Load Paths in a Catamaran

Wow, this is better than any comedy currently on TV

" REPEAT - fatigue limit is a stress RANGE. You seem to think it is related to the number of cycles. .."

So, in a graph that you supplied you cannot interpret how to read a graph. Why am i no longer shocked?!

Well in the known world of mathematics a standard cartesian graph[1] is represented by 2 coordinates, and X value and a Y value. When there is curve or line on said grid from x and y values, one can read along one axis and get a value for the other...so simple it's child's play.

On that laughable note...I'm drawing stumps. As my friends always said, you cant educate pork!

[1] Read a maths book!

 

Gareth
It has taken me quite a while to get back to this. I had a few distractions. You can see that there has been some silly input from Ad Hoc that deserved to be challenged.

Concerning your calculations, you have not taken into account the torsion in the hulls. I am not referring to any deflection in the hull but the simple fact that the beams have greater constraint than the simple beam you have considered. It means both ends have a transverse torque. I know you have stated they do not resolve any longitudinal torque but their fixity will take lateral moment produced from one beam to the other down the length of the hull. I believe your analysis overstates the deflection by a factor of about 4.

This link shows the sort of constraint on the beams:
http://www.engineersedge.com/beam_bending/beam_bending13.htm
It also provides applicable formulas for the free but guided end arrangement.

The stress level is also lower than you calculate for the 300mm beams. However these beams will experience cyclic reversing stress so allowable stress without any safety factor would only be about 55MPa. Hence what you have is OK if you are happy with a safety factor of about 1.2.

Not allowing your beams to carry longitudinal torsion is a conservative approach but then they will offer little resistance compared with a single beam of twice the diameter and same thickness. The polar moment is diameter to the third power for the same thickness tube.

Putting the same amount of metal as the two beams into a large single beam results in a fraction under the allowable deflection. The notable difference is that the shear stress is only 11MPa. So it has a safety factor of around 3 whereas your 2 beams are on the endurance limit.

There are only two connections required compared with 4 for two beams. Also it will only be 6m long compared with probably 7-8m for the smaller ones.

Like I said very early on, this is a difficult load case and a single beam handles it nicely. In practice the beam could be built into the bridge structure.

Irrespective of all this it pays to ask a designer how this load case is resolved in the structure. It is clearly not as simple as many believe. If it was simple there would be more providing calculations - your input is of value.

I have played around with numerous cat models around 1m long and this demonstrated the efficiency of a single cross beam. I have also looked at it for pedal boat size cat and tri hulls. I have not been close enough to full-scale cruising cat design to see how the loads are managed but it does not surprise me when people describe how bridge cabins fail. A single torque tube or box could easily be built into the bridge structure. If I was buying a big cat this is what I would be looking for.


Rick W.

 

I have been using fatigue limit and endurance limit interchangably. Both are stress values however endurance limit is normally taken as the cyclic stress range that material will carry forever. It is the fatigue limit where the S-N curve asymptotes past the knee. The knee is sharper and at lower cycles for steel than aluminium.

The S-N curve flattens out after 10e7 cycles in steel and more like 10e8 for aluminium.

Rick W

 

Its been a number of days since I had a chance catch up with this thread, can we jump back to my post #18.
I want to determine as to what is the best way to place the UD glass in the mast and rear connecting beams.
Incorporated into the bulkhead edges as in Stefano's example or wider flat flanges either side to make it an I beam?
As I see it the UD at the mast connecting bulkhead is there mostly to take the transverse flexing and the mast compression load, and therefore was assuming that the flat flange approach was more efficient?

The cockpit lockers in front and saloon seating behind the mast bulkhead incorporate the I beam into a boxed section to provide the torsional rigidity along with the rear and forebeam.

Andrew

 

AndrewK

In saying "..the best way to place the UD glass.."...i assume you mean for strain?...ie to reduce the stress levels?

Do you have a sketch of your layout to get a better idea of what you're actually suggesting.

 

Ad Hoc
Yes align the UD to reduce strain. I have never done any electronic sketches, only by old fashioned pen and paper, will see what I can do.
All things being equal I have seen this done three different ways; 1. bulkhead edge de-cored and the UD placed into the edge, 2. UD drapped over the bulkhead to form a U channel, 3. flat solid glass flange top and bottom of the bulkhead.

