Bracket sets in the Yingzao fashi

By Andrew I-kang Li

This page contains a demonstration of the composition of bracket sets (dougong) according to the 12th-century Chinese building manual Yingzao fashi. It operates in the Nitros environment, developed by Prof. Takehiko Nagakura.

For more information on the building system of the Yingzao fashi, see "Chinese wood frame construction of the twelfth century."

Introduction

In the simplified version of bracket sets that we consider here, there are 496 possible sets. The matrix above shows 40 sets, arranged vertically by "complexity" and horizontally by grade. By "complexity" is meant the number of horizontal layers, which is by no means the only factor affecting "complexity." The grade is the size of the modular unit fen. There are eight grades. (See below.)

Hierarchical structure

The chart above shows the top-down hierarchy of the bracket set structure. It can be expressed in the following string grammar.

S --> A C

C --> B C

A --> lu dou, hua gong, nidao gong, man gong, zhutou fang

B --> hua gong

B --> hua gong, guazi gong, man gong, su fang

C --> shuatou hua gong, ling gong, liaoyan fang

C --> shuatou, hua gong, guazi gong, man gong, liaoyan fang

Note the four types of components, which combine in specific ways:

Dou (blocks)

For the sake of simplicity, the only type of block included here is the lu dou. There are numerous other types, but they have been omitted. The lu dou is the large block at the bottom of the bracket set. It sits on the column or lan'e beam.

Hua gong (flower arms)

These are the arms perpendicular to the wall. They all have the same name, even though their size may vary.

Other gong (other arms)

Unlike the hua gong, the other arms have different names and sizes, depending on their position in the bracket set. The guazi gong and man gong usually occur together, and support a purlin.

Fang (purlins)

These support the rafters and span between bracket sets. These have different names, according to their position in the bracket set. The zhutou fang lies above the column. The liaoyan fang is the outermost purlin, closest to the eaves. The su fang is any other purlin.

Explicit parameters

These are the parameters which are actually employed in the computation of the models.

Position

This is expressed as (xo, yo, zo).

Grade

The Yingzao fashi gives dimensions of components in the modular unit fen. The fen has eight grades (1 through 8) which give the absolute values shown below. The cun is an absolute unit; 1 cun = 3.20 cm.

For more information on the grade, click here.

Number of segments

Hua gong (flower arms), the arms perpendicular to the wall, can be considered to be composed of two end pieces and an odd number of repeated segments in between. The number of segments depends on the arm's position: the higher it is in the bracket set, the longer it is and the more segments it has.

Implicit parameters

These are parameters which, while not used as parameters in the computation, manifest themselves as branching points or iterations of loops. They are parameters inasmuch as they are used in the Yingzao fashi to describe bracket sets.

It is an interesting question to investigate the nature of the various structural descriptions of bracket sets: the one presented here, which conforms to the top-down hierarchy of Nitros; shape grammar; and the text of the Yingzao fashi, as revealed in the naming of components and procedures, to name three possibilities.

Number of jumps (tiao)

This is, roughly speaking, the number of horizontal layers of components in the bracket set. It is related to the number of times the place-holding component "top" is elaborated into "top_and_bottom_sets."

Single vs. double arm (dan gong vs. chong gong)

This is the choice between elaborating the place-holding component "top" into "single_top_set" or "double_top_set."

"Stolen" vs. "accounted heart" (tou xin vs. ji xin)

This corresponds between elaborating the place-holding component "middle" into "tou_xin_middle_set" or "ji_xin_middle_set."