This paper firstly introduces "warping theory" presented in literature cite[1], then use it to solve a lot of examples.

Based on "warping theory", this paper primarily includes several parts of research below for open cross-section thin-walled components:(1)Basal hypotheses, fundamental concepts, essential tools, and practical calculation formulas of "warping theory" are briefly introduced, and its applications on complicated conditions such as varied-section beams are concretely illustrated by example.

Based on the three new supposition and the tow new mechanical tools: moment vector and radius vector , the warping theory introduced the analytical method of the rotation of a cross section around a fixed axis, so as to make the space stability of the thin-walled member complanate and one-dimensioned.

A series of warping shape functions is derived according to the successive corrective concept of warping based on the first warping theory, by which a high order warping theory for torsional analysis of composite thin walled beams with single cell closed section of arbitrary shape is prsented.