Shear lag analysis of thin-walled box girders based on a new generalized displacement

In many papers about the shear lag analysis of thin-walled box girders, the maximum angular rotation attributable to the in-plane shear deformation of flanges is adopted as generalized displacement. However, the generalized displacement is not very simple and clear and the analytical procedure is relatively complicated. Moreover, various types of warping displacement function for shear lag were assumed which may cause some confusion. In this paper, a new method for analyzing shear lag effect in thin-walled box girders is proposed in which the additional deflection induced by shear lag effect is adopted as the generalized displacement. Based on the generalized moment 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 quadratic parabola is demonstrated to be the reasonable curve of the warping displacement function in the shear lag effect analysis of a box girder and the accuracy of the degrees of the warping functions is evaluated. The so-called negative shear lag is illustrated through the generalized moment. The governing differential equation and the 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 provided. A very simple and convenient formula of the shear lag warping stress is proposed which has the same form as that of the bending stress of elementary beam. A finite beam segment element with 8 degrees of freedom is developed to analyze the shear lag effect in complex continuous box girders with varying depth. Two plexiglass models of continuous box girders are analyzed and the calculated results are in agreement with the test results, which validates the analytical method and the element presented.