SEMI-ANALYTIC SOLUTION FOR SHEAR LAG EFFECT OF CANTILEVER BOX GIRDERS WITH VARYING DEPTH

By using the free vibration mode of an Euler beam as Ritz base function, a new Ritz method is proposed to solve the set of shear lag differential equations of a varying depth box girder. Firstly, the modal analysis of a uniform cross-sectional Euler beam which is the same length and boundary condition with the box girder is carried out. The vertical deflection and the shear rotation of the box girder are expressed by the linear combination of the model and its derivative. And then the set of shear-lag differential equations of the box girder obtained by the calculus of variations are transformed into a set of linear algebraic equations. Then, the influences of the number of modes and variation ratio of section height on the errors are investigated. The numerical examples show that:the more significant the height of the box girder varies, the slower the Ritz method converges; but the results by Ritz method would converge to the analytic solution with the increasing of the number of modes. The errors of shear lag coefficients are less than 5%, when more than 12 of modes are included.