A Photo & Discussion Forum for Wharram Design Enthusiasts
This might be a good place to add a few words on beams in general. Don't be afraid of the figures they are very simple.
I will start with a simple solid 4x2 timber beam on edge, and look at what we might use instead. First we must put a figure on the vertical value for later comparison. This we get by multiplying together the important factors of the beam.
So first is the width 2", X a value for the material [q], X the depth cubed. [4x4x4]. This comes to 128 q.
Since we are only comparing changes in size here not in material we do not need to look up a value for q.
So already we see as we expect that making the beam twice as wide will double the value as also would using a material of twice the value. What is less obvious at the start perhaps is that doubling the depth leads to an increase of [ 2 x2 x 2 ] = 8 times the value. This is where the magic of hollow beams , I beams etc. lies.
Now to look at an I beam of 5 x 2 with top and bottom of 1" each and a ply web 3" deep. Since this is only a demonstration of general possibilities I will assume the web has zero width or weight.
The value is calculated simply be getting the figure for the solid 5 x 2 and subtracting the figure for the 3 x 2 void in the middle.
So 5 x 3 is [ 2 x q x 5 x5 x 5 = 250 q. And 3 x2 void [ 2 x q x3 x 3 x 3 = 54 q ]
Since this is an estimate I am going to say that 250 - 54 = 200 .
So 200q is the value of this beam.
And the old 4 x2 only scored 128 . This beam is approx. 50% stronger !!
Now look at the weight. It is basically two 2x1 instead of one 4x2. It is half the weight.
Yes believe it or not only a very small piece bigger but half the weight and half as strong again.
Truly this is almost a form of magic. And did you see - no calculator - no computer program - nothing very difficult at all I believe.
Now if anyone is left a comment on computer programs.
It was always possible to design boats safely by envisaging a worst case and building to that. What these programs do extra is model a full range of possibilities, so a designer can choose to build lighter depending on his expected real conditions - even down to a structure that has a life of only a series of races.
If I race my bomb shelter against him I know who will win. If we have a collision I also know who will lose.
A mate of mines young fella is going to study marine engineering In Tasmania. I'll give him a bit of time and then slug him with questions.
Gud on ya!
Congratulations to Galwaybay! This is a very comprehensive and valuable contribution to this discussion!
Thanks and regards, Armin
Aww Shucks you are all too kind. Lots of good stuff raised here -
Thom I am unsure, have you finished these beams and used them ? I suspect it was hard work getting the glass to lay down on the corners we only use this glass for gentle curves as it springs back up off the sharp ones. Even at half this weight 300g is difficult to use on corners sharper than waterpipe.
The horizontal loads are really quite light in normal sailing but pounding into headseas is another story and even a small collision can create a substantial load.
Without knowing enough of the details regardingThom's beams -- perhaps the foam web and putruded sections were wrapped in ample E glass reinforcing, well keyed for bonding purpose and then the whole beam was resin infused in one shot-- I don't know. But on the whole I am with you Galway.
Sure it is possible to gain a lowered weight advantage by increasing the depth of an I beam, and I think it is possible to achieve sufficient diagonal bracing of the entire structure to make up for the loss of horizontal stiffness in the individual beams.......adding weight to total structure. This woulcd be a significant departure from classic Wharram design though, so is not worth persuing in this thread.
What is of relevance is the effort in achieving an aesthetic effect fitting the Wharram ethic, and here I would go with wood.
Thanks for the formula Galway Bay - but I have a question: in your case the material (solid wood) is the same. Do you have any comparative values for the material coefficient q? For example on my pahi, the original beams are laminated from solid timber, but if I made a similar sized beam from plywood, maybe I-beam construction, how would this compare? (The original beams to plan actually contain oval cutouts to lighten them but these are definitely weak points for letting water in, that's why I've replaced with a solid laminated beam.) Also how can I design for enough strength where the beam locating bolts are fitted (horizontally through the beam trough)? I haven't seen the tiki-style beam upgrade plans, but I understand they don't use the bolt at all, whereas I'd prefer to keep it.
Thanks Galway bay. I think if one is to change the plans, there are two ways:
-trial and error (usually more expensive) but this is why Tom delForge's discussion is going, because he made plastic beams still holding after 3 years. i really like the idea of severe testing as in aviation and have friends in self-build ultra lights and planes - but they test after sticking to the plan!!
- calculations like engineers do, but in the world of amateur builders, I've gotten "professional" and engineers advice (which I sunk the money and time into) which wasn't so good - so it should be someone with catamaran experience.
I didn't think of the hollow beams being stronger than whole ones, and would have made them whole to limit rot, if out of wood..
To Andy BestDunkley: I had some without the hardwood triangle under the bolt. As I posted before, I believe (due to trial and error) this is the key point which avoids splitting the lamitation.
Can anyone PM me a scanned plan the Tiki i-beam in exchange for a Pahi beam plan, for consultation only. As the Pahi came later, I would expect an evolution with a reason. Jim seems to have done his calculations, and then a lot of trial and error...
Andy - The quantity you need is called Young's Modulus Of Inertia. It is available for all materials. I have not checked for ply but if you think about it wood is uni-directional fibre, ply is bi. So 50% of ply is only core material in any one direction. I would be slow to use it as structural material in the sort of compact beams we use although with much larger sizes it would become useful. It is of course excellent for core material as with the web in an I beam, where it has great resistance to the shear loads as the top and bottom faces try to "slide" past one another under load. The ply embedded in the laminated faces also gives huge stability to these. I packed the beams out solid for 6" long at each lashing. I would consider the same at the bolt position but I used blocks on the bottom of the beam instead of the bolt.
The failure of my beams was due to water saturation. Seemed wetting could happen but not drying. The failures were of the glue joints at the bottom of the hollow sections and rotting timber. This has turned me against hollow beams.
Wharram's beams were basically 8" X 4" with hollow sections so small as to do almost nothing except add to the complexity of building. I decided to use a solid 8" X 4" as my base value and my beams are similar to the example given, but scaled up. My beam 1 & 3 have faces 2 1/2" deep and beam 2 is a little heavier in all dimensions. It carries the mast. Partly these decisions were based on what timber I had on the shelf.
My new are 2 X 35kg plus 1 X 40kg = 110 kg. I suspect the old should have been about 50kg ea. but were a lot more due to water saturation. So the old beams best case 4 1/2 X 50kg. = 225kg. A weight saving of 115kg. and in practice more. Yes I do feel it in the boat's sailing performance.
I also felt it in the building time and in my wallet. I built the full set in a week part-time evenings plus all Saturday, not including painting.
I have been waiting for some eagle-eyes to point out that in the example given in the earlier post the horizontal value is only 50% of original. This can be easily overcome with a small increase [ + 25% ] in width. However I was limited by using the old troughs and was not able to compensate fully. But after some severe use I am happy.