enclose greater area for less surface."

    Using two beams, you do not just add the torsional stiffness of each beam...

    For a thought experiment: your two beams are round and buried in sockets in the hull, but there is nothing keeping them from rotating - infact they are lubricated to rotate easier. This way the torsional stiffness of each beam becomes zero.
    Are your hulls now free to move independently of each other?

    Answer is no. You should try it if you can not see it, try to move the two beams closer and the torsional stiffness between the hulls will decrease.

    Hello, Ad Hoc

    ""..An "I" beam has little to no moment carrying capacity .." can you explain what you mean by this?"

    So a triangular or tube shaft is stiffer and stronger in torsion right?
     
  8. marshmat
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    marshmat Senior Member

    An I-beam works wonderfully in bending, but has very little resistance to torsion. If you rigidly fix one end, and twist the other end as if the beam were a driveshaft, it offers very little resistance. Hollow or box sections tend to be much stiffer than I-beams in torsion.

    Looking at sigurd's thought experiment above, with the freely rotating crossbeams- if I read correctly, it looks like each of these beams is now loaded (almost) purely in bending. If we rigidly fix one hull (bolt it to the pier, say) and force the bow of the other hull down and the stern up, this movement would be resisted by the two freely rotating crossbeams acting essentially as cantilevered beams. Move them closer together and the moment on the beams increases for the same movement of the hull, so less torsional stiffness.

    I suspect that what Rick is talking about is a hollow or box section crossbeam, rigidly fixed to the hull. In this case, the moment created by one hull pitching up while the other is fixed would become a torsion force in the crossbeam. If you're transferring the entire load torsionally, it would make sense that a single beam would be more structurally efficient than two smaller beams. But that's assuming the entire load is torsional, which I think is only a reasonable assumption if you're talking about a single, midships beam. The two smaller beams (if rigidly fixed to the hulls) would be in some combination of torsion and bending. It's certainly plausible that this could work out to be superior to a single torsion beam at midships.

    Still, if we're after maximum torsional stiffness, I'd think we ought to be looking at variations on the X-beam style. (One crossbeam from port bow to starboard stern, one from starboard bow to port stern, rigidly fixed where they cross at the mast step and rigidly fixed to each hull. Could add bow and stern crossbeams too.)
     
  9. Guest625101138

    Guest625101138 Previous Member

    I agree with you that it is not additive but do the sums on what is required to prevent the deflection I described in my earlier post. Then compare with what can be done with a single beam.

    Rick W
     
  10. Guest625101138

    Guest625101138 Previous Member

    I need to see the simple maths you describe. If it is so simple then prove it to me. I have set up the example earlier. Show me the numbers!

    Just give me the calculations for two beams that will limit the deflection to the nominated level.

    Rick W
     
  11. Ad Hoc
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    Ad Hoc Naval Architect

    Rick

    Firstly, you still have not answered the Q, "..An "I" beam has little to no moment carrying capacity .." can you explain what you mean by this? I know what an I-beam can or cannot do, but from how you describe this, i need to understand your definition. Therefore, can you please explain to me this statement.

    "Take an example of a 4T catamaran that is 12m long and 8m beam. The boat is supported on dry land for repairs. The port hull is supported at the very stern on blocks and the starboard hull is supported at the very bow also on blocks. There is no support for the bow of the port hull or stern of the starboard hull. This is the same case of the cat operating in a quarter sea - arguably more severe but there would be dynamic loads when operating.."

    Firstly, there is no definition of what is connecting the two hulls together. Therefore how can i comment. Is there 1 beam or 2, is the single beam just say 300mm wide or is it 3.0m wide, your 'thought' experiment is lacking in the essential detail to provide an answer.

    Secondly, just taking their own weight, by removing blocks, is not a sufficient test. Since the hulls will be stiff, but more importantly one assumes the cross beams are stiff too. (If you are expecting 100mm deflection doing this, then your beams are not stiff enough at all). The weight will be distributed evenly. In a dynamic sea load case the two hulls are being force vertically, in opposite direction, this is very different from a simple evenly distributed gravity case by a large order of magnitude.

    So, going back to your 'example', if you have one small single beam midships, take off the blocks, (or in a large sea hulls being forced) as your two hulls rotate, the extreme ends, will displace an amount Y positive and Y negative. This displacement is directly related to a force, call it F.

    This single beam must transmit the moment, which has become a torsional load of Y times F. Where Y is the distance from the midships beam to the extreme end of the hull.

