Machine graded lumber and Fb ratings

[Alan Gage]

Had the lumber yard send out some 2x4 rafters yesterday. Wanted something better than the regular S-P-F (Spruce Pine Fir) we have around here and they said they had Southern Pine as well. I said that would be good.

Well I go look at what's been dropped off later and I see that it's not southern pine at all but regular old S-P-F. So I look for the grade rating and don't see it. Instead I have the Fb and E ratings (2100Fb and 1.8E). The stamp says "machine rated".  I have a vague idea of what Fb and E are but the actual numbers don't mean much to me so it's off to the internet. Some interesting reading on machine rating and some good charts comparing machine rated Fb numbers to manual inspection grades (SS, No.1, No.2, etc...).

From what I can see my 2100Fb SPF 2x4s would be SS (Select Structural). So I'm happy with that. Going to the AWC span calculator confirms that it doesn't matter what species you have, 2100Fb is 2100Fb. That makes me happy too.

But what if I have a 2x4 rated at 2100Fb and a 2x6 rated at 2100Fb? That, apparently, is not the same, as you get a lot more span with the 2x6 according to the calculator.  So what I'm still left wondering is how does the Fb rating relate to the dimensions of the board? How do you tell if a 2x6 rated at 1200Fb can carry more load than a 2x4 rated at 2100Fb?

Admittedly I've only skimmed the links below and could probably find the answer with more internet searching but I've got to do some actual work today and thought it might be an interesting conversation.

Here's a good overview of machine testing and Fb rating numbers:

http://www.harvest-timber.com/HarvestTimber/PDFs/DougFirTechnical/WWPA_Machine_Stress.pdf

And a more in depth one with the comparison chart I mentioned above:

http://www.fpl.fs.fed.us/documnts/fplgtr/fplgtr07.pdf

Alan

[Alan Gage]

So I'd assumed from the 2100Fb rating on the 2x4s that were sent out that they'd pulled them from a special pile. But upon looking closer I see some 2x4s they'd sent out earlier in the week, which I didn't specify to be anything special, are also stamped as 2100Fb. Seems strange that if that's such a good rating that even their "regular" lumber would be such high quality.

Alan

[Alan Gage]

Did a little more looking this afternoon. Frustrating because I'm obviously missing something simple about the Fb calculation but I seem to be unable to find the answer anywhere, just the same basic definition of what Fb is:

Bending (Fb) – When loads are applied, structural members bend,
producing tension in the fibers along the face farthest from the applied load,
and compression in the fibers along the face nearest to the applied load.
These induced stresses are designated as "extreme fiber stress in bending"
(Fb). Single member Fb design values are used in design where the strength
of an individual piece, such as a beam, may be solely responsible for carrying
a specific design load. Repetitive member Fb design values are used in
design when three or more load sharing members, such as joists, rafters, or
studs, are spaced no more than 24 inches apart and are joined by flooring,
sheathing or other load-distributing elements. Repetitive member stresses
are also used where three or more pieces are adjacent, such as decking and
built-up beams.

Then I find charts giving the Fb rating for certain wood types but there's no specific size of the lumber listed. Only that the rating applies to lumber 2-4 inches wide and 2-4 inches thick. So that could be anything from a 2x2 to a 4x4.

So how do I use this Fb number to calculate how much load my piece of lumber can handle. For example I found a chart that says the Fb for SPF, 2-4" thick, is 875 for grades No.1/No. 2 and 1250 for select structural. What size is that number based off of? How do you go from that number to the 2100 Fb rating that my 2x4s have been given.  I'm missing something basic here but can't figure out what it is. How do you take the basic Fb number given for a species and grade on a chart and extrapolate that into a 2x10 of that grade and species sitting in front of you?

Alan

[MountainDon]

I'm out of my league on this too.      My understanding is that MSR (machine stress rated) lumber is used by manufacturers such as truss manufacturers, more than simply sold to the general public. I could be wrong on that. 

The actual stick of lumber (again my understanding, and that could be incorrect) is run through a machine and non destructively tested for it Fb and E. The tabulated Fb values are applicable to lumber loaded on edge. So a 2x6 sized piece will get a higher value than a 2x4 sized stick.    Maybe?     (the reasoning behind that is that I do recall that the lumber is rated on edge and that if used flat there is a correction made)   Again, no guarantees that ay of this is correct.....

