While I completely agree that Eddie needs an engineer to design the bridge for liability reasons, I would not dismiss either wood or steel at this point.
Derek & bugstruck:
Just as a feasibility demonstration, not a design:
Even with 2x10 or 2x12 decking, could one get significant load sharing between beams, above that provided by the decking, by blocking between the beams? In a 10' span, it would normally be blocked at the center just to prevent warping and twisting of the beams. If the beam spacing were reduced to 7" centers, and the beams were blocked at 2.5', 5', and 7.5' with sections of 2x6 (This works out to 7" centers for the beams), the situation changes significantly.
For the rear tires, there would usually be at least two beams directly under the tires, so we can take full credit for them and the combination of blocking and decking might allow at least half credit for each of the two beams to either side of these two. If we happened to get one beam directly under the center of the rear tire, depending on tire width we would either have 3 beams directly under the tires, or very, very close (the inside-to-inside spacing of the first & third beams on 7" centers would be 12-1/2"), and again we could take full credit for three beams.
The front tires are a little more difficult, but I think the worst case would be with one beam directly under the tire and two outboard beams not under it. Again, at 7" on centers, inside edge to inside edge of the two outboard beams is only 12-1/2" . With 2x10 or 2x12 decking, I think the combination of decking and blocking would still be strong enough to allow full credit for three beams. This is not as clear cut as for the rear tires, but with both decking & blocking, the beams further out are still going to make some contribution.
This is similar to Piloon's idea, but I believe it allows better load sharing, or lets say easier blocking.
This would still be less expensive than steel and probably easier to build. The fastener schedule for the blocking would have to be detailed, but I bet 4 Simpson SDS 1/4 x 3 screws (they look more like lag bolts) in each side of each block would be sufficient.
I am not certain why span tables are not be sufficient to get a reasonable concept. While they don't cover the point load case, they are properly calculated for distributed loads, and I tend to trust published tables more than individual calculations from an engineer. Anyone can have a bad day, but a published table has been checked and double checked many times. And, maximum shear is the same for equal loads, point or distributed.
Derek, can you comment?
The way I look at this, the span table shows that a 12' No.2 or better beam can span 12' on 12" centers at 150 psf live load. What this also means is that a single beam should support 150 pounds per linear foot of distributed load. By only spaning 10' instead of 12' we pick up a lot of safety factor, above that built into the span table.
If we used one beam to span 12', it would be able to support 1800 lb, distributed. Certainly it can support at least an equal weight when it only spans 10', and in reality it can support more. So, each set of 3 beams could potentially handle a minimum of 5400 lb, distributed. While I realize that point loading near the center of the span is a more stressing case, the calculator at the
efunda web site shows that the deflection for a centered point load is ~ 160% of that for a distributed load for a 10' span. (Yup, I used the steel I beam calculator, but since the equations are of the same form for any material, the
ratio of the results will be the same.)
So, three 2x12 wooden beams 10' long could reasonably be expected to hold a 3375 lb centered point load. There would be three beams supporting each side of the tractor.
For a 4000 lb tractor, plus a 2000 lb implement, if the weight were evenly distributed side to side, we could put the entire weight at the center of the span, 3000 lb on each side, and still be OK.
Clearly this is not going to ever happen on the bridge. If all the weight were on the front wheels, there would be no traction, and if all the weight were on the rear, there would be no steering. Any other static loading is more benign.
And no, this doesn't include impact loads and does not leave a lot of spare capacity for pedestrians. OTOH if someone is driving on this bridge fast enough to produce significant impact loads, or with any significant number of pedestrians, the failure mechanism is going to be running something or someone over.
So, if we beef up the original thought, we get a bridge which fills the bill, and is still reasonably priced.
