Barge to carry a single pick-up truck

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

 

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.

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