The Finite Segment Element Analysis Of Thin-walled Continuous Box Girder With Special Support

With the grate development of transportation, thin-walled box section beams getextensive application and development in bridge design because of its superiority of spacestructure; in order to fulfill the requirements of surrounding environment or cross–line,cross-interference of the road network is very common and the skew bridge type adopt moreand more. In the design of wide-box beam especially wide-flange beam, the shear lag effect isvery prominent and generate very serious negative impact on the bridge that attention must bepaid. Thus, although much research on shear lag effect of orthogonal thin-walled box beamhas been done by domestic and foreign scholars, it is rarely seen under the conditions of skew,box beam stress is more complicated and difficult to control in the design. In this paper, asystematic theoretical derivation is done for the flexural torsional analysis of thin-walledcontinuous box girder with special support, and combined with the finite element theory, amethod of the one-dimensional finite beam segment element on flexural torsional analysis ofthin-walled continuous box girder is proposed which is realistic and reliable in box girderanalytic theory.Firstly in the paper, the shear lag effect of box girder is considered on the basis of theelementary beam theory, the bending differential equations are established through rationallyselecting bending warping displacement mode of box girder and using the energy variationalprinciple; and under the influence of shear deformation, the restraint torsion differentialequations are established through considering constraint torsional warping displacement mode,the stress-strain relationship and structural equilibrium conditions; respectively solvinghomogeneous differential equation, the bending torsional displacement function of box girderis obtained. Then the integral constant as an intermediate variable is used to derive bendingand restrained torsion element stiffness matrix under the effect of shear lag, and thus totalstiffness matrix of bending and torsion is superimposed and assembled. According toreciprocal theorem of the principle of virtual work, unit load is equivalent to get rod endequivalent nodal force. Finally, considering the force characteristics under the special supportconditions of box girder, the nodal displacement and nodal force are converted intosupporting coordinate system from centroid coordinate system and torsion coordinate system,and the corresponding parameter expressions are obtained. Based on the above, thethin-walled box girder with special support is analyzed in the method of finite element, andultimately the finite element solution considering shear lag effect is acquired.According to the finite element analysis process, one-dimensional finite elementcomputing program of thin-walled box girder bending-torsion is worked out from theapplication of FORTRAN language, and its reliability and practical significance are verifiedby comparison with the test model and the ANSYS model. By the theoretical derivation and experimental modal analysis, the following importantconclusions can be drawn:①Shear lag effect is more obvious under special support conditions, and generally itis more prominent at the fulcrum cross section near the midspan than at the midspan section.②The trend of the shear lag moment diagram and the bending moment diagram isvery similar; but relatively the numerical value and the line shape are verydifferent.③As the skew angle increasing, the bending moment and shear lag momentdecreases, but the torsional warping bimoment increases and its local rapid attenuation isobvious.④Under eccentric load, the proportion of shear-lag moment in the overall force ofskew box girder is very high that can not be ignored in analysis.