Analytical Solution And Engineering Application Of Shear Lag Effect Of Simply-supported Box Girders Under Multiple Concentrating Forces

Currently, it is mature to study the shear lag effect theory of simply supported box girder with single concentrated force, bending moment and uniform load. However, for the analysis of shear lag effect of simply supported box girder under multiple loads, the principle of superposition method is usually used to solve the problem. The analytical expressions of shear lag effect of box girder are deduced based on the combination of theoretical calculation and numerical simulation. The influence factors of shear lag effect of box girder are analyzed in this paper and the main contents and results are as follows:(1) Based on the principle of minimum potential energy and the principle of energy variational method, the analytic solution of shear lag effect under the combined action of multiple concentrated force, single concentrated force and uniform force and beam moment is deduced.(2) The control differential equation of simply supported box girder is deduced by energy variational method, the analytic solution of the shear lag effect of box girder under two and three concentrated forces is deduced by MATLAB and the analytical solution of shear lag effect is derived at a plurality of simple box girders concentrated force. Combined with the principle of superposition method, ANSYS finite element method and the analytic solution of this paper are used to compute the results of shear lag effect under two and three concentrated forces and the correctness of the analytical solution is verified.(3) Using energy variational principle, the differential equation of box girder control is established, the analytic solution of the shear lag effect of the simply supported box girder under the action of beam moment and uniform force, beam moment and single concentration force and uniform force and single concentration force are deduced. By analyzing the difference function coefficient of longitudinal displacement at a variety of individual loads and loads the interaction, give difference function coefficient of longitudinal displacement under the floor load more and the coefficients of the longitudinal displacement difference function are multiplied by the corresponding load,and all the results are summed. The longitudinal displacement difference function coefficient of box girder with bending moment,concentrated force and uniform force and expressions are obtained by this principle. The correctness of the analytical solution is verified by the superposition method.(4) Taking the simple box girder as an example, the effect of roof thickness, web thickness, cantilever length and height of box girder on shear lag effect of box girder is analyzed by finite element method and analytic solution. The results show that the variation of web and roof thickness has little effect on the shear lag effect of box girder; roof cantilever length changes on the greater influence on the shear lag coefficient on the cantilever; the shear lag coefficient for web and roof junction effect is not obvious; the variation of box girder height has a great influence on the shear lag effect of box girder and increasing the height of the box girder within a certain range can effectively reduce the shear lag effect of the roof.