Comparing notes on span tables or calculators

[ponderosae]

Looking at Southern pine, for example, it seems odd to me that spans for floor joists would be greater than spans for ridge beams, when the distance between boards is much greater in floor joists (given that multiple boards are used for ridge beams). And looking at a calculator for just beams by themselves (not necessarily in a floor or a roof), when spacing them only one inch apart it vastly increases their load capacity. So I'd expect multiple member roof ridges to allow for a greater span than floor joists, yet the opposite seems to be listed:

AWC Maximum Span Calculator for Wood Joists and Rafters

Species: Southern pine
Size: 2x12
Grade: No. 1
Member Type: Floor Joists
Deflection Limit: L/360
Spacing: 12 in.
Exterior Exposure: no
Live Load (psf): 50
Dead Load (psf): 10

The Maximum Horizontal Span is:
20 ft. 1 in.
with a minimum bearing length of 0.71 in.
required at each end of the member.

___

Southern Pine Size Selection Tables
Tables 15-20: Roof Ridge Beams

These tables are for gravity loads only... All tables are based on uniformly distributed loads only... applicable to members used under dry-service contitions... the compression edge of the beam must be laterally supported at intervals of 24" or less...

Table 17: 50 psf Ground Snow Load, 10 psf Dead Load

Clear Opening: 16'
Grade No. 1
(4) 2x12s

_____

Wood Beam Calculator (cornell.edu)

Species: Southern Pine
Grade: No. 1
Span (ft): 16'
Spacing: 1 in.
Live load (psf): 50
Dead load (psf): 10
Live load deflection: L/360
Total load deflection: L/240

Load type: a) uniformly-distributed load
Lateral Support: at supports and point loads

Lightest choice: 2x6
Next Lightest: Double 2x4

(now increase the live load**)

**Live load (psf): 1125
Dead load (psf): 10
Lightest choice: 2x12
Next Lightest: 2x14

It looks like the big difference with this last calculator was all about the spacing, because when I plug in a 20 foot span with 12 inch spacing it corresponds to the first calculator at 50psf live and 10psf dead loads, to recommend a 2x12 board as well (or larger when the load increases with that spacing). So it seems odd that four 2x12s spaced at zero inches apart can only span 16 feet for the ridge beam, according to the table for that (when the last calculator says they can span 46 feet when spaced one inch apart and handle the same load).

[Don P]

I don't know the specifics of how their calcs are working, I've backchecked mine a time or two against the awc one and we seem to be on the same page. The equations behind beam calcs is generally the same for similar load conditions. If something is not making sense it is usually a GIGO problem. You can usually backcheck the output longhand to see where the problem is creeping in. under the publications tab on the awc website you can download DA6, standard beam equations. You'll also find read only versions of the NDS there which is the reference for wood construction. In their you wil find the adjustment factors , for instance the repetitive member increase in base design bending Fb of 15%, duration of load adjustments, etc. The supplement of base design values is also on that tab listing major lumber species.

What are we up to here ponderosae, are you building something in particular, learning, ..?  Tell us a little about yourself and what you're up to, I don't know if I'm talking to a school student or a bona fide NASA engineer :D. It helps tailor answers or tells me to ask you questions.

I'll start off so you know who I am. I'm just a country carpenter, a little long in the tooth, which just means I've seen a little and learned a little along the way. I can help with simple things but I'll let you know if we are getting beyond my knowledge.

[ponderosae]

Thanks for the info. I'm mostly building lots of big shelves, but in the process I'm taking a look at how other things are built too.

I was also comparing between the Southern Pine tables, and they say for a 16 foot span to use three 2x12s for 40psf load (total), and four 2x12s for 60psf load. So the fourth 2x12 added more psf than the average for each one in the set of three. Maybe that was an increase for the repetetive member there. So does this mean a beam can brace itself? Is the extra strength coming from increased lateral stability, when the beam has multiple members? I'd suppose so, although they say to brace them as well (with the top edges of the rafters I presume, which wouldn't amount to as much as the floor bracing, so perhaps they aren't considered to be as stable of a beam anyway).

[Don P]

There is a 15% repetitive member bending strength increase for 3 or more members spaced 24" or closer together. typical floor joists, rafters and built up beams take advantage of that. I was at a talk with one of the engineers at awc, it is ok to take a 10% increase in Fb for 2 members under those conditions. The reason is that the multiple members have load sharing and better distribution of defects as compared to a single member.

It sounds like you're comparing uniformly loaded simply supported beams. I'd start by converting your psf loads to total loads on the beams you are comparing. The simple beam calcs in the toolbox here might help level the playing field there.
http://forestryforum.com/members/donp/beamindex.htm
The top one is the simplest and most manual, the third one is closer to the awc calc. Being a sawyer I needed the ability to enter different sizes than stock. The other calcs get into different conditions.
For inputs you can work a problem on the awc calc and scroll to the bottom to see what the adjusted design values are, check that when you see anomalies as well, see if you have differing design values when comparing things.

A beam does brace itself laterally depending on span and geometry. As the unbraced length increases and the depth to thickness ratio gets more slender it can cut into capacity, you aren't into that there. There is also a size factor. You do need to read chapters 2&3 in the NDS for some background on all that.

