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I am building a bridge across a small stream. I have 3 hemlock planks that are 24 feet long, and are 6 inches by 4 inches in dimension. The hemlock planks are positioned so that the 6 inch sides are vertical, and the 4 inch sides are horizontal.

The 3 hemlock beams are resting on the sides of the river bank. There are no supports in the middle for the planks. The beams overlap the banks of the stream by about 4 feet on either side, so there is 16 feet of unsupported beam crossing the stream.

I am putting 2x6 planking on top of the hemlock beams to complete the top-side of the bridge.

I want to calculate if I can drive my 1.5 ton ATV across the bridge. Will the hemlock beams support its weight, or will they crack when my ATV gets into the middle of the bridge?

isherwood
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Richard Price
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    https://diy.stackexchange.com/questions/172181/bridge-across-tax-ditch – Jeff Wheeler Nov 16 '20 at 02:46
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    You say there are 3 beams, but you also say there’s “no support in the middle for the planks”. Does that mean 2 beams are on one side of the bridge and one beam on the other side? How wide is the bridge? – Lee Sam Nov 16 '20 at 02:58
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    Is there a grade stamp on each beam? – Lee Sam Nov 16 '20 at 07:03
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    The elephant in the room nobody's noticed: What are the ends sitting on? If they're just resting on the dirt, then A) they'll sink in over time and _every_ time they're driven over will speed the sinking, and B) they'll start rotting out from being in contact with wet soil. – FreeMan Nov 16 '20 at 16:23
  • One could do some ballpark estimating....https://en.wikipedia.org/wiki/Flexural_strength – Jon Raynor Nov 16 '20 at 18:50
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    @FreeMan, that only matters if the bridge survives long enough for you to drive over it a second time. – Mark Nov 17 '20 at 03:20
  • Reminds me of this: https://www.reddit.com/r/calvinandhobbes/comments/aakfde/determining_the_load_limit_of_bridges/ – Nav Nov 17 '20 at 14:35
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    Time to learn about bridge trusses. Simple beams need to be absurdly large for any significant span. – Ecnerwal Nov 17 '20 at 15:18
  • More info needed - how often does the stream level rise due to rain? How deep can it get? What buttress are there at the ends? What's the wading depth of your vehicle - would a ford be better? (and more fun) Have you considered a culvert with 3 or more large buried pipes through to carry the flow? – Criggie Nov 17 '20 at 18:56
  • This is a simple analysis problem for an undergraduate mechanical or civil engineer. You can make it more complex and do a finite element analysis that takes real geometry and boundary conditions into account, but a beam analysis using the truck weight as load should tell you enough. – duffymo Nov 17 '20 at 20:10
  • Gut feel: No. Rough beam calculation: No. Four 12x4s: maybe. – Mattman944 Nov 18 '20 at 13:58
  • One issue you should be thinking about is the durability of hemlock. Hemlock is good for interior structural timber, interior trim, and joinery, but it is susceptible to rot outdoors unless treated. I would be concerned about the areas in contact with the ground or that are damp from dew, humidity, rain and all those conditions that encourage fungus. You can get all the engineering data you need from the The Encyclopedia of Wood, published by the USDA. There are three species in use in North America and they have somewhat different characteristics. – John Dec 28 '20 at 11:14

4 Answers4

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From conventional Hemlock Span tables it seems your 4x6s are only good for about 10' span at 40LBS live load. Your load is much higher when the trucks out in the middle of the bridge.

I think this is what you've got: enter image description here

Can you get 2x12s? or better, get an engineer to run the numbers. You will need to calculate the actual load and deflection and not just rely on flooring span tables since your load is very specific and not distributed over the entire span.

Peter Duniho
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mark f
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  • 3000lbs at 40psf is only 12x6¼ft of floor space. That doesn't seem entirely unreasonable (I'm not saying that the proposed bridge is safe, just that this answer could do with some more details) – Sanchises Nov 17 '20 at 15:32
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For a good answer you'd have to do the engineering calculations but maybe just do a sanity check before digging into that.

You could think about this. A single 4x6 standing on edge is not that much different from two 2x6's. Your three 4x6's are not that much different from six 2x6's. Let's say your bridge is six feet wide.

Under a floor in your house, 6' wide with six 2x6 joists spaced 12" on center, you could span 11' - 12-1/2' depending on the type and grade of wood. That's not designed around where the floor would collapse, rather where the floor will be stiff and not "bouncy."

But that's a floor people walk on and put furniture on, not a bridge people drive a truck across. At 16', I am going to say there's no way that's adequate.

batsplatsterson
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Note this answer is only based on basic engineering knowledge and not on experience in building bridges or using wood as structural elements. There are probably more things to consider using wood as it is a natural material and the properties can vary extremely (wrong grain direction = no strength).

A rough back of the envelope bending stress calculation for the beams (not the planks) when they are fixed on one side:

Bending moment: 1.5 t * 10 m/s^2 * (16 ft/4) = 18 kNm

Section modulus: ( (6 in)^2 * 3 * 4 in)/6 = 72 in^3

Maximum bending stress: 18 kNm / 72 in^3 = 15 MPa = 15000 kPa

According to this document the rupture strength of dry hemlock is around 60000 kPa. So based on that it would be fine, even green hemlock is listed with 43000 kPa.

The deflection would be around 2 inches, which sounds a bit much.

Now even if it would be a steel bridge with the above results, you'd want to apply a big safety margin as your life depends on it, so at least a factor of 5 or something like that. Which means you can only use a fifth of the strength which would reduce the usable strength down to 8600 kPa to 12000 kPa.

Which is below the calculated 15000 kPa bending stress. So you'd need more beams or bigger beams to support that load.

Please note again, I'm not an expert in that area and you should consult one if you value your life or your ATV.

FreeMan
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Arsenal
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  • In your section modulus calc, what the *3 for? (3 separate beams?) If the point load is centered on the bridge, can you really divide all the stress between the three beams or will the center ones stress be double each of the other two? – mark f Nov 17 '20 at 20:26
  • Working load at 25% of the expected failure point?!?! Unsafe! – Loren Pechtel Nov 18 '20 at 05:29
  • @markf yes the *3 is for the three separate beams increasing the effective cross section. The stress will divide almost evenly if your wheels are between the beams. The deflection of the beams will equalize. – Arsenal Nov 18 '20 at 06:57
  • @LorenPechtel those factors are not unrealistic. – Arsenal Nov 18 '20 at 06:58
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    Recommend at least 10X margin on rupture. And nobody has considered the weight of the wood which is considerable. What about dynamic loading? Will it always be you carefully driving? – Mattman944 Nov 18 '20 at 14:02
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This simple trick greatly increases strength your construction can take: Put smaller planks on top such that they rest close to edges. Longer you have second set - better.

enter image description here

Predrag Ivosev
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    I have no idea what I'm looking at. – Nelson Nov 18 '20 at 04:08
  • @Nelson I think it's supposed to be a vehicle climbing onto a bridge made with 2 sets of horizontal beams without any connections between them except at the ends. – Dan Is Fiddling By Firelight Nov 18 '20 at 06:24
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    This is an interesting idea, if you can expand on it, I'm sure you could turn around those downvotes. – ThomasRedstone Nov 19 '20 at 15:59
  • Looks to me like the suggestion is to put these additional shorter beams on top of the OP's bridge, concentrating the force to the edges of the main bridge beams – izzy Dec 16 '20 at 13:48
  • Please feel free to [edit] more information into your answer. As it stands, many of us are confused by what you're saying. – FreeMan Dec 28 '20 at 14:10