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Author Topic: Cantilever calculations, designing a cabin....  (Read 850 times)

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Offline Roachven

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Cantilever calculations, designing a cabin....
« on: July 14, 2017, 09:28:49 am »
Howdy everyone,

Ok so this is not timber framing, it's a stick frame with some post and beam elements, please tell me if I'm posting in the wrong place.....

I'm designing a cabin for my friends to be built on my land.  I'm trying to learn how to properly calculate loads and size beams and lumber.  No enforced code in our area so I get to be the saywer, architect, engineer, carpenter etc, but I want to do it right.  I've struggled through plenty of building projects here in the past, but this is my first attempt at doing a detailed design of all the framing elements before actually starting.  I'm milling all the wood from the land here.  I've been using sketchup for the design. 

First question (for the engineers out there)….  Am I calculating the load correctly for the cantilever roof overhang? 

For purlins, I plan to use nominal 2x4s (1.5x3.5) on end 16” on center with a 2' overhang. 

I've never calculated a cantilever before but here is the equation I have for a cantilever beam - uniformly distributed load.

M max (at fixed end) = wl˛/2

w= 16” on center purlin spacing x 75lbs per square foot snow load plus dead load.
l= 2' overhang


Here's my calculation….  M = (w )16”x75lbs(l˛)2'x2'/2 = 2400 (lbs per square inch)

Section modulus for 1.5”x3.5” = 1.5x3.5x3.5/6 = 3.0625 (inches cubed)

fb (actual bending stress) = 2400/3.0625 = 783.673…..


I am fairly confident at this point on calculating beams, joists and rafters, but this is the first time I've tried to calculate a cantilever, just wanted to check. 

I've also got a question related to the bird's mouths on the rafters I will ask that in another post on this same topic. 

Thanks for any help in advance.
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Offline Roachven

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Re: Cantilever calculations, designing a cabin....
« Reply #1 on: July 14, 2017, 09:59:03 am »
 

 
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2001 Skandic SWT Snowmobile (winter log skidding)
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Offline Roachven

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Re: Cantilever calculations, designing a cabin....
« Reply #2 on: July 14, 2017, 10:04:22 am »
Second Question …..  I am concerned about the depth of the birds mouth for the upper rafters, I realize it is way too deep (cuts through almost half of the 2x8 rafter).   Does anyone have a suggestion on how else I could join the rafter to the top ridge beam? 

Thanks
 

 
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Offline Ox

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Re: Cantilever calculations, designing a cabin....
« Reply #3 on: July 14, 2017, 10:59:53 am »
I'm not smart enough to help you with anything other than the birds mouth for your upper rafters.  Old timers say they ain't weakening the rafter near as much as one thinks because they're actually sitting on another piece, so it's almost like nothing is different.  It's not like there's a whole notch cut out that is filled with air - it's filled with wood. 

So my half a cent is your birds mouth cuts will likely be fine.

All the rest:  somebody that's smart will likely be along shortly.
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Re: Cantilever calculations, designing a cabin....
« Reply #4 on: July 14, 2017, 11:19:18 am »
code rules state that the bird's mouth should not be more than 1/4 to 1/3 the distance  of the timber height.
More importantly you need a minimum of 2" of the seat, where the rafter sits on the supporting timber.

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Offline grouch

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Re: Cantilever calculations, designing a cabin....
« Reply #5 on: July 14, 2017, 05:43:38 pm »
I'd be a lot more worried about wind uplift than loading on that overhang.
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Offline rjwoelk

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Re: Cantilever calculations, designing a cabin....
« Reply #6 on: July 14, 2017, 06:11:13 pm »
My thoughts are that a overhang at the top would be no different then the over hang at the bottom. You will have less snow load (if you had snow) at the top than  the bottom. I would call a truss company and ask them. The worse they could do is not tell you.
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Offline Planman1954

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Re: Cantilever calculations, designing a cabin....
« Reply #7 on: July 14, 2017, 06:37:43 pm »
A quick and simple strengthening of the birds mouth would be to simply nail a scab, or short 2xwhatever block on one side of the rather. This will reinforce it. I'd make it about two feet long...simple retrofit.
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Offline Don P

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Re: Cantilever calculations, designing a cabin....
« Reply #8 on: July 15, 2017, 09:12:19 am »
I've run into this situation and asked an engineer. Actually that birdsmouth at the top is a real problem. The inside corner of the notch concentrates the stress of the span below it to that corner and it wants to split from there. Make that notch as small as possible or bevel the top of the beam and don't notch at all. I believe code states 1/4 depth notch max, 1-1/2" bearing min. You can also put a beveled 2x lengthwise along the face of the beam underneath the rafters to help reinforce that weakened area and bear the rafter if it does try to split. The notion of wood replacing removed wood is certainly out there but I can't think of an instance where it is true... banish the thought  :).

