To build a Standard Gambrel truss only requires the Pythagorean theorem and knowing the width of the gambrel. A standard Gambrel is 1/2 as high as its width, has equal length slopes (labeled 'c'), and fits inside a semi-circle. The slopes meet at a 45 degree angle from the center, and each end will be cut at a 22.5 degree angle.
So basically if you know the Pythagorean theorem, and the width - you can calculate the length of each slope.
If you see the square (two sides are dashed lines) in the picture above - the diagonal splitting the square is the same length as the height and half of the width (This is labeled 'h'). We need to find the length of a:
Pythagorean Theorem:
a^2 + b^2 = h^2
Since this is a square, a and b are equal, so: 2a^2 = h^2
or: a^2 = ( h^2 / 2)
To calculate b, we take half the width 'h', and subtract 'a' that we just calculated.
b = h - a
And finally, to calculate the length of the slope, use the Pythagorean Theorem again:
a^2 + b^2 = c^2
So to put it all into one formula:
(h^2)/2 + ( h - sqrt((h^2) / 2) )^2 = c^2
If you are trying to build an 8 x 8 shed, the Gambrel width will be 8', so: h = w/2 = 4
(4^2)/2 + ( 4 - sqrt((4^2) / 2) ) ^2 = c^2
8 + ( 4 - sqrt(8) ) ^2 = c^2
8 + 1.37 = c^2
sqrt(9.37) = c
3.06ft = c
So each slope is: 36.72 inches
