Wooden bridge beams, revisited

[MTFrank]

I need to build a bridge across my creek. Found a post on the topic from some years ago and have a question. One of the replies had a formula for calculating beam size:
(w*d^2)/(9*L) x (k/f)
Where (k/f) is the modulus of rupture (MOR). It gave the MOR for hemlock as 750. I need to look at other wood species, but all the tables I find give something wildly different for hemlock. Can anyone (hello LD1?) point me to the wood species table used by this formula?

 

[bcp]

I Googled and found 4 places that had hemlock at 750. All 4 were error 404.

Maybe try several online calculators and compare results.

https://www.google.com/search?q=wood+beam+calculator

Bruce

 

[KennyG]

Be a little careful here. You usually want to design to limit deflection, not design to failure, so we use Modulus of Elasticity, not rupture. Also, you will find that most of the formulas are based on uniform load. Bridge beams are closer to point loaded, so you have to cut the capacity in half. I never worry a lot about wood species because of the variability and just use pine and an extra factor for safety.

 

[WranglerX]

Might want to look into different wood types for support beams also treated vs untreated...

 

[LD1]

I agree on designing for MOE vs MOR.

Point-loading a wood beam becomes tough to find calculations for. 90% of charts, formulas, and tables that you can find are for evenly distributed loads. And even for house beams/headers the results are often listed in PLF (pounds per lineal foot).

American wood council has some good span tables/charts Calculators & Tools

As does southerpine.com Span Tables - Southern Pine

But lets start with some basics first....
1. How far are you spanning?
2. How high of a crossing are you spanning?
3. What weight are you needing to safely carry?
4. What wood are you wanting? Common SYP treated stuff....or are you wanting an exotic untreated (but naturally rot resistant) wood like cedar, or white oak, or locust, etc etc?

 

[KennyG]

Point load capacity at center is simple. It's half of total distributed load capacity.

 

[quicksandfarmer]

Point load capacity at center is simple. It's half of total distributed load capacity.

And that's the worst case.

 

[dstig1]

I had read that the codes folks have recently reduced the limits on framing lumber for joists spans as lumber these days does not have the same quality as when the tables were previously populated, so that is something to think about.

And it further raises the question of quality. What exactly are you going to use? Properly graded lumber is what was used to hit those numbers (which of course include safety factors for the wide variability that wood has). Are you going to saw your own lumber? What about grading it and defects?

And as other noted yes platform engineering is done for stiffness (deflection) not strength (failure). A platform that is designed to strength instead of stiffness will feel like a trampoline when you walk on it from all the deflection.

 

[LD1]

Point load capacity at center is simple. It's half of total distributed load capacity.

Not always.

I reference a chart alot that shows headers. For things like polebarns and it shows different load scenarios. Cause a polebarn header with 8' OC posts and 4' OC trusses.....the headers have a point load at mid-span. Its one of the few charts I have found that shows these numbers.

It shows a bunch of gluelam stuff as well as single and built up headers.

A 2x12 #1 SYP spanning 20' shows a uniform loading of no more than 72 plf. 72 pounds per foot for 20' is 1440lb total load. Yet the single point load at midspan is only about 1/3....coming in at 489# max.

And sometimes the point load can be greater than half the uniform load.
Take a #1 2x8 spanning 6'. Uniform load is 311 plf (311 x 6) which is 1866 pounds total. But the point load 1226.....which is about 2/3 of the uniform load.

Short spans seem to favor point loading being greater than 1/2 uniform. And longer spans to fall short of being able to sustain 1/2 uniform loading.

The shorter spans are probably limited by either localized fiber compression on the bearing points or simple shear. Whereas the longer spans, deflection is alot more pronounced with smaller loads.

But this is a good chart for buildings and barns. Not so much for bridges that use treated lumber and in wet areas

https://www.anthonyforest.com/assets/pdf/apa/glulam/Post_Frame.pdf

 

[KennyG]

LD1, I have no idea why the tables show different values. I always went from the wood beam loading tables in Marks Handbook for Mechanical Engineers. It says that the loading in the tables are for uniform loading and to use half the value for a single load at mid-span. Other loading you have to do a detailed calculation. I think the 1/2 value comes directly from the stress formulas. The same relationship is shown for steel beams.

In any event, using a healthy factor of safety when using wood beams is always a good idea, especially if they are not gluelam.

 

[LD1]

LD1, I have no idea why the tables show different values. I always went from the wood beam loading tables in Marks Handbook for Mechanical Engineers. It says that the loading in the tables are for uniform loading and to use half the value for a single load at mid-span. Other loading you have to do a detailed calculation. I think the 1/2 value comes directly from the stress formulas. The same relationship is shown for steel beams.

In any event, using a healthy factor of safety when using wood beams is always a good idea, especially if they are not gluelam.

If you look at the chart though....for most common spans like 8' to 16' the numbers are pretty darn close to 1/2.

But the real short or real long spans is where deviation occurs.

Which makes sense. Because long spans...even with steel, stress is rarely the limiting factor....rather deflection is. And on really short spans....deflection is hardly a factor. Rather local stress or deformation right at the supports.

But it's real tough to find any good charts for wet-service and treated lumber. And with the cost of lumber and posts vs some scrap yard steel beams.....it's usually cheaper to build with steel anyway.

But I'm still curious as to the conditions of this proposed bridge. Span and potential loading, etc.

 

[paulsharvey]

I was also going to point to Southern Pine Council for info, but someone beat me to it.

 

[paulsharvey]

No idea what size creek this is; but it might be worth looking at running double barrel 48" culverts? That's gonna cleanly span a 9 ft wide stream, without limiting flow; ans depending on what your allowed to do in the water (DEP/ACoE), you could probably choke down a 12 ft wide, 1 ft deep creek to easily flow in double 48".

Edit: might consider 38"×60" ERCP if you don't want the height of 48" pipe; and this also makes for a wider pipe crossing; double 38x60 ercp would span 11-12 ft wide (12" gap between, on upto 24" gap); and 38" high (actually OD is probably close to 44"; but 2.5" is going to be below the invert). Them figure 12" coverage; so top of embankment would be roughly 53.5" above your pipe invert/flowline. You would want either a headwall, soil cement bags, rip rap, or poured mitered end section, to avoid erosion in flood stage.

 

[paulsharvey]

Getting a bit crazier; people have used 8 ft diameter steel tanks as a culvert; if it's a ravine; all this depends on legal issues; ie navigatable water way or sovereign submerged lands, ect.