[ponderosae]

Thank you! Yeah, I guess the most common information on beams has to do with floors, but I was also interested in roofs, because shelves can be built to hang off of one, for instance. I'd rather support them off the floor, of course.

[ponderosae]

Oh yeah, speaking of floors, I think it may have occurred to me what was going on with the figures.  The ridge beam would be more like a girder, so it involves the tributary areas of all the rafters combined, whereas each rafter only involves the tributary area between one on either side (and that would be similar for joists, compared to a girder beam they are supported by). So when they say a larger beam may support half of the roof or floor load, it wouldn't compare to a span table for the smaller beams, which only involves their spacing between others. Even though there is no spacing between built-up boards for a beam supporting those, it actually involves half of the area that the beams on top if it span. I was just thinking of its dimensions alone and wondering why it wasn't spanning farther based on that (but I took the beam out of context there).

[Don P]

Correct, I did a little looking at the cornell calc and math along those lines last night. Their calc and the awc calc would be inappropriate for sizing a ridgebeam, girder or header for the reason you figured out.

Go here and plug in some numbers;
 http://forestryforum.com/members/donp/ddsimplebeam.html
Load 5000
span 192 (16')
width 4.5 (a 3 ply built up beam)
depth 11.25 (a 2x12)
species and grade #1 SYP
In the right, blue, column are the adjustment factors to the base design values
Hit 10 year, 3 or more members, 4x12, no,no
click "show result"

Notice the section modulus required vs input in the bending section, close, deflection barely fails, that is the control but just barely, both bending and deflection are right a max.

Notice the next section, base design values on the left, adjusted values on the right. Go back up and change the duration of load to 10 years and click again, see adjusted bending drop. Play with changing those adjustment inputs and watch as it changes the design values.

Then, change the width in the left column to 6" ( a 4 ply girder), run the load up to 6666 lbs (25% more load) and keep the other inputs as original. Notice the bending input and required, the margin is pretty much the same, deflection is the same. Adding that 4th ply gives you 25% more capacity.

[ponderosae]

That's interesting, thanks.

By the way, I was also wondering why the ridge beam tables recommend up to 4 ply, but after that, larger solid lumber is listed. I was thinking maybe it had to do with how they recommended joining the plys together (based on AWC details for conventional wood frame construction), which say to use 20d nails. But I'd think 20d nails would only be long enough to put 3 plys together. Maybe they nail from both sides or use longer ones. I guess bolts could be used for wider built up beams, if necessary.

[Don P]

Many building departments are going to want to see bolts at 4 ply. With 3 ply it would be nailed from both sides and the fasteners can be inspected, at 4 it is usually bolted.

If the girder is top loaded the connections are simply holding the plies in place. If the girder is side loaded, then the connections are transferring load from the outer ply to the inner ones. This is imperfect at best with the outer plies taking the lions share of the load, /beyond a point it isn't worth adding more plies, it is time to change materials.

Time to introduce you to the heavy timber calc. Open the drop down dimensional lumber calc here and the drop down heavy timber calc. Play with them a little noticing the design values for the same species and grade in dimensional lumber vs heavy timber. Because it is more difficult to know what is contained within a heavy timber the assigned strength take quite a hit compared to dimensional lumber.

So, if you are hitting strength limits it is often better to look to engineered material for a long span or heavy load, glulam https://aitc-glulam.org/ or LVL https://lpcorp.com/media/1367/lp-solidstart-lvl-technical-guide-english.pdf
Now that you have a sense of the design strength values for lumber pay attention to the design values for those products, just about double.

This is a good series of educational articles;
https://bct.eco.umass.edu/publications/articles/sizing-engineered-beams-and-headers/
Dang, I didn't realize he had retired. He has written many great engineering articles in the trade mags over the years.

[Don P]

Ah, I just followed a link you posted elsewhere to the southernpine roof ridgebeam tables. The "larger solid timber" you saw listed in those tables is specifying glulam rather than solid timbers.

[ponderosae]

Thanks for the info, right I was just looking at the dimensions of the larger single pieces there. Then I was thinking the number of built-up pieces would be good for adding stability to the point where they were approximately square. However, they say that in some situations the glued laminated beams are specified when 4 boards together no longer meet design standards (whatever that means).

One explanation of a design standard for limiting built-up beams to 4 pieces has to do with side loads:

"Flush beams with loads applied to only one side need special attention, specifically when the member is 7” wide. Our literature addresses this condition by stating that 7” wide beams should be side-loaded only when loads are applied to both sides of the members (to minimize rotation). The potential for rotation of a beam increases as the load is applied farther away from the centerline of the beam (the wider the beam the more rotation potential)."

But in the case of a ridge beam, it would be getting loads applied to both sides at the top usually, as far as the rafters are slanted. Something else I read says that "Long slender beams that are restrained against axial rotation at their points of support but are otherwise free to twist and to deflect laterally will buckle"... and "Built-up columns of nearly square cross section with the lumber nailed or bolted together will not support loads as great as if the lumber were glued together. The reason is that shear distortions can occur in the mechanical joints".

So I'd guess it could be about the design standards of fastening more than four boards together effectively in this situation, for a beam or column (where if it has to be larger than that, the forces on the fasteners may be larger as well).