Question on Tension in a Rafter (Collar) Tie

[ziggle314]

Hi folks,

I am an electrical engineer who is doing some reading on structural engineering -- purely recreational. I am analyzing the following situation.

I found an article in the Journal of Lightweight Construction that presented the following formula for the tension in the rafter tie and I decided to derive this equation myself using the method of sections on half the roof.

I mentioned this equation in a blog post on my recreational efforts and I received the following comment.

One thing I note from your analysis is that the thrust T is fine for calculating the load upon the tie to rafter connection, but since this analysis considers only half the roof, the same effect on the other half of the roof would therefore create a tensile force in the tie member of 2 x T.

I find this comment confusing. Is the tensile force in the rafter tie really twice the force it exerts on the ends? If I had a weight hanging from a rope mounted to a ceiling, it seems like the rope is pulling on the ceiling and the weight with equal and opposite forces, yet would be under a tension equal to the weight of the load.

 

[BAretired]

You have not defined W.

If W is the total uniformly distributed load over length L, then the total load over span 2L is 2W. The simple span moment is M = 2W*(2L)/8 or WL/2. The tension in the tie is M/h or WL/2h.

Taking your expression
T = W/2 * H/h * run/rise
But run/rise = L/H
So T = W/2 *H/h * L/H = W/2 * L/h = WL/2h which agrees with the above calculation.

Your sketch shows forces T acting outward on each wall which is incorrect. T is the tension in the tie. It acts inward on each of the tied rafters. That means the tie connection at each rafter must be capable of resisting a horizontal force of T. The force on each wall is W and is vertical.

BA

 

[hokie66]

It is not you that is confused. If the force in the tie is T at both ends, it is T in the middle. You can't believe everything that you read on the internet.

 

[ziggle314]

Great responses!

BARetired:
Thanks for reviewing the drawing. As you state, W is the uniformly distributed load projected horizontally and T should be on the tie and not on the walls.

hokie66:
That is what I was thinking. Thank you.