Take the section of the standard timber, the cai, as the module of the building: it is 15 fen high and 10 fen wide, and every member is dimensioned in fen.
1 cai = 15 fen (height) × 10 fen (width)
The raised-beam frame: purlins at any height
Instead of a triangle, stack beams one above another, each shorter than the one below and raised on short posts, and lay a purlin on each beam-end; the heights of the purlins then set the section of the roof, which may be curved at will.
The Chinese tailiang (“lifting beam”) frame is not triangulated: its beams work in bending, like shelves, and the rafters simply span from purlin to purlin. That makes it heavier than a truss for the same span, but it has one great freedom. Because each purlin rests on its own post, its height can be chosen independently, which is exactly what the rule of jǔzhé requires. The concave Chinese roof is a consequence of this frame; a truss, whose rafters are single straight members, can only make a straight roof.
In the south of China a second system, chuandou, puts a slender column under every purlin and threads tie-beams through the columns; it uses smaller timber and is common in houses.
Related rules
Between two stacked arms leave a spacer of 6 fen, the zhi; a cai plus a zhi, 21 fen, is a “full timber” (zucai) and the vertical step of each tier of a bracket set.
zucai = 15 + 6 = 21 fen
Build the bracket set (puzuo) of blocks (dou) and arms (gong) crossing at right angles, each tier projecting no more than 30 fen beyond the one below; a set of n projecting tiers is called an (n + 3)-puzuo, from four to eight.
projection per tier ≤ 30 fen · rise per tier = 21 fen · puzuo = tiers + 3
Where the eaves must project far, replace the outer arms by slanting levers (ang) that run down and out beyond the bracket set and rise inward to be held down under an interior purlin.
For a great hall, measure the distance between the front and back eave purlins and raise the ridge purlin above them by one third of it; for lesser halls, by about a quarter.
rise = ⅓ × depth between eave purlins (halls); ≈ ¼ (+ a small addition) for ting-tang halls
Draw a straight line from the ridge purlin to the eave purlin and lower the first purlin below the ridge from it by one tenth of the rise; from that point draw a new line to the eave purlin and lower the next purlin by one twentieth; continue, halving each time.
drop₁ = H⁄10 · drop₂ = H⁄20 · drop₃ = H⁄40 · …
Cite this page Chris Paton, “The raised-beam frame: purlins at any height”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/tailiang-frame. Text, drawings and models licensed under CC BY-NC 4.0.