Research On Application Of Transfer Matrix Method In Structural Analysis Of Steel Bridges

Transfer matrix method, a structural analysis method lying between force method and displacement method, can be applied to structural static, dynamic and stability analysis through the multiplication of matrixes by computer based on precise solution of the control differential equations of structure. This method with advantages of clear mechanical conception and high calculation precision can be conveniently programmed. Static structural analysis of steel bridges with this method is proposed in this paper. Taking Continuous beam bridge, circular arc bridge, skew box girder bridge and cable-stayed bridge as study samples, this method is employed to solve internal forces and displacement of the four categories of bridges respectively.Basic conceptions, expressions and calculation principle concerned are introduced by taking the analysis of an indeterminate beam with single span as an example and the feasibility of this method applied in static analysis of member structure is demonstrated.Considering the mechanic characteristics of the four types of steel bridges, detailed formulae of field transfer matrix and point matrix of each bridge are derived respectively. According to different boundary conditions, the boundary conditional and compatible expressions can be obtained and the solution of each bridge is carried out by recurrence calculation. Calculation examples show that the results obtained by this method agree with those obtained by matrix displacement method.To make the calculation model more actual, the factors of arbitrary load, arbitrary support and variable cross section have been considered. With this method the restrictions in calculating continuous beam can be overcome as well. In the analysis of steel circular arc bridge, the establishment of field transfer matrix is based on the precise solution of differential equations of circular arc element, which makes the calculation results more precise than that with matrix displacement method. What's more, circular arc bridge with variable cross section can be solved too. As for the establishment of the calculation model of steel skew box girder bridge, skew box bridge with arbitrary planar shape under arbitrary load is taken into full consideration, which conforms to the calculation of skew box bridges with variable cross section as well. The analysis of cable-stayed bridge is based on the planar mechanical model of cable-stayed bridge being transformed into continuous beam on the elastic supports. As a result, the solution to varieties of cable-stayed bridge with arbitrary span and support can be accomplished.The implementation of transfer matrix method on static structural analysis of steel bridges provides a convenient calculation method with high precision for large-scale bridges' preparatory design.