Assessment of Common Rafter Size

[Brian_Weekley]

I think I understand the beam calculations pretty well.  However, I'd like to get a better understanding of how to calculate the size needed for a common rafter.  In particular, how the roof pitch might come into play.

For this example:



Dimensions:
Rafter length=9.90 feet (119 inches)
Proposed rafter size=4 x 6 inches
Rafter spacing=2 feet
Pitch=12/12
Run=7 feet (84 inches)

Loads:
Snow=70 PSF
Dead=10 PSF

Load per rafter:
Since the roof is not flat, the snow load would not be calculated based on the total surface area, rather the run (2 feet x 7 feet=14 SF).  Therefore, snow load per rafter=14 SF x 70 PSF=980 lbs.  However, the dead load would be based on the total surface area=2 feet x 9.90 feet x 10 PSF=200 lbs (rounding up)  Therefore, the estimated total load per rafter=980 + 200=1180 lbs.

Using "Don P's" beam calculator available in the red toolbox found in the left margin...

Design Values for No. 2 Pine (Posts and Timbers):
Max Fiberstress=450 PSI
Modus of Elasticity=0.9 Million PSI
Max Shear=125 PSI

Caveats:
1.  According to the chart, a 4x6 doesn't completely meet the definition of a beam and stringer (defined as 5x5 inches or greater)
2.  A pitched rafter is not a simple, horizontal beam

Questions:
Can the beam calculator still be applied for this purpose?  Here's my rationale:  as you increase the pitch of the rafter, it would begin to act more like post than a beam.  Obviously, if you raise the rafter 90 degrees, it would be a post.  Therefore, I would think the horizontal beam calculator would be a worse case assessment for a rafter.  With that said, I would also think the value used for span in the calculation would not be 119 inches, but the run span of 84 inches.  Plugging in these numbers here's what you get...

Results for a 4 x 6 inch rafter:
Span=119 inches:  bending and deflection fails, but shear passes
Span=84 inches:  bending fails. deflection and shear passes



Is this a reasonable assessment, or am I way off base here?  Are there any other considerations necessary for where the rafter narrows at the seat in the plate?  Any feedback from the more experienced timber framers would be greatly appreciated!

Thanks, Brian

[Jay C. White Cloud]

Hey "Brain,"

I am sure Jim will be of more serves at the moment, but at a glance, I can tell you the "calcs" for rafters is completely different than beams, as there is some trig. involved around the pitch component.  Think of it as compression math for posts, plus bending-modulus of rupture for beam averaged, blah, blah, blah.  Jim will probably straighten things out and make more sense, wish I wasn't so busy (and tired.)  Will follow along and help if I can.

Regards,

jay

(give me call if you get in a pinch and just need to talk through "rafter stuff," I'm in the office almost every night from 21:00 till 22:00.)

[Jim_Rogers]

My first comment would be that we never use #1 grade beams. I don't know if you're sawing your own stock to make these rafters or not. But trying to buy #1 could be a challenge, at best.

We always use grade #2 as a basis.

Next you don't say exactly what the span or run is of the rafter. The run is half the span. Is the span 15' and the run 7.5'?

If so then the run is used for snow load. And the rafter length is used for dead load. You have that part right.

With that high a snow load you most likely will have to move these rafters closer together to get lower load per rafter.

Or you modify the "given" value by applying the "repetitive" use factor. What that is is a given value increase due to the fact that you have multiple rafters sharing the load.
If your rafter size is that close to need to use it then you may need to increase it's depth.
In increasing your depth from 4x6 to 4x7 you change it's category from post and timbers to beams and stringers. You can't use beams and stringers value category for a 4x6. The rule is that the depth must be more than 2" of the width in order to use beams and stringers. A 4x6 does not qualify. A 4x6 is in the post and timbers category.
Change the load by moving the spacing, or increase the rafter depth until it passes on all three tests.

Good luck and I hope this has helped you.

Jim Rogers.

[Brian_Weekley]

Thanks guys.

I had a few mistakes that I corrected.  Yes, the run is 7 feet, not 7.5.  I also re-ran using Pine #2 numbers.

Jim, a few more questions if you don't mind...

Would you use the rafter length or the rafter run in the calculation?  This makes a big difference.  Because the rafter is pitched, it just doesn't make sense to me to consider the full rafter length for bending.  Also, I will have a metal roof.  Therefore, I would think the probability is extremely low that the full snow load would ever be realized.  Is there a correction factor for using a metal roof? 

[Jay C. White Cloud]

There is the "rub," in it and why for most jobs I still go to the P.E. for assistance.  Roof calcs involve much more that simple or complex beam load calculations, you have potential wind loads and deflections, potential for uneven loading calculations, etc.  Whenever I have "looked over the shoulder," or "peeked behind the curtain," when it comes to roof engineering formula, I see "trig. formula," which addresses that deflection criteria you referenced.  Maybe one of our P.E. types could step in at this point and reflect some of that math just for "educational purposes."  I following along with you on this.

Regards,

jay

[bmike]

Not a PE, and not sure how that particular spreadsheet works, but I have one I use that allows you to adjust for pitch,  type of roof (slippery surface?), exposure factor, etc.

How mine works:
When calculating the area to load the rafter, use the rafter run x the width of the spacing (assuming uniform loads).
When putting in the length of the rafter for the calc, use the actual length from bearing to bearing point. This should be longer than the run you used for the area calc (the diagonal). So the load is derived from the horizontal area, but is spread over the length of the beam - essentially penalizing you for having a longer beam than the area you are carrying.

But then you get into pitch reductions and type of roof, and eventually sideloading with wind (if doing lateral calcs) and even unbalanced snow load. When in doubt, get help, as Jay suggests.

[Jim_Rogers]

Would you use the rafter length or the rafter run in the calculation? 

You would actually use both. I use the rafter run for the snow load (live load) calculation. Then the rafter length for the dead load calculation. These two loads are then added together to get the "combined" load.

Is there a correction factor for using a metal roof?

There is but I don't know what it is. I maybe able to look it up but I don't have time right now. Maybe after work tonight.

As far as snow load on a roof. The load duration is less with a metal roof. When the metal roof heats up in the sun after the snow storm has left the area then the snow will slide off.
This reduces the "duration" of the load. But until that happens your roof has to hold it up. To be conservative and to make it stronger, I don't use that factor. It will not save you much money. And it will help you to sleep at night knowing that the roof will not collapse under the snow load.

Jim Rogers

[Roger Nair]

Brian, I am a carpenter not an engineer, so for what it's worth....  Normally deflection calcs are made not on the total length but on the length between the bearings, on the material free to deflect.  Therefore I believe it is safe to measure the length from the underside inside abuttment of the rafter and the plate parallel to the top to the underside abuttment of the rafters.  That may shorten the span 9 inches or such.  I would also look into changing the rafter dimension instead of decreasing rafter spacing.  A 3 x 7 will be stronger than a 4 x 6 and will require less bd/ft.  A 3 x 8 will be much stronger than a 4 x 6 at the cost of the identical bd/ft.  The calculator will ease playing with the dimensions to a point of freedom.

[Brian_Weekley]

Follow-up:  After Jim checked the calculations with his program, it seems like a 4x7 should do the job.  One reason is that by increasing the depth from 6 to 7 inches, the design values shift from the "post and timber" category to the "beams and stringers" category.  Apparently, there is also a slight correction to dead load based on angle that I did not account for.  Jim:  thanks for the reality check and the offline info!  I now feel confident to get stock to make my rafters.