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.