This article, by using mathematical expressions, offers a scientific framework for understanding how the grading system of Qing′s structural carpentry determines the design and construction in the grand style timber architecture.The Qing′s grand style timber structure, which is ready for prefabrication and assembly, is extremely hierarchical oriented and significantly standardized. The general procedure in designing a grand style timber structure is to start with the grade that defines the basic module (dou kou); next comes with the number of bracket set (cuan), the number of longitudinal bays and the number of purlins which affect its plan and cross section; thirdly choose a roof type that determines its longitudinal section and the facade as well. A series of formulae are conducted to help depict the layout, cross sectional roof curvature and special longitudinal treatments in 4 sloped and 9 spined roofs respectively.
The purpose of this paper is to explore the significance of Chinese invaded cities in the urban planning history through a comparative view of the modern urban planning theories and methodologies of Qingdao (Tsingtau) and those of the developed world from the late 19th century to mid 20th century. After reviewing the German Plan in 1898～1906 and the Japanese Plan in 1941, the paper concludes that the basis grounds of the urban planning practices in Qingdao between 1897～1945 were of the realistic physical planning, rather than of the commonly assumed utopian garden city. Therefore, Qingdao, once being a modern planning lab objectively, helped forward the theories and methodologies of the world′s modern urban planning between the late 19th century and mid 20th century.