 

AndrewK

A sketch is a sketch...by pen or electronic...doesn't bother me. I generally prefer to do mine by hand on pen and paper, for ease and speed. If you just scan in what you've got, from a piece of paper, with the main features....then see where to go from there.

Since a sketch will explain so much more than mere words...

 

Alloy vs. steel

This thread should be titled, When Engineers Get Into Knife Fights! I'm not an engineer. I thought that steel would not accumulate fatigue if not flexed past a certain point but that aluminum alloys would accumulate all flexing and ultimately fail. The question here seems to imply that all materials accumulate sub-critical stresses and eventually fail. Comments?

 

They do not - if the stress is below the endurance limit the component will survive. This is the basis of spring design.

You will find endurance limit quoted for most engineering materials but the data is more comprehensive for materials that have been around for a long time.

The S-N curve for steel has a distinct knee around 10e7 cycles. The S-N curve for aluminium does not have a sharp knee. You need test data at least to 10e8 to get some idea of endurance limit. If you are operating aluminium at high cycle loading around the stated endurance limit (often stated at 10e8 cycles) then you should allow some margin.

The endurance limit is always given for parent metal and usually in direct stress. If you weld the metal or conduct other heat treatment then this will reduce the endurance limit. Of course most connections also involve stress raisers so you need to work on the maximum stress.

The attached gives a good explanation of fatigue and endurance limit.

Rick W

 

BigCat

I am somewhat reluctant to wade into this again owing to other peoples perception of how one designs for fatigue and what fatigue really is. To use the basic SN curve approach as the basis for a design just emphasis the lack of understanding that is required to design correctly and effectively for fatigue. Laboratory made SN curves are fine for teaching and lecturing about the theory of fatigue and how to derive it and what is means, but as a method for a fatigue resistant structural design is very poor. At best, it demonstrates that one is just an observer or recently introduced into fatigue as a design concept.

The problem with fatigue, apart from some of the obvious, is the actual understanding of what it is and how to use this knowledge. It is significantly more complex than the simple DIY type of SN curves as some seem to incorrectly suggest. For example: which alloy, which curve, what type of joint, what is the loading history etc etc.

One needs to calculate the stress range to see what is or is not appropriate, determine the pattern and variation of nominal unloading on the structure in each cycle, not to mention the FAT class that may be appropriate for the joint on an SN curve, and whether thickness correction factors need to take place and so on and so forth.

A standard SN curve is an ideal material and all SN curves are produced under uniaxial loading or constant amplitude loading. Unless you search out those of variable amplitude loading, or obtain an SN curve that defines both how do you know which you are using?. The classic SN curve has the “nominal” cut-off values, or endurance limit. However, for the same material and class of joint, a variable amplitude loading curve has a lower cut-off limit because there shall be the occasional stress range occurring above the “endurance limit”. Hence this shall produce some propagation thus reducing the lower stress range limit. In aluminium especially, this renders the aluminium to have no fatigue limit.

Then we get to BS8118 for example, the bench mark for all fatigue design is all based upon uniaxial loading of “ideal” materials. It does attempt to provide “fudge factors” for variations, but is very limited and almost “guessing” on this score.

A ship structure for example, is not produced as an ‘ideal’. It is fabricated in a dirty environment not a laboratory.. As soon as the alloy is fabricated, the simple SN curve you wish to use is pretty meaningless. It cannot be used. The fabricate process must be taken into account. Not only that, since the SN curves are uniaxial loading what occurs under biaxial or triaxial loading? There is no or very little data on this, not to mention the six degrees of freedom the structure is capable of displacing. Hence what fudge factors to use here?

Then there is the subject of fabrication and what this does to the “ideal” alloy. FAT curves do help in appreciating the differences of certain joints. There are numerous sources during fabrication that reduces the fatigue life. From bending/forming to welding and the quality of the weld. The size of the weld bead etc. A very good paper reviewing this is given here from SNAME's Journal of Ship Production several years ago:
http://www.ingentaconnect.com/content/sname/jsp/2004/00000020/00000003/art00004

Then there is the environment. Sea water on welded aluminium structures can reduce the “allowable” design stress for a given “nominal” design life by up to as much as 90% of the static life.

Right at the end, one needs to work out the geometric stress raiser of the structural joint. This is generally achieved these days by the Hot Spot stress approach. FEA can establish, under very strict guidelines for doing this, a nominal stress and a peak stress (owing to the localised structural discontinuity) of the associated joint. This can then be used as another input for the stress concentration factor. So this eventually becomes the first review of any structure before one really considers what curve or how the structure is being fabricated. Once the above procedure has been done, the joint may require further redesign to account for all the fatigue ‘raisers’ that are introduced, which the designer has no control over.

