Abstract：Research purposes: In this paper, the shear deformation and shear lag effect are considered comprehensively, and especially the self-equilibrium conditions for the shear lag warping stress and bending moment are introduced. Then the analytical solution of the vertical bending of trapezoidal U-shaped girder is obtained based on the energy variation method, the spatial mechanical behavior of U-shaped girder is studied in detail. And the validity of the analytical solution of this paper is verified by comparing with the numerical solution of finite element. Research conclusions:(1) Relative to the neutral axis(x-axis), since the transverse asymmetry of trapezoidal U-shaped girder is prominent, so commonly used traditional shear lag theory is difficult to truly reflect the mechanical mechanism of this kind of structure without the introduction of self-equilibrium conditions about shear warping stress and bending moment. (