Just a carpenter, your overhang equation looks correct. I think at 75 psf, down is greater than uplift.
The canti equation part for this calc is the same;
http://www.timbertoolbox.com/Calcs/ohangunild.htm

Offline Roachven

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Re: Cantilever calculations, designing a cabin....
« Reply #9 on: July 15, 2017, 10:00:53 am »
Thanks everyone for replies! ;D

First I want to state that I am well aware that the birdsmouth for the upper rafters in my drawings are WAY too deep and I WILL NOT build it this way. 

Plan man, Thanks for the scab idea.  Don, thanks for checking my calcs and affirming that the birdsmouth is too deep.

Don, when you ran into the same problem what did the engineer recommend?  Did you just size the birds mouth to the 1.5" minimum horizontal bearing? 

Another idea I had was to either let in the rafters a half inch into the horizontal surface of the beam so that the bottom of the rafter would still have a bearing surface even with the birds mouth.  I suppose I could also just cut the birdsmouths, set the rafters and then nail a 2x6 along the beam right under the rafters to serve the same purpose.  I will probably use the scab idea too for extra reinforcement, but I will make it probably 4+ feet. 

I'm not too worried about the wind uplift, I will probably use timberlocks to fasten the rafters down and probably 6" ring shank pole barn nails for the purlins. 

Snowload here on the other hand is a major factor.....  An average winter (although nothing seems average anymore) here we will see 4 feet of snow on the ground from December till April.  Three and a half years ago, we got about 30 inches of snow about December 4th.  It never melted and more accumulated on top of my sawmill shed roof all winter.  The sawmill shed is a 4/12 pitch with metal roofing but that snow still hung on till about April 20th or so..... I was glad I was not nearby when it finally slid off.   :o  I personally think I underbuilt the sawmill shed a bit and I just got lucky it didn't collapse that winter.  I'm tired of underbuilding and then worrying about stuff.....

Any more thoughts on the 1.5 in minimum bearing surface on the horizontal portion of the birds mouth?

Thanks again everyone for reading/replying. :)
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Offline Roachven

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Re: Cantilever calculations, designing a cabin....
« Reply #10 on: July 15, 2017, 10:07:52 am »
Oh yeah and thank you also Jim for affirming the birdsmouth cut is too deep....

Jim mentioned 2" minimum seat....  any other opinions about minimum horizontal bearing for birdsmouths(1.5" or 2")?
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Offline Don P

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Re: Cantilever calculations, designing a cabin....
« Reply #11 on: July 15, 2017, 02:20:35 pm »
I used a 1-1/2" notch and a beveled 2x4 underneath the rafters nailed to the beam to support it. another way is to bevel the top of the beam or attach a beveled strip to the top to support an unnotched rafter.
Building codes typically call out 1.5" min bearing on wood, 3" min on masonry. That is a minimum, you should check that whatever you use is sufficient not to crush though. a 1.5x1.5" area is only 2.25 square inches, you'll be hard pressed to carry more than about 800 lbs on the side grain of the beam without crushing.

You also need blocking to keep those purlins from rolling. Is there a reason not to do the overhangs typically with lookouts from an inboard rafter rather than purlins?

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Re: Cantilever calculations, designing a cabin....
« Reply #12 on: July 17, 2017, 08:00:05 am »
Don, I do plan on putting blocking between the 2x4 rafters, thanks for mentioning though.  Honestly the main reason I am doing purlins is that it is the easiest thing for me to wrap my head around.  I started building with round poles and logs and purlins is what I always have done for everything since.  Wouldn't lookouts cause me to need the outside rafter to be shorter than the other rafters?  Then I would need to cut a deeper birdsmouth which I'm trying to avoid?  I just can't visualize any way to do it with lookouts that would save any wood or make sense structurally. 

Do you know any formulas for max lbs/sq ft on minimum bearing surface?  ???
Thanks

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Offline Don P

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Re: Cantilever calculations, designing a cabin....
« Reply #13 on: July 18, 2017, 06:45:44 pm »
Quote
Do you know any formulas for max lbs/sq ft on minimum bearing surface?
Wood has two kinds of design values for maximum allowable compression force, usually you are most concerned with the maximum allowable load perpendicular to grain, side grain crushing. The second is max allowable compression parallel to grain, end grain compression. Usually end grain compression is at least double side grain so generally what we are most concerned with is compression perp to grain, the post biting into the beam.

In this case conservatively you have load roughly perp to grain of the rafter bearing on perp to grain on the beam. (the birdsmouth is actually mostly perp grain but it is beginning to slope towards end grain in the notch and you can adjust allowable bearing value upward a little using the Hankinson formula to take full advantage if needed.

For example SPF lumber has an allowable perp to grain compression value of 425psi. If you have a minimum notch of 1.5" x 1.5" of rafter width=2.25 square inches of bearing surface X 425 psi allowable= 956.25 lbs allowable on that bearing. Take half the rafter span + overhang (horizontal measure) X 2' oc spacing X (75+10 psf) and check to see if that is less than the allowable load. Adjust the bearing as necessary. Check the beam as well, the weaker species controls. Dougfir is good for 625psi perp to grain.

These are a couple of sketches I had of lookout framing, you can see an applied beveled cant strip on top of the first ridgebeam;