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)
Rules · Structure · Modules · Entablatures
The bracket set steps out 30 fen a tier
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
The great block (lu dou) sits on the column head; in its cross-slots rest an arm running along the façade and a “flower arm” (huagong) running outward. On the end of each outward arm a small block carries the next, longer arm and a transverse arm, so that the load of the eaves is gathered, tier by tier, back onto the column. The count of “puzuo” includes the great block, the top member and the beam-end as well as the projecting tiers; hence four puzuo for a single tier.
The number of tiers expressed rank: the grandest Song halls used seven or eight puzuo. Under the Qing, when the roof loads came to be carried more by beams, bracket sets shrank to a fraction of their Tang size and multiplied along the eaves as ornament.
Related rules
There are eight grades of cai, from 9 × 6 cun down to 4½ × 3 cun; use the first for great halls of nine or eleven bays and the smallest for pavilions and ceiling coffers.
grades 1–8: 9×6, 8¼×5½, 7½×5, 7.2×4.8, 6.6×4.4, 6×4, 5¼×3½, 4½×3 cun
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
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.
Set the heads of the outer columns inward: on the front and back by 1 fen for every chi of height (1/100), on the ends by 8 li per chi (8/1000); the corner columns lean both ways.
lean = 1/100 of height (front) · 8/1000 (flanks)
Fix the bay (the distance between column centres) and derive every other member from it by fixed ratios: the column from the bay, the brackets and beams from the column, the rafters and their spacing from the brackets, the eaves from the rafters.
Cite this page Chris Paton, “The bracket set steps out 30 fen a tier”, The Textbook of Architecture, https://textbookofarchitecture.com/rule/dougong-puzuo. Text, drawings and models licensed under CC BY-NC 4.0.