Need help with log rafter calculations.

[Joe Hillmann]

I am in the process of milling logs to build a cabin.
I am planning to use log rafters spaced every 24 inches with one face milled.
The rafters will be popple/aspen.
I am in the north so planning for 40 pounds/square foot for snow load.
The rafters will be 14 feet long(168 inches) and 12/12 pitch.

I am using the log beam calculator from the tool box and would like some input to make sure I am using it correctly. https://forestryforum.com/members/donp/logbeamcalc.htm

For total load on beams I am using 1120 pounds.  That is 14feet(length of rafter) x 2feet(rafter spacing) x40(pounds per square foot)

For span of beam I put in 156"(the length of the unsupported underside of the rafter)

For the wood I picked #2 Aspen(not sure if it should be 1, 2, or 3 so I went in the middle.

This is telling me my logs should be 7.97 inches in diameter.

My questions are:
   Did I do this right?
And
  Is that size the small end diameter in the round or do I need to measure down from the milled face?

[Don P]

I see a couple of problems, see if this checks out.
First is the snow load is taken on the horizontal span of the roof. At a 12/12 pitch and a 14' rafter length, the horizontal run is 10'.
Next, you used the snow load of 40psf but neglected the weight of the materials themselves. The dead load is usually assumed to be 10-15 psf. Technically that is calculated on the slope but in common practice most folks use the same run of the roof. Being steep, so longer along the slope, I'm going to use 15psf. That would be a combined live load of 40psf + a dead load of 15psf for a total of 55psf.

Figuring tributary area 2' spacing x 10' span x 55 psf = ~1100 lbs total load
I'm using a span of 115" and coming up with a 6.8" dia in a sawn round timber beam (SRTB). The log standard is silent on where that is measured, only specifying that max taper is 1/8" per foot. For round beams Hahney says that is midspan dia and I feel that is a safe assumption for SRTB's bearing the taper rules in mind. So your minimum small end dia inside the bark, ignore the max 3/10 dia flat, is ~6-1/4", midspan, where bending moment is maximum is ~6-13/16" min. That will yield a roof with a max deflection of L/360. If this has no brittle finishes like plaster you can use the bending strength diameters and accept more sag... but I wouldn't, I'd just be conservative and stay a little bigger.

Holler if any of that is unclear or just plain wrong.
This might also be of interest to @DDW_OR 

[Joe Hillmann]

I see a couple of problems, see if this checks out.
First is the snow load is taken on the horizontal span of the roof. At a 12/12 pitch and a 14' rafter length, the horizontal run is 10'.

I wasn't sure on that.  Some other calculators said "horizontal span"  this one just said "span".

Next, you used the snow load of 40psf but neglected the weight of the materials themselves. The dead load is usually assumed to be 10-15 psf. Technically that is calculated on the slope but in common practice most folks use the same run of the roof. Being steep, so longer along the slope, I'm going to use 15psf. That would be a combined live load of 40psf + a dead load of 15psf for a total of 55psf.
I also wasn't sure on that  I didn't know if it should be 40 and that was snow load and roof weight or if it was just snow weight and I had to add an extra 10 or 20 for the weight of the roof itself.

Figuring tributary area 2' spacing x 10' span x 55 psf = ~1100 lbs total load up with a 6.8" dia in a sawn round timber beam (SRTB). The log standard is silent on where that is measured, only specifying that max taper is 1/8" per foot. For round beams Hahney says that is midspan dia and I feel that is a safe assumption for SRTB's bearing the taper rules in mind. So your minimum small end dia inside the bark, ignore the max 3/10 dia flat, is ~6-1/4", midspan, where bending moment is maximum is ~6-13/16" min. That will yield a roof with a max deflection of L/360. If this has no brittle finishes like plaster you can use the bending strength diameters and accept more sag... but I wouldn't, I'd just be conservative and stay a little bigger.

I also saw the the mention of "mid length" diameter for unsawn logs but no mention of it for the sawn logs.

As far as the L/360,  I intend to  have the board roof on the outside be the finished interior ceiling so flex isn't much of an issue.  The smaller I can go the easier it will be for me to find enough logs of the right size. I also intend to have a knee wall about 3 feet in to take some of the weight so the flex will be even less.


Holler if any of that is unclear or just plain wrong.
This might also be of interest to @DDW_OR

Thanks for the help. 

[DDW_OR]

before i was in a boat on a lake
now i have lost the boat.


for me i am building a lean-to to the south side of the 30x64 polebarn
under 1/2 of the lean-to i plan to put an insulated work shop and a chicken coop under the other half

the barn side is 12 ft high
the outside is 8 foot
the width is 18 ft wide
the max length of the sawmill is 21 ft

so will 2x12x21 on 24 inch centers work for the rafters?

most snow has been 7 inch that lasted 1 week

[Don P]

I'm assuming the rafters are spanning the 18' width running from the 12' wall to the 8' wall

The best calc for dimensional lumber is to use the one here;
Maximum Span Calculator for Wood Joists and Rafters (awc.org)
You didn't give a species and grade, in SPF(south) #1 works, in SPF (canadian) #2 works. That calc is for nominal, store bought, dimensions. If you are sawing something else we can redo.

Are you also needing to span a 21 foot opening with a beam that those rafters are resting on on the 8' tall side? If so what species?

11 here, I better hit the hay but I'll check back in the morning.

[DDW_OR]

the 8 ft wall is a standard stud wall.

Pine and fir milled onsite

1.5x11x21, or 1.5x12x21, or whole logs with the little end at 12 inches

For log cutting i make a measuring stick like this.



 

[DDW_OR]

so my idea of 2x12x21 on 16 inch centers will work
my milled lumber will not be "Select Structural"
it will be "near clear" green

i used the following values in the calculator

Douglas fir - south
2x12
rafters (snow load)
L/360
spacing 16
Exterior exposure, No, No
snow load 40
dead load 20

result was
The Maximum Horizontal Span is:
19 ft. 1 in.
with a minimum bearing length of 0.98 in.
required at each end of the member.

Property	Value
Species	Douglas Fir-South
Grade	Select Structural
Size	2x12
Modulus of Elasticity (E)	1400000 psi
Bending Strength (Fb)	1785.37 psi
Bearing Strength (Fcp)	520 psi
Shear Strength (Fv)	207 psi

[Joe Hillmann]

I started milling the rafters and joists for my build.  I ended up going with the smallest dimension possible.  But since the logs aren't consistent in size I have some that are just are just big enough and some that are 2 inches bigger than needed.  My thought  is if I alternate:big, small, big, small. and if the small ones are just barely big enough the big ones next to them can help support them a bit.

Also in milling I have found that very few of my logs are actually straight so it may make for interesting ceilings in the house.