| The section of tapered member changed forms close to moment diagram under load, its material distributes reasonable, shape is lightness and beauty. Because of it has advantages which is light-weight, the shape is artistic, the manufacture is convenient, construction quickly, dependable quality, construction capital pay-off quickly, tapered member developed rapidly in recent years in our country. There are many researches about tapered member domestic and overseas, but the limitation of majority researches is ultimate bearing capacity, rarely has the research in equivalent bending moment coefficient. Current specifications《Technical specification for steed structure of light-weight Buildings with gabled frames》about stability calculation of tapered rigid-frame-column reference to member of uniform section calculation formula. But in-plane equivalent bending moment coefficient only had to made stipulations to tapered rigid-frame-column with brace, made no stipulations to tapered rigid-frame-column without brace, this has brought inconvenience for the design and the engineering practice. Based on balance method and the theory of the finite element, equivalent bending moment coefficient of no sway rigid wedge variable cross-section frame column is further researched, obtaining some valuable achievements, which provide reference for engineering application and code revision. This paper achieves the main research results are as follows:(1) The paper derive theoretical solution of in-plane equivalent bending moment coefficient of tapered rigid-frame-column without brace under three kind of typical stress situations according to balance method and the mathematical computation software Maple.(2) With the single factor change's method, it has analyzed the factors in theoretical solution which influence in-plane equivalent bending moment coefficient, and has made nonlinear analysis to equivalent bending moment coefficient under considering initial geometric imperfection and residual stress of material by means large-scale general finite element software Ansys. It has verified theoretical solution of in-plane equivalent bending moment coefficient by nonlinear analysis results.(3) Calculated in-plane equivalent bending moment coefficient of tapered rigid-frame-column without brace under three kind of typical stress situations according to theoretical solution, and carried on the fitting to the massive calculation result by software Matlab, proposed a series practical calculation formula which provide guidance to engineering practice.(4) Combined with research result of equivalent bending moment coefficient governing code《Technical specification for steed structure of light-weight Buildings with gabled frames》, the stable ultimate load-carrying capacity in plane of no sway rigid wedge variable cross-section frame column is calculated, which is compared with ANSYS results. By comparison, the regulation results, which is smaller than the ANSYS result, is more secure and the reliable basis of design.
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