    As such the beam is doing nothing. Since the rotation, or pivot point is at midships. Just try and stop a door closing by placing you hand on the hinge!! The end of the door still keeps moving, just as the end of the hulls do.

    If you now have this same single beam, but place it at say the aft end.

    The pivot point has now changed. The two hulls are not free to rotate about midships, owing to the beam aft. The stiffness of the beam will move the pivot point. How far aft depends on the stiffness of the beam and its location. However, it will in general, be almost coincident with the aft beam again. Why, because the the fore ends are free to displace as much as they like, there is no resistance to any displacement. The only resistance is aft, the single beam.
    As before, take the distance as Y and the same force F, since it is the same vessel only change is location of the beam. Now, the distance is no longer Y from midships to the end of the hull, but almost the entire length of the hull, so for example the distance is now say 2Y. The moment applied is now 2Y times F, ie twice the moment. This single beam must now resist twice the torsional moment as before.

    If you now place 2 beams, one aft and one fwd. The ends are no longer free to displace, there is resistance to this displacement. As the fore end lifts up on the port, and the stbd goes down, the beam, at this fore end, is forced into the classical elongated "S" shape, as it resists the relative displacements between the two ends. The pivot point has now returned to midships, again assuming symmetry.

    This beam (up fwd or aft) is now in pure torsion.

    You then design a structural member to take this torsional load.

    Making a statement of "..Give me the stresses in the cross beams.." indicates that you are copying ideas from other vessels, rather than actually calculating the stresses. Since each design is unique and as such has a unique solution. The stress in one boat will not be the same in another, if the vessels are not the same nor if the beams are not the same. It is a meaningless statement.
     
  12. Ad Hoc
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    Ad Hoc Naval Architect

    Sigurd

    "..So a triangular or tube shaft is stiffer and stronger in torsion right?.."

    well, stiffer than what...i assume you mean an I-beam?..then yes. It is not stronger, this is related to the material properties; definitions!

    Torsion relates to the shear stress and angle of twist being applied. Shear flow around a structural member is very important. An I-beam is an "open cell", as such has no shear flow, hence the torsional stiffness is very low. Whereas a closed section, like a triangle, or better stiff a box, is significantly stiffer.

    As an example. If you were to calculate the % difference in torsional stiffness between and open cell channel "U" and a closed cell box "[]", it is actually 250,000%....whopping difference huh!
     
  13. Guest625101138

    Guest625101138 Previous Member

    My reference to the "I" beam is respect to the torsional moment as we are discussing torsion.

    A single beam in my case would be located near midships - for a sailing cat it would also carry the mast compression load as well. For this calculation though neglect any mast loads. I did not say it would necessarily be a small beam. I said a single beam will do the job and implied it was as good as two if it was adequate to handle the torsional loads. The load case is shown in the attached image.

    You can nominate any beams you like and locate them as you like to link the hulls. Assume the hulls have identical weight and located mid length. The hulls are 1m wide at the widest and taper to the bow and stern.

    Now show me your calculations for the beams. Show me the maths. Give me actual stress in your beams to limit the deflection I have described.

    If you show me your design I will give you a design for a single beam and we will see what could be built lighter.

    Rick W
     

    Attached Files:

  14. Ad Hoc
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    Ad Hoc Naval Architect

    Rick

    I assume you have read my post above?..if so, the explanation is crystal clear. If you do not understand the concept, that is not my problem. It is basic structural principals. It has nothing to do with "numbers" or "stress" values. Structural theory doesn't change with different numbers, it remains the same, it is an absolute.

    Changing your geometry and applied loads change the numbers, it does not affect the theory one bit.

    As shown in your little sketch, which it appears you fail to recognise. Applying the load at midships, indicated by the yellow arrows, and if your single beam is also at midships, the beam is in pure bending, there is no torsion. If you unable to grasp this concept, there is no point discussing this further, as it will be a circular argument.
     

  15. Guest625101138

    Guest625101138 Previous Member


    I will give you the benefit of the doubt here and assume you did not appreciate that the port hull is supported only at the stern and the starboard hull only at the bow. The red blocks elevate these two points off the ground.

    Without connecting beams the bow of the port hull will fall to the ground as will the stern of the starboard hull. As drawn the hulls are not statically stable.

    If you did grasp this from the image then I hope you are not designing boats for anyone.

    Rick W
     
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