Rafter Thrust - Math Check, Please

I'm calculating the rafter thrust for common rafters at 33" OC to determine how much tension will be applied at the tie beam tenons. My math yields a horizontal thrust of 712 lbs per rafter (same as the load) for a 6:12 pitch. Have I got that right?

Multiplying the total load per rafter by 11 gives a total horizontal thrust being transmitted to the top plate of 7,832 lbs. That horizontal thrust will be held by 4 bents. That means that each of the two middle bents will have a tension of 2,611 lbs at the tie beam tenon. Right?

With two pegs, each connector will have 1,305 lbs applied at full design load?


Thanks!

Kevin - you also need to consider the lever arm of the distance from where your load comes in to where the tie is. 2' below the plate, correct?

I'll peak at the loading Monday when I get back in front of the computer.

Mike

Mike,

Yep. 2'.

Bump, I'm quite interested in this so I'll take a stab hoping for correction.

I didn't follow all well but am assuming 11 rafters and the thrust at each post top is 2611 lbs. The plate needs to take this without rolling off.
Following Mike's comment, the bending moment in the post at the tie mortise would be 2,611 lbs x 2'= 5222 ft-lbs.

I looked at the post as a beam overhanging a support (the tie), with a point load on the end (the thrust). The "beam", our posts section at the point of maximum bending, is the post less mortise. I looked at it using this calc I had;
http://windyhilllogworks.com/Calcs/pointloadcantilever.htm
I'm not sure that is entirely correct in that there is also an axial load down the post as well as the thrust's bending load...but in that area the tie provides lateral support.

Don, if we are seeking the thrust on the tie and pegs can we put bending moments aside and evaluate the problem as a simple lever? So the force on the tie equals the height of the post divided by post height minus the drop of the tie times the force applied to the top of the post.

Ahh, Thanks Roger