Off hand I do not know how to do the calculations or how to relate the stamp info on the MSR to the usual "#1", "#2", "select structural" that we see on visually graded lumber.

[MountainDon]

AH-HAH!!!!   The AWC span calculator has Fb numbers listed for many of the species!  I don't know how long they've been listed; I just don't recall seeing the Fb values listed ever before. Could be myopia.      So there's the answer as to how to figure it out!  As long as one has a computer and an internet connection it is easy. 

From what I have recently learned we may be seeing more and more MSR lumber being made available to us ordinary folks.

[Alan Gage]

I saw the Fb values in the span calculator. Handy to be able to use it that way. I still want to know how it's calculated though. The values in the span calculator don't do much good, as far as I can see, if you get your numbers from a chart that tells you the Fb for a given species is "xx" but doesn't tell you how to extrapolate that into the total Fb (maybe wrong terminology) for a 2x4, 2x6, 2x8, etc.

Also, the Fb doesn't appear to be available for all species in the span calculator.

Alan

[Squirl]

Great thread.  Thanks for the insight.

[MountainDon]

The values in the span calculator don't do much good, as far as I can see, if you get your numbers from a chart that tells you the Fb for a given species is "xx" but doesn't tell you how to extrapolate that into the total Fb (maybe wrong terminology) for a 2x4, 2x6, 2x8, etc.

Maybe I'm being obtuse about that... but it seems to me that if you have the Fb number that is stamped on any piece of lumber you use that the same way you'd use the Gr.2 stamp. (or whatever visual grade there is)  That is the AWC calculator does the hard work as to what size, what spacing, snow load and so on.     I suppose there could also be tables developed in a fashion as in the current tables in the IRC. Virtually nobody is doing any hard math to determine the spans for visually graded lumber. Should be no different for MSR lumber.

As for not having Fb numbers for some species, that is likely because those species are not graded by machine. That's a guess but I think a valid one.


Apparently when the mill has a run of lumber that will be machine graded some sticks are destructively tested to obtain a relationship between stiffness and bending strength. A grading machine rolls the lumber flatwise through a series of offset top and bottom rollers that push on the board and determine its' stiffness, the modulus of elasticity.  A grader works the tail end of the MSR machine. This combination decreases the variability inherent in visual grading alone and design values for the same piece of lumber from above may be higher.

[Alan Gage]

Maybe I'm being obtuse about that... but it seems to me that if you have the Fb number that is stamped on any piece of lumber you use that the same way you'd use the Gr.2 stamp. (or whatever visual grade there is)  That is the AWC calculator does the hard work as to what size, what spacing, snow load and so on.   

Maybe I'm being obtuse

Yeah, no problem if I have the piece of graded wood in front of me and I can just look up on the calculator. I guess I'm still not really sure what the Fb rating means though. At first I thought it was just a simple measure of how much weight a board could withstand before a certain amount of deflection. But if that's the case why would a 2x6 rated at 1650Fb be rated for a larger span than a 2x4 at 2100Fb? In my mind the Fb number should get progressively higher as the strength of the board goes up. But that's apparently not how it works and that's what has me confused.

Alan

Alan

[MountainDon]

I believe the Fb numbers should be handled just like we handle "Select Structural", "Nbr 2", Nbr 1", "Stud" etc. It's like a grade but it's not just visually graded. That is why the AWC calculator has all the different grades listed.

.... why would a 2x6 rated at 1650Fb be rated for a larger span than a 2x4 at 2100Fb?

The same as a 2x4 select structural being listed for a span of 6-1 while under the same conditions, same species a 2x6 grade 2 is listed to span 9-4. The extra depth of the 2x6 imparts a great increase in strength. 

[MountainDon]

Here's something someone I know has sent me on this...

Since the '20's lumber has been graded visually. A grader flips every
board and visually inspects it, finds the controlling defect,
determines the grade based on the amount of wood occupied by the
defect and marks the grade. This requires an intimate knowledge of how
trees work, one must often instantly know where they are in the tree
in order to determine the extent of the defect. The grader is the
highest paid employee in the sawmill. There is of neccessity some
margin in the allowable design values of visually graded lumber.

