Barge to carry a single pick-up truck

Yes, that is right. So given the previously described deck, what is allowable unsupported span?

DogCavalry said:

Given a tire load of 4.5 tons, and a deck of douglas fir 3.5", 9cm thick, how far apart can the deck beams be, before the deck breaks under load? Given a contact patch of 10" 25cm square.

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BoothBoatworks has noted that your tyre load is 900 lbs / sq.ft - this is equivalent to approx 4,400 kg / square metre in metric units. Or 4.4 tonnes / sq.m.

Can the deck be regarded as being homogenous? In other words, will every 3.5 " thick deck plank be glued to it's neighbour on each side such that the whole deck is effectively one big sheet of timber that is 3.5" thick?
If the deck planks are not fully bonded to each other, then they are 'on their own', and they effectively don't know about their neighbours - and this will affect the strength of the deck and the maximum load that it can take.

DogCavalry said:

Deck beams cross the decking. Their composition and structure is irrelevant to the deck plank strength calculation, and in fact is not determined. Spacing of deck beams is what the question is supposed to determine.

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I would respectfully suggest that the deck beams are relevant to the deck plank strength calculation.
For a start, the beams need to be strong enough to support the mass of the deck and the cargo sitting on it.
It all comes down to the deck panel size - and if you can introduce some longitudinal stringers under the deck, in addition to the transverse deck beams, then you will considerably reduce the size of the unsupported panel of deck, which then means that the deck thickness can be decreased, or the load can be increased.

All of this will cost a lot of $$'s to build a timber barge - and it will take up a lot of John's time, time that he could perhaps spend more usefully bringing in $$'s by building houses for others. When you factor this cost in, then the barge is looking to be an expensive proposition.

Maybe it is time to look at second hand landing craft / barges for sale again now?
This link was posted on page 2 of this thread :
Landing crafts for sale in Canada - Daily Boats https://dailyboats.com/ca/boats-for-sale/type-power/class-power-landingcraft/region-north-america/country-canada/

This 30' steel landing craft could probably carry your loaded pick-up truck - it has an inboard diesel with an azipod drive leg, and they say the price is $40,000 - I presume that this is CAN$ rather than US$, as it is in Ontario.
1995 Commercial Boats 30' Steel Landing Craft for sale. View price, photos and Buy 1995 Commercial Boats 30' Steel Landing Craft #347142 https://dailyboats.com/ca/boat/347142-buy-commercial-boats-30-steel-landing-craft-for-sale

Here is another steel landing craft for sale in Ontario for $50k, but it has an Outboard engine.
2016 2016 Steel Landing Craft W/ Pilot House C/W Trailer 33 X 10 for sale. View price, photos and Buy 2016 2016 Steel Landing Craft W/ Pilot House C/W Trailer 33 X 10 #163417 https://dailyboats.com/ca/boat/163417-buy-2016-steel-landing-craft-w-pilot-house-cw-trailer-33-x-10-for-sale

Here is a 'little' (25') ally landing craft for sale in BC for $56k, but it might not be big enough for your pick up?
2010 Custom Built Landing Crafts for sale. View price, photos and Buy 2010 Custom Built Landing Crafts #50232 https://dailyboats.com/ca/boat/50232-buy-custom-built-landing-crafts-for-sale

This 36' Eagle Craft looks ideal for what you want - it was specifically designed to carry a twin cab truck - but it is probably very expensive.
36 Landing Craft - EagleCraft https://eaglecraft.com/landing-craft/36-landing-craft/

I normally don't give advice on structural matters, but it's not all that simple as what's the unssuported span. First you need total lenght and width of the deck, to be able to consider it as a diafragm with fixed edges (meaning the hull). Then we need GVW, number of axles and tires and tire size. If I take 4.5t per wheel and 4 wheels that's 18t for GVW. Then we apply the load model, for bridges in Canada wheel contact is a square 25x25cm, in the US a rectangle 20x10 inches. Tire pressure also plays a role.
Only afterwards can we talk about span reduction or stiffeners, it also matters how this is done, if it's a bulkhead or a simple beam.

Right. A 20'*50' surface, or 6m×15m. All deck planks bonded to all others, so a continuous membrane. No other components, other than regularly spaced supports. Bulkheads in this case, which may be considered, for purpose of calculation to have infinite strength. Since the shortest length of a conceivable wheeled load places the nearest tire to the subject tire at least 3 bulkheads away, the load may be considered a monowheel.

If that's your thinking just place two longitudinal bulkheads spaced for your trucks axle width and be done with it. Put some C channel steel on the deck so the truck can only go over there and it's done. You can make the rest of the deck however thick or thin you want, it won't matter to the trucks load. By the time the bulkheads are as thick as the tire width and tall enough to give the necessary freeboard for the displacement you don't need to calculations.

Thanks for the suggestion.
I will ask a civil engineer. Quant Suff

I asked a structural engineer. Assuming the load as described, where deck boards run longitudinally, and are born on transverse members, corresponding to frames in classical boat building, but monolithic and full depth, maximum allowable free span is 32" or 0.8m. So building laterals spaced 0.8m center to center gives a good safety margin.

The reason I didn't use @Rumars ' suggestion about U channel is that that only works for 1 vehicle/axle length, and strictly on/off. The ability to drive vehicles on and off, wherever they may need to be on the deck, or load and unload with a skid steer justifies a deck that can manage that load anywhere on deck.

The sketch is the layout of components at a raked end. Designed for many smaller components so that the completed assembly behaves like fingerjointed or scarfed lumber.
And here is a 12'x40' dock (3.4mx12m). It is on a stiff-leg, where that delivers a 1.4 ton point load. This structure will easily manage big loads, distributed, but loads don't come like that. Certainly not rolling loads. This one would fail at the deck, not the internal structure.

Why do I think I could use the same amount of materials to build a much larger platform?

montero said:

Why do I think I could use the same amount of materials to build a much larger platform?

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Because maybe you could, and also because maybe you can't interpret the drawing, or understand the SOR, or count. Maybe you think labour is worthless, but 14000 USD is prohibitively expensive for a barge that size. I couldn't say. Post a sketch, then do a material takeoff and post that as well, then I can answer the question.

DogCavalry said:

The sketch is the layout of components at a raked end.

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Maybe too late now, but I would add some diagonals, to prevent warping and twisting between the cells.

Ad Hoc said:

Maybe too late now, but I would add some diagonals, to prevent warping and twisting between the cells.

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Well, too late for that particular dock, but not too late for the hypothetical barge. Torsion down the length of it from a 6 ton skid steer driving around is definitely something to consider.

So just to clearly state a part of the SOR which may have got lost in the scrum: I am a carpenter, not a welder, so the structure must be built of wood, by one or two people, in a month, with limited equipment. The dock pictured was built by three people in 3 weeks, with only a skillsaw and some impact drivers.

The completed dock was splashed with the marina's travel lift.

montero said:

Why do I think I could use the same amount of materials to build a much larger platform?

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Go ahead and provide a deflection calc that compares spans on yours and his…love to see it.

Well, I made an inaccurate statement a couple days ago. It is in the air now, so rather than edit the post, I will point it out and fix it. I ought to have said one or two helpers, as well as myself. Not realistic to do it alone in that time frame. Actually, dock pictured is12x40, where the corresponding barge would be 16x48. 50% more deck area, and 50% thicker as well. Better to say, a proper crew in a month.

BoothBoatworks said:

So you're only concerned with the deck plating currently and not deck structure?
Deck plating calcs are just simple pressure calcs. Your tire load is 900psf.

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Amusing. Then he wasnever seen again. I have had similar conversations with flat earthers.