Shear Lag Analysis of Thin-Walled Box Girders Adopting Additional Deflection as Generalized Displacement

Abstract

The shear lag effect is one of the very important mechanical characteristics of thin-walled box girders and has been studied over several decades. However, the generalized displacement adopted in many papers is not very simple or clear, and the analytical procedure is somewhat complicated. In this paper, a new method for analyzing the shear lag effect in thin-walled box girders is proposed in which the additional deflection induced by the shear lag effect is adopted as a generalized displacement to describe the shear lag deformation state. Based on the generalized moment for shear lag defined in this paper, the shear lag deformation state is separated from the flexural deformation state of the corresponding elementary beam and analyzed as a fundamental deformation state. The governing differential equation and boundary condition for the additional deflection are established by applying the principle of minimum potential energy, and the initial parameter solution to the differential equation is given. A very simple and convenient formula of shear lag warping stress is proposed that has the same form as that of the bending stress of the elementary beam. A finite beam segment element with eight degrees of freedom is developed to analyze the shear lag effect in complex continuous box girders with varying depth. An example of a simply supported concrete box girder is provided in which the results obtained by the present method are compared with those by FEM, finite-strip method, and other existing analytic methods. A three-span continuous box-girder model with varying depth is also analyzed, and the calculated results are in a good agreement with the test results on the whole, which validates the analytical method and the element presented.