Thursday, February 15, 2018

The geometry of a 1870's barn

 This Vermont barn was built in the 1870's . It has been used for storage for the last 20 years.

I prepared a report on its history and structure for its owners so they could consider repair and reconstruction with some real knowledge - not just good memories and/or worry about costs.

The barn was well built by a farmer who knew his land and a framer skilled at his trade.
The frame is regular, much of it still sturdy. Its mortises,  tenons, and pegs are still secure.

Its bents use dropped girts and posts to purlins which support  common rafters, a framing system regularly used in the Hudson Valley watershed, not often seen in this area of Vermont.

While I was not asked about the barn's geometry, as I laid out the plan and the frame I could see the geometry clearly - not complex, quite simple, repetitive, and straightforward.

Here is the 3rd bent and the lower level floor plan.
The bent is one of the 4 timber frames across the barn that are then fastened together with plates and girts. Walls and flooring have been left out.
The plan is mainly the post locations. I have not included the exterior wall girts.  The braces which are visible in the photograph to the right are barely noted.

The floor plan could easily have been laid out using circle geometry.

I have added Laurie Smith's diagram for drawing a square beginning with a circle. It is a very clear description.

For his websites see:


Here is my drawing of the floor plan with its posts laid out using circles. The first  (top) 2 bays are of equal depth and width.  The dashed green line shows the layout determined by the circles.

The lower bay (between bent 3 and 4) is not as deep. Perhaps the land dropped off too steeply, or the lumber available was not as long. The dotted red line in the lower right rectangle shows how the crossing of the arcs of the square determined the depth of the bay. 

The base of bent 3 is vague on purpose. I don't really know the depth of many of the lower level posts. The land slopes west to east. The floor on the east end has been built up over the years with layers of discarded boards.  The right end has been reconfigured for cows; the left end has a false ceiling.
The main  barn level of the bents is divided into thirds. The  posts are the height of a third of the bay's width - the space they outline is a square. I've drawn it in red. The dropped girts are set at the point where the arcs of the square cross. Also drawn in red.
This is similar to how the lower level east bay's depth was determined.
The posts that support the purlins ( the roof beams ) are centered on the squares below. The height of the ridge is also determined by where the arcs of the loft square cross.

Lastly the location of the lower girt which becomes the plate for the wing is determined by the Rule of Thirds.

Such basic practical geometry tools! They are  those described by Serlio, Palladio, and Asher Benjamin - circles, arcs, lines - applied in very simple ways with impressive results.

Well thought out, straightforward without fancy flourish, the space and the frame speak to me. But I am simply the one who documented this, sharing the power, the grace, that I found.

The barn, after 150 years, is no longer essential. It is very possible that it may not survive until a new purpose discovers it.


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