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What size I-beam to use for a bridgeover stream?J Pasked 3 years ago

I want to build a bridge over a creek on my property so that I can drive

my riding lawnmower over it and mow the other side. So 400 to 500pounds would be the heaviest weight to go over it. I want to use I-beamsthat are 25 foot in length with decking on top. I'm planning on putting 2 x8 or 2 x 10 treated for supports and to make the beams more solid.What I am wondering is what size I-beams to use. I know that if I put asteel support under the beam (like the round steel poles that you see in alot of basements for support) in the middle of the creek that would beplenty of support but I'd rather not have to do that. I don't know anengineer and was wondering ifI could just span 25' without the supportin the middle and what would be the lightest weight beamI could use todo this. I'm not planning on using a crane, I'm just hoping I can get someguys to help me put it in place.Any suggestions would be greatlyappreciated.Thank you

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tomsing98answered 3 years ago

I'm not sure what you mean when you say you're going to put a 2x8 forsupport. Support where?

Here's a table of standard I-beams and their properties:http://www.structural-drafting-net-exper...These beams have narrowflanges, and are called "S-sections".

Here's another: http://www.structural-drafting-net-exper...These havewider flanges, and are called, appropriately, "wide flange beams" or "W-sections".

The first thing you need to do is figure out what load the bridge willcarry. You say you're going to have a 500 lb load. That's a concentratedload, which is worst when it's in the center of the bridge. But you shouldadd in the distributed load as well - the weight of the decking, and if youget snow in your area, you'll want to add weight for that. The depth ofsnow you should plan for is going to depend on where you live. Figure on20 lb/sq ft for each foot of snow depth.

There's one more thing you should consider - the weight of the I-beamsthemselves. But you haven't selected them yet, you say? Well, nobodysaid engineering was easy. You'll have to use an iterative process. Sotake a guess of a beam you think would be appropriate from one of the

tables. The number after the x tells you how much the beam weighs, perfoot. You've got 25 feet, and two beams, so if you pick a W12x30, you'vegot 30 lb/ft * 25 ft * 2 = 1500 lb.

Now add all the distributed loads up. Let's say you have a 25 ft x 6 ftbridge, and live in the south, where snow 1 ft deep would be a LOT ofsnow. Then you've got 25 ft x 6 ft x 1 ft x 20 lb/ft^3 = 3000 lb of snow. Ifyou're using 1 inch yellow pine boards for the deck, pine weighs about 40

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lb/ft^3 when wet; figure it might be as much as 60 lb/ft^3 when it's wet.Your deck weighs 25 ft x 6 ft x 1/12 ft x 60 lb/ft 3 = 750 lb. That's a totaldistributed load of 5250 lb. And your concentrated load is 500 lb.

Now, divide both of those by 2. That's the weight on each I-beam (I'massuming you're using one beam on either side of the bridge). 2625 lbdistributed and 250 lb concentrated. Now multiply them by 5. That way,when you put off painting and it rusts, or you're driving your tractor wayover on one side, or you get a record snowfall, or you get some poorlymade steel that isn't as strong as it should be, you won't go crashingdown into the creek with a lawn tractor on top of you. F = 13125 lbdistributed and W = 1250 lb concentrated.

Now, the stress on the beam from the distributed and concentrated loadscan be expressed in terms of the length of the beam, L, and the sectionmodulus of the beam (which is related to the cross-sectional shape), S. Lis 25 ft, and S is given in the I-beam tables (click "Properties" at the topof the page, and read the value in the Elastic Properties, Axis X-X, Scolumn). For our assumption of a W12x30 beam, S is 38.6 in^3. Thestress is given by

stress = (M1 + M2) / SM1 = W * L / 4M2 = F * L / 8

For our case,

M1 = 1250 lb * 25 ft / 4 = 7812.5 lb ftM2 = 13125 lb * 25 ft / 8 = 41015.6 lb ftstress = (7812.5 lb ft + 41015.6 lb ft) / 38.6 in^3

We need to keep track of units - we'll convert the numerator from lb ft tolb in by multiplying by 12 in / ft.

stress = (7812.5 lb ft + 41015.6 lb ft) * (12 in / ft) / 38.6 in^3stress = (48828 lb ft) * (12 in / ft) / 38.6 in^3stress = 585937.2 lb in / 38.6 in^3stress = 585937.2 lb in / 38.6 in^3stress = 15179.7 lb/in^2

So, the maximum stress on the steel beam would be about 15200lb/in^2. You want the steel to be able to support this much stress withoutpermanently deforming, or "yielding". (Think of a paper clip - you canbend it a little bit, and it will spring back to the original shape, but if youbend it further, it will remain in the deformed position - that's yielding.)

A36 structural steel has a yield strength of about 36000 lb/in 2, so15200 lb/in^2 is acceptable. That means that a W12x30 beam isacceptable. But remember, a 25 foot piece will weigh 750 lb. You mightwant to go smaller.

When you go smaller, your distributed weight will go down. But we canavoid recalculating everything if we assume that the weight is the same.That means we can go back to our stress equation,

stress = (M1 + M2) / S

Now, 36000 lb/in^2 is more than twice the stress we calculated. If weallow our stress to go up by a factor of 2 without changing the load, thatmeans we allow our section modulus to go DOWN by a factor of 2. So,take a look at the I-beam tables, and look for a beam with S of around

38.6 in^3 / 2 = 19.3 in^3. Remember, you want something less than 30lb/ft.

We could go with a W12x19 (19 lb/ft, or 475 lb for a 25 ft beam). Itdoesn't look like there's anything appropriate in the S-sections that wouldbe any lighter.

Source:

So, that's an example. Remember to take into account the appropriateweight of snow, decking material (if you're not using pine, make sure touse the correct density, and add about 50% for the weight of water), andalso any railings you put up. And make sure you know what kind of steelyou're getting - different types of steels have different strengths. A36 iscommon, but since it's your butt on the tractor, you should probably makesure.

I hope that helps!

Asker's rating & comment

Thank you for your quick and thorough feedback. I'm new to this forumand this was my first question and I didn't know I would get anyone toanswer so fast. I appreciate the fact that you figured all the calculations

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and gave me the web addresses of the beam charts. This was extremelyhelpful.

1

benjamin rohitanswered 3 years ago

you need to give the width of the creek so that we can calculate the load

distribution for the given wait and then find the bending fro the isection.you can easily span 25 with that i section but increase the no of isections.

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