Lesson 13 of 13 · Capstone
One Small Structure, End to End
Nothing new is taught here. One building, from bare ground to a material order, using every lesson you have worked. Set its size and pitch, and the whole thing computes — then answer for it without being told which method to reach for.
Step one
The three stages of the build
Not new material — the order of operations. Each block names the lessons it stands on.
Stage one · lessons 1, 3 and 4
Get it square before anything goes vertical
Stake the outline, measure both sides, compute what the diagonal must be, and move a corner until the tape agrees with the arithmetic. A building that starts out of square stays out of square, and every trade that follows pays for it in scribed trim and tapered rips.
The diagonal is the square root of one side squared plus the other squared. If your tape reads longer than that, the corner is open and you pull it in. Shorter, and it is closed and you push it out. Move about half the error and measure again.
Write the run down in feet and inches AND in decimal feet before you start, because the roof arithmetic in stage two wants decimals and the tape does not give you any.
Stage two · lessons 5, 6, 7 and 8
Put a roof on it and a way up to it
Halve the span to get the run. Multiply the run by the pitch over twelve to get the rise. Take the square root of twelve squared plus the pitch squared to get the inches of rafter you gain per foot of run, multiply by the run, and you have the line length. Add the tail for the overhang, measured along the slope and not along the ground.
If the building has hips, the same run drives them, but they travel the diagonal, so their per-foot number is built on 288 rather than 144.
If there is a loft or a step up to the door, the rise divides by the maximum riser and rounds up, then divides back out into equal risers, and the treads are always one fewer than the risers.
Stage three · lessons 2 and 12
Turn all of it into an order
Now the numbers become a list somebody can price. Floor area for the deck sheathing. Roof area — which is not the footprint, because the roof is longer than the span it covers; it is the rafter length times the building length, times two sides. Perimeter for the plates and the trim. Volume in cubic yards if anything is being poured.
Add the waste before you divide, divide by what one unit actually covers, and round up. Then write the unit beside every figure, because a takeoff without units is how square feet get ordered as linear feet.
That list, in your handwriting, is the whole of this class made useful.
Step two
Build it on the screen first
Set the shed. Every figure below is computed from the three sliders, and every one of them came from a lesson you have already worked.
Hands on it, off the screen. Take the numbers this panel gives you for a shed you would actually want, and write the material order out longhand on a sheet of paper. Sheets, plates, rafters with a length beside each, and a unit next to every figure.
Then take it to a yard and price it. When somebody behind a counter can fill your order without asking you a single question, you have finished this class — whatever the certificate says.
Step three
Prove it without being told the method
Three questions, one per stage, drawing on everything. Nobody tells you which formula to reach for. Miss one and you are sent back to the stage, and the stage names its lessons.
All three stages solid. That is the class.
You can square a layout, cut a roof, build a legal stair, find a radius you cannot reach, run an offset, and turn every bit of it into an order a supplier can fill. Thirteen lessons, and not one of them asked you to memorise a table.
Trades Geometry
The last of thirteen. Written by our founder, Dr. Gene A Constant, and donated to the Foundation. Published by Global Sovereign University Press.
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