Common Rafter Question

I am trying to learn some of the basic engineering calculations that apply to timber frames. I am not an engineer, but I'm beginning to grasp some of the principles. I'm stumped on a common rafter issue. That is, what type of calculation is used to determine the maximum span between ties? For example, if I have a 16 x 20 stand-alone common rafter structure, would it be appropriate to simply put posts and ties at the ends, 20 feet apart? I'd think not, as the middle would surely bow out due to the thrust of the rafters. What type of calculation is used to determine the maximum spacing between ties? Thanks to anyone who can point me in the right direction. I understand, of course, that any calculations I do will need to be checked and approved by a qualified engineer.

Joel,
I'm trying to help myself answer my question by searching my timer framing journals on dvd. I can't get into the index. It's, I think, got an "idx" entension, and my computer tells me that it can't open it. Is this the file with the index in it? Help. Thanks.
Dale

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Worked like a charm.
That Ed Levin is one smart guy. # 39, 1996

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 2412, 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 F, = F, + 2 tan S. Our 2,520 roof load induces thrust of 1,260 lbs. in a 12:12 roof. In a 9:12 roof, the same load would impart 1,680 lbs. of thrust. Load and thrust would be equal in a 6:li roof, and by the time you get down to 3:12 pitch, thrust has grown to 5,040, twice gravity load.