How to calculate rafter thrust? -Help! 1

[theclimber]

I have built a new roof over my house. It's a 12:12 pitch and spans 22' total. This will be a cathedral ceiling, but I installed a ridge board (2x12) not a ridge beam. I have installed collar ties (2x4@16"oc)at about 8' high above the plates.

I installed the rafters (2x8 16"oc) to a 2x12 ridge board, and to resist thrust at the plates, installed aircraft cable @32" oc from rafter to rafter at the plate. I thought it would be fine, but now I'm second guessing myself.

Why did I use aircraft cable of all things? - I guess I thought it would look different, and I couldn't readily find 22' long dimensional lumber. Since I'm a rigger by trade I happened to have a reel of unused cable.

A thorough search of the code book shows rafter ties necessary if no ceiling joists or floor system running parallel to the rafters, but the size required isn't even mentioned.

I know the snow loads, dead loads and the specs of the cable, but I need to know how to calculate the horizontal thrust these cables must resist, can anyone help?

Can I take any reduction for the area located above the collar ties?

Thanks,

Jeff

 

[SlideRuleEra]

blake989 - From one of the joints at the base (either side, since the truss is symmetric)you can calculate the force in rafter:
1. The net vertical component ajoint at the base is 275 lb (up).
2. Therefore the vertical component of the force in the rafter has to be 275 lb (down).
3. Since the force in the rafter can only act along it's axis, the rafter must "push" on the joint (rafter in compression) with a force of 389 lb (275 lb / sin 45 deg).
4. Since the rafter is "pushing" on the lower joint, it must also "push" on the apex joint (with 389 lb) to stay in equilibrium.
5. The vertical component is of the force from the rafter is 275 lb (up).
6. However, there are two identical rafters, both in compression and both "pushing" with vertical components of 275 lb each. The total of 275 lb + 275 lb (up) balances the the 550 lb vertical load (down) at the apex.
7. Of course you have to make sure that the horizontal forces at the apex are in equilibrium also. Because the truss is symmetric, they are:
(389 lb x cos 45 deg) "pushing right" = (389 lb x cos 45 deg) "pushing left".

One thing that adds to the tedious nature of this problem is the fact that all the angles are 45 deg with sin = cos. I always disliked that kind of problem, hard to tell which "0.707" you are talking about.

 

[soiset]

I think you'll want to check your connection capacity. What is the geometry? Single shear, double shear? How did you make the connection? The cable strength is probably your last worry. I haven't run the calcs, but at 733 lbs in single shear in a perpendicular load through two 1.5" rafters, you are probably not making it. What kind of wood is it?

 

[theclimber]

Let's put this another way. If I had used 1x or 2x wood rafter ties in place of the cables, no one would bat an eye, because that's how it's usually done. I checked the code book, and the specified connection between rafter tie and rafter are three 8d nails face nailed.

What is the shear capacity of 3 8d nails before withdrawal?

Certainly I imagine it to be less than the tensile strength of the cable or the shear capacity of the 1/2" through-bolted connection?

Is there a way to upload a .jpg onto this forum? I could take a picture of the connection- I think it would put some of you at ease.

Thanks for all the input!

J

P.S. The inspector came by and signed off on the roof framing. - He didn't even ask about the cables. I guess that means everything's safe, right?

 

[SlideRuleEra]

theclimber – Here are some typical numbers for your situation:

Assume all lumber is either douglas fur or southern pine and is 1.5 in thick.
Assume all nails embedded at least 11 diameters.

One, 8d common nail: Safe lateral load (shear) = 78 lb.

One through-bolt, 1/2 in diameter, in single shear:
Safe load perpendicular to grain = 250 lb. (Worst Case) or
Safe load parallel to grain = 550 lb. (Best Case)
The limit is determined by the strength of the wood, not the strength of the steel bolt.

Calculated maximum cable tension is 733 lb. This is to be resisted by connections with a safe load capacity of less than 550 lb. Sounds like it could be an invitation for “trouble”.

If ceiling joists were used instead of the cables to tie the bottom of the rafters together, there would be a couple of differences:

1. The ceiling joist should be 16 in o.c (instead of the cables at 32 in o.c.). This would tie all the rafter together. Then tension in the ceiling joists would be 733 lb / 2 = 367 lb.

2. The classic Department of Agriculture Handbook No. 73, “Wood-Frame House Construction” by L. O. Anderson specifies 5 each, 10d common nails for the connections between rafters and ceiling joists.

One, 10d common nail: Safe lateral load (shear) = 94 lb

Calculated maximum tension in ceiling joists of 367 lb. This is to be resisted by connections with a safe load capacity of 470 lb (5 nails x 94 lb/nail). Sounds good to me.

Source for allowable loading on nails and bolts:
“Standard Handbook for Civil Engineers”, Third Edition
Frederick S. Merritt, Editor
McGraw-Hill Book Company, Publisher

 

[boo1]

ok one load case done, four more to go...