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Author Topic: Thrust formula confusion  (Read 713 times)

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Offline rkb5916

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Thrust formula confusion
« on: January 20, 2017, 06:11:29 pm »
I've been studying Chappell's A Timber Framer's Workshop and I'm getting confused with horizontal thrust at the tie beam to post joint. In his example he uses a high cape without collar or rafter ties.  He suggests adding these members to reduce thrust, but there are no formulas for how they do this.   Any help?
Also, did I do the math correctly...
12/12 pitch, 16x40 = 640sf @ 40 combined load = 25600 lbs / 4 bays = 6400; 3200 per rafter)
Thrust (lever formula)  = Fx (L/c)
L = 16' c = 10'
Fx= .5W/Pitch = .5 (3200) / 1 = 1600
1600 (16/10) = 2560lbs thrust

Thanks for any help

Offline Heartwood

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Re: Thrust formula confusion
« Reply #1 on: January 21, 2017, 09:02:38 am »
Ed Levin's articles on Joinery Engineering inTimber Framing issues 38 & 39 explains how this can be calculated algebraically or graphically thru vector analysis (free body diagram); those articles are also in the Guild's Joinery & Design Workbook Vol. 1. I bet you could find some tutorials online on an engineering website.
I don't have Steve's book with me so can't address his specific example, but you take that 1600 lb. thrust on each rafter and extrapolate it to each post based on the number of rafters per bay. Note that the actual moment and stress on the tie joint in a high posted cape is magnified by the length of the cantilever above the tie beam, and this determines the joint design and size of the post required. So the thrust is only part of the calculation.
Here's a quote from Ed's article:
"Whether you come at it by the algebraic or the graphical method, it's possible to generalize a principal about thrust in simple rafter roofs: The resultant force always acts at an angle to the level whose pitch is twice the roof pitch. So in a 12: 12 roof the vector sum of thrust and gravity load is pitched at 24:12, in a 6:12 roof the resultant acts at 12:12, etc. Hence roof thrust can be quantified as follows: For simple rafter roofs (no collars, struts, kingposts, etc. to muddy the waters), with roof slope S (in degrees), the thrust is equal to the roof load divided by twice the tangent of the slope, or Fx = Fy / 2 tan S."

Offline Don P

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Re: Thrust formula confusion
« Reply #2 on: January 21, 2017, 09:41:43 am »
Can you define the variables?
I suspect you are working above my level of knowledge.
The vertical gravity load on the roof translates into an axial thrust running down the length (axis) of the rafter. We usually want the horizontal component of that load that is working against the walls shoving them outward. There's the vectors.

These are a couple of calcs I wrote awhile ago that might help a little. I have notes from some classes here somewhere, holler if you want more reading and I'll scan and pm you that stuff.
http://www.timbertoolbox.com/Calcs/RafterThrust.htm
http://www.timbertoolbox.com/Calcs/raisedtiethrust.htm

This is a biggie;

 Note that the actual moment and stress on the tie joint in a high posted cape is magnified by the length of the cantilever above the tie beam, and this determines the joint design and size of the post required. So the thrust is only part of the calculation.

Offline rkb5916

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Re: Thrust formula confusion
« Reply #3 on: January 21, 2017, 11:42:33 am »
Using the formula provided by heartwood (Fx=Fy/2 tan S) I can enter my numbers.   6400lbs / 2 tan 63.43 = 1600 pounds of thrust.  (I used 63.43 due to "12: 12 roof the vector sum of thrust and gravity load is pitched at 24:12"

Using Don's Rafter Thrust calculator I get 1600

As you both noted I need to account for the lever formula to find thrust at the post/tie beam
Chappell provides this formula as Fx (L/c) where Fx = horizontal thrust at top of post
L = post length, feet
c = post length from foot to tie beam
So...1600 (16/10) =2560 lbs of horizontal force on the tie beam joint

This equals my original calculations so I'm feeling confident I can use 2560lbs when determining peg and tenon strength requirements

Thanks guys

Offline Heartwood

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Re: Thrust formula confusion
« Reply #4 on: January 22, 2017, 09:58:24 am »
Just as important than the pegs or tenon size, or more so, is the post size. 1600 lbs over a 6' cantilever produces a moment at the tie joint of 115,200 in. lbs. You need to plug that number into your section modulus required calc (including species and grade variables, Fb=Moment/Section Modulus) being sure to subtract the volume removed by the mortise and peg holes. If this is a mystery, read the above mentioned articles or hire an engineer (always the best option). That seems like a big cantilever that would require huge posts.

Offline rkb5916

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Re: Thrust formula confusion
« Reply #5 on: January 22, 2017, 12:47:55 pm »
Ok, let's assume 8x8 post with a 2" through mortise and" peg. Section modulus would be:
Post 8x8^2 = 512
Mortise 2x8^2 = 128
Peg 6x1^2 =6
So 512-128-6 = 378

115200 / 378 = 304.76

Modulus of rupture for balsam fir is 5500
Chappell states our calculation should be 6 to 8 times less than this (5500/8=687.5) so I should be okay...I think

I can't find volumes 38 and 39 in back issues so I'll order the workbook you suggested

Offline Heartwood

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Re: Thrust formula confusion
« Reply #6 on: January 22, 2017, 01:27:05 pm »
The S calc is not bd^2, but rather should be bd^2/6.
Fb required then is 1828+.
I use Fb rather than Modulus of Rupture.
Bottom line is I would never use a post above tie beam longer than 2' (maybe 4' with a very beefy post) without a ridge or purlin plates.

Offline rkb5916

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Re: Thrust formula confusion
« Reply #7 on: January 22, 2017, 01:36:10 pm »
Copy
With a 12 / 12 pitch I could easily drop that down from a 6' cantilever down to 2' and still have decent headroom (it will be used basically as a storage attic anyway)...or add a rafter tie
Thanks for the help

Offline Don P

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Re: Thrust formula confusion
« Reply #8 on: January 22, 2017, 10:07:46 pm »
There's a couple of ways of thinking/ going there. If you keep the posts at 6' a rafter tie can be lowered to 8'  and the thrust on the post goes away. If you place a tie too high all it does is put a high bending stress on the rafter and it doesn't really restrain the thrust at the rafter feet.