Okay raymond111, I read your question again and it is not necessary
for you to answer my request for clarification. We will do exactly
what you have asked for. I will use the 2000# tractor weight as a
point load at the bridge center. This will give us a "worst case"
solution, but we don't have enough information (such as axle loads) to
do anything else. We will not consider the beam weight or decking.
Case 1 (two beams 3 feet apart):
M (maximum bending moment) = Pl/4
D (deflection at center of span) = Pl^3/48EI (D is limited to l/360 = 1.2")
P = point load (per beam) = 2000/2 = 1000#
l = 36'
E (modulus of elasticity) = 30,000,000 psi (constant for steel)
I (moment of inertia of beam)
M = Pl/4 = (1000 x 36)/4 = 9,000 ft lb = 108,000 in lb
The required section modulus of the beam (S) can then be found:
S = M/19,800 psi (allowable bending stress) = 5.45 in^3
Solving the deflection formula for I we have:
NOTE: 1728 is a conversion factor to get the answer in proper units
I = Pl^3/48ED = [(1000 x 36^3) / (48 x 30,000,000 x 1.2)] x 1728 = 46.7 in^4
Looking in the AISC handbook for 8' wide flange beams (I assume that
when you say "H beam" you actually mean wide flange):
W8x15 I = 48.1 S = 11.8 Depth = 8.12" Width = 4.015' Weight = 15 lb per ft
Case 2 (two beams 5 feet apart and a third one in the middle):
I don't know exactly how to handle this case. If the 2 x 8 lumber
transfered the 2000# load uniformly across the 3 beams, it would be an
easy solution. We could just divide the 2000# load by 3 and calculate
a smaller beam. However, that is not what would happen. The two
outside beams would still carry most of the load. The 2 x 8 deck
spanning 3' between the beams will certainly support foot traffic.
Putting two beams at 5' and one in the center would cut the deck span
down to 2 1/2' and would certainly make the bridge stronger. I would
suggest running 3 of the 8W15 beams in this case.
I hope this makes sense to you and all is understood. Please ask for a
clarification if there is anything else I can help you with.
Good luck with your bridge, Redhoss