In the 60's we started seeing MSR grades in engineered products. A
grading machine rolls the lumber flatwise through a series of offset
top and bottom rollers that push on the board and determine its'
stiffness, the modulus of elasticity. From destructively testing many
pieces per run a relationship is derived between stiffness and bending
strength. A grader works the tail end of the MSR machine. This
combination decreases the variability inherent in visual grading alone
and design values for the same piece of lumber from above may be
higher. The lumber did not improve, the sorting did.

We will be seeing more MSR lumber at the retail level as time goes by.
SYP will likely be moving that way much more aggressively. Another
thing to remember is that lumber is sold through brokers. When an MSR
mill has fulfilled it's orders it does not shut down, it continues to
produce lumber and markets it through a broker to retailers. It is no
different than going in to buy #2 and finding the store full of select
struc at the same price... supply and demand.

Fb as used in the industry is a base design value used in bending
calculations. It describes the basic bending strength of the material
itself. Fb is an allowable stress (safety factor here) vs. ultimate
breaking stress (modulus of rupture). It is adjusted depending on the
end use of the lumber, we derate the design value if the wood will be
above 19% moisture in service as we know that wet wood is weaker than
dry wood. We increase the design value for a rafter that is subjected
to snow loads since we know that loads of short duration can be
shrugged off more easily by wood. These adjustments, the base design
values for visually graded lumber and the section properties of common
lumber and timber dimensions are available in the free download of the
Supplement to the NDS available at awc.org.

Engineering;
Fb, extreme fiberstress in bending, is checked at the extreme fiber,
in a simple beam we are talking about the bottommost strap of wood on
the beam (a joist or rafter is a beam too).

Take a piece of wood like a popsicle stick and bend it until it begins
to fail. Notice the failure begins at midspan at that outermost
(extreme) fiber, the material begins to tear and seperate. The middle
of span is the point of greatest bending moment, the highest bending
stress, there is the point at which we are calculating the stress in a
uniformly loaded simple beam (a single beam spanning between two
supports).

Provided the stresses in the beam do not exceed the elastic limits of
the material, the stresses in the other fibers depthwise is directly
proportional to their distance from the neutral axis of the beam. If
the tensile stress is 1000 psi at the bottom edge of a 10" deep
rectangular beam the compressive stress is 1000 lbs at the top edge.
There is zero stress at the 5" point, 500 lbs of compressive stress
2.5" from the top edge and 500 lbs of tensile stress 2.5" from the
bottom

Remember Fb is just the strength of the material not the strength of
the timber. The maximum allowable internal moment in the beam is a
function of the material strength and the section modulus of the
timber. The section modulus is based on the shape of the beam.
M=fbS_m

The best way to lower the stress in the extreme fiber is to move it
away from the neutral axis of the beam, make the beam deeper, increase
it's section modulus (one of the section properties used in sizing a
beam... area, section modulus and moment of inertia are the section
properties used for shear, bending and deflection respectively) The
section modulus is calculated by the formula bd²/6 (breadth
times depth squared divided by 6). The take away from that formula,
depth is squared. To make a beam stronger make it deeper rather than
wider, within reason. An I beam takes a more expensive material and
puts the steel where it is needed, at the extreme top and bottom of
the beam and seperates them with a thin web, an I joist does the same,
a floor truss is doing the same thing basically.

Let's use the flexure formula to derive a maximum allowable bending moment.
M=Fb x S (section modulus)
use a 2x4, S=(1.5 x 3.5 x 3.5)/6... S=3.063"³
M=2100x3.063 or 6432 in-lbs
My brain works on trucks, torque wrenches and foot-lbs divide it by 12
and we have a max allowable moment of 536 ft-lbs

Work it for a 2x6, did you get S=7.563"³ ... look back at
the 2x4's section modulus, that was an impressive jump. Mmax=1323.5
ft-lbs we're still talking moments not loads and spans but you can see
it is over twice as strong as the 2x4 just from the geometry of the
stick.

Now work a 4x4... the 2x6 is stronger

The beam formula for a uniformly loaded simple beam is WL/8, total
uniformly distributed load times span in feet divided by 8
Mix it up, lets get a load for a 12' span
1323.5/12'=110.29 x 8=882 lbs