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Engineers have often attempted to analyze the structures of wooden ships as if they were homogeneous box girders. This is a common misapplication of beam theory. Actually, a wooden ship, especially as it ages, more closely resembles a rather weakly bound bundle of reeds. These reeds are free to slide past each other. If traditionally built wooden ships were box girders, then one would expect to see many tensile failures amidships in the upper deck of a severely hogged vessel; however, this is not the case. Failures in longitudinal structure are infrequent and tend to be scattered almost uniformly throughout the vessel. The idea of "strength decks" or "extreme fiber" is largely irrelevant to the meaningful analysis of old wooden ships. Microscopic investigation reveal a generally low level of stress in "hogged" structural members. There often is evidence of plastic behavior, creep, around fastenings. Large overall deflections in the hull can be achieved with a very small amount of creep around the fastenings.
http://www.tricoastal.com/woodship.html
What a fantastic quote! It proves what I've been trying to say all this time! It shows that you cannot apply modern, typical, homogenous box-girder design to wooden sailing vessel design of at least the 19th century. The reason why is that the old wooden ship design was Keel/rib based. All (or most) of the stresses were supposed to be handled by the keel. The rest of the vessel, Like the man says, was "a rather weakly bound bundle of reeds." The design methods are so different that you cannot use the modern box-girder method to analyze the old keel/rib method. And the converse is true, you cannot apply the failures of the keel/rib method of design to a wooden vessel designed according to the modern box-girder method.
What I've been doing is to design a wooden vessel according to the modern, keeless, box-girder design method. In the box-girder design the frame and the planking share in the stresses (unlike the keel/rib design. As he said, there was "a generally low level of stress" in the hogged members.). The computations I did above were based on the box-girder design. Therefore, just as the man says above, what I've been doing cannot be compared to the wooden sailing ships.
In this design the "reeds" cannot be free to slide past each other. Not only do they need to be securely fastened to the frame, but they also need be securely fastened to each other (which was not done in the old ships). By fastening the members to each other, they become, in some respects, a larger whole. Thus, in my rough estimate computations, I treated the top deck as a single unit crossection of 1 by 50 cubits. One would want to refine the calculations by considering each plank individually and how it is fastened to the other structural members. Any volunteers?
As he says above, the permanent hogging happened because of creep around fasteners. This allowed the ends to droop in respect to center due to the streamlined design of the ships. Creep around fasteners on barges would not result in permanent hogging, rather it would allow the barge to flex more readily than at first, which would not be good thing either.
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There has probably not been any need or demand for any that size.
So that bit of evidence hits the bottom.
Not at all. It is demand and economics that determines the size of any ship built. Just because ocean going barges are not built as large as the Ark, that does not mean that they could not be built that big. Just consider supertankers. These ships are nothing more that huge, box-girder barges with just enough rounding at the bow and stern to make it economical to push them through the water. They are not streamlined ships.
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Look. Build yourself a long thin box out of any material you have. Support each end, then remove the sides. The center sags. You can support the middle only, and get the same results. Now put the sides back and remove the top and bottom. Surprise! Not nearly as much sag as when the sides are removed. If you have ever built anything at all, you should know this.
In my computations above I included the sides which are needed for the very reasons you mentioned. And more than that, I computed the amount of compression/tension stresses these necessary members carry == approximatly 9% of the total compression/tension stresses each.
OK, lets compute the shear stress (Fv) for the sides for the design I have been working with.
First you find the shear (V) V = w (l/2 - d)
Where V is shear in lbs. w is in lbs per liner foot of the crossection of the box-girder. l is the length of the vessel. d is the depth of the beam. Also, w is equal to the density (D) of the structural material times the crossection area (A) w = DA
So we get: V = DA (300 / 2 - 30) = 120DA
Shear stress is Fv = 1.5 V / A lbs / square cubit.
By substitution we get Fv = 1.5 (120DA) / A
This reduces to Fv = 180 D lbs/cu^2
I have here a list of specific gravity (G) and "maximum shear stress parallal to grain" for several types of wood.
First we'll compute the psi for a specific gravity of 1 with a cubit of 21 inches then convert that to the specific gravity of the woods and compare the computed shear stress (Fv) with the maxim shear stress parallel to grain.
Fv = 180 * .03606 * 21^3 / 441 = 136.3 psi
Hard Woods---G------Fv------Max shear stress
White Ash___.60___ 81.78 psi__ 1910 psi
Rock Elm ___.63___ 85.87 _____ 1920
Live Oak ___.88__ 119.94 _____ 2660
Soft Woods
Douglas Fir .46___ 62.70 _____ 1000
Western
___Hemlock -.45___ 61.34 _____ 1290
Tamarack ___.53___ 72.24 _____ 1280
So as you can see, the computed Shear Stress (Fv) is far below the maxim shear stress parallel to grain of most any wood. Your concerns about shear stress are not very well founded.
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The bundle of reeds metaphor implies that the ship is comparatively poor at resisting longitudinal loads due to a weakness in shear.
How true! The shear stress was too great for the sides because the keel was unable to handle the compression/tension stresses and passed on the bending to the side planks. They broke because they were not designed to handle shear stress and the ship sank. The whole problem is the keel/rib design.
The problem with the Keel/rib design is that the keel is simply not tall enough to handle the stresses properly. This is easily illustrated by using a 2 by 4 piece of lumber. Lay it flat between two saw horses, get your kids to walk across, and it will bend quite easily. Set it on edge, and it will hardly bend at all. Why? simply because when it was flat the top and bottom surfaces were only about 1.75 inches apart. But when it was on edge the top and bottom surfaces were about 3.75 inches apart.
The top and bottom surfaces of keels in most wooden sailing vessels likely ran only 10 to 15 feet apart. This is contrasted with the distance between top and bottom surfaces of box-girder designs where, like in my ark design, the distance between the top and bottom is some 45 feet. It is greater than that for supertankers. The greater the difference between the top and bottom surfaces of the stress bearing members the stronger the ship and the greater the stress that can be handled.
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I assumed such a framework, but no framework will give you as solid a structure as you assume. Each individual member will move relative to every other and be subjected to a reduced version of the stress described.
The frame I have envisions would consist of longitudinal, transverse and vertical members each some 18 to 21 inches through. They would be securely fastened at the verticies and the entire substructure would be diaganally cross-braced longitudinally and transversely. It might not look pretty, but it would be strong. To be certain the members would all move some and one would want to calculate all that sometime.
It is this cross-braced truss substructure that would handle torsion forces. Tortional stresses are less than shear stresses, and shear stresses are less than compression/tension stresses. I really doubt that it would be hard to over-design a box-girder vessel agains torsion stresses.
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What I did above was to get a rough estimate.
Too rough.
Where are your calculations to back that up.
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