Once one has done all this, then one can actually appreciate the complexity in designing for fatigue. I’ve just given a very very short summary of ‘some’ of the factors and influences to give a broad picture.

If it were as simple as looking at one single SN curve, everyone would be an expert!

 

yeah, you can't make a boat that floats unless you have the deep understanding of fatigue like ad hoc.

they all sink immediately.

 

With g=9.81 m/s^2, this leads to 9810 N of vertical shear force transmitted with each beam. That results 46 N/mm^2 stress and 26mm of deflection at the end if magnitude of twisting of the hull is to be assumed insignificant and torsional strength of the hull adequate.
Using the link Rick provided on post #77 here.

Almost 4 times as much flexing for the single beam solution ignoring twisting of the hull.

first quote as referenced above :

So how is it Rick, are you going to comment on that question in bold by Sigurd ?
In reality the hulls would twist a little, but in the 2 beam solution also those beams have a little torsional stiffness ignored also. These will propably cansel each other out when conserning total flex if designed properly.
And mast & rigging could take a significant part of this kind of loading as well.
Ignoring that and bringing the beams a bit closer to each other that 4 times stiffer might become 3 times stiffer, but 2 beams still seems beter than one single at the center if stiffness is the driving factor and hulls have adequate torsional strength for other reasons anyway.
With a hull you can increase torsional stiffness of platform as you can enclose greater area for less surface. That's the way Ricks last quoted comment can be converted to and represents this effect beter as "diameter" of hull is easily much greater than even the large single alloy beam.

Or did the stuff Ad Hoc wrote set you off the subject too far already.
Some of it was quite unbeleavable.

 

If you go back to my analysis at #77 you will see the comparison of a single beam and twin beams. I am happy to review any well put analysis of the load case using any connection arrangement. My numbers show a single beam gives a lower weight solution than twin beams.

Of course AD Hoc's nonsense about there being no moment to resolve is consistent with his poor understanding of many aspects of engineering. He only confuses things so best to ignore his opinions.

The single beam allows very simple analysis as well. Once you get the two beams you ned to look at joint detail and stress raiser plus there will be some benefit from the connection supporting torque but then there is a combination of stresses. If I was doing a design for a large cat I would only rely on proper FEM results. You never know there may be someone here who has already done it.

Rick W

 

I have now read your post #77 several times and yet to find how a single beam could give a lower weight solution than twin beams. Instead I find that 2 beam solution is lighter for given weight than 1 beam solution, or rather the numbers show that 2 beam solution is upto 4 times stiffer than 1 beam solution for a given total beam weight.

I would like to see your numbers showing otherwise as you claim it to be if you don't mind.

Unfortinately post #77 does not have those numbers.
It claims that 1 beam with ID=580mm and OD=600mm will result about 100mm flex while my post (based on the link you provided on post #77) shows that 2 beam solution gives just 26mm of flex with same total weight beams under stated assumptions. Therefore it could be made lighter than 1 beam solution while still flexing less than allowed.

I would also like to see how you get the 11Mpa value for the 1 beam case instead of 22MPa.
Wasn't the craft weight 4000kg and length 12m, therefore support force approximately 19.62 kN and lever 6m giving 117.72 kNm of torque level for the single beam. Is that correct or do I remember the original question wrong ?

 

Agree with both your moment value and the stress value. I had an error in the calculation for stress in the single beam.

Irrespective the torsional stress is only 22MPa and could be taken higher by reducing the thickness as it is below the endurance limit.

The twin beam solution is limited by bending stress. The direct stress in the twin beams due to bending is 47MPa. So there is less safety margin than in the case with a single beam. Deflection is not the control in the two beam case it is the stress value.

As noted in posts above, deflection is not an issue unless you are overstressing part of the structure. In this particular case I nominated 100mm as being tolerable. From what I see and hear about in practice I get the impression the load case is not often analysed.

If the boat was simply two hulls without accommodation bridge then the beams would ideally be oval rather then round to reduce windage. Making the beam oval with long axis longitudinally will disadvantage the twin beam case as well because it will reduce the area moment for the bending case more dramatically than the polar moment for the torque tube.

The compression load on a single mast would be able to be supported on a large single beam used for torsion control as well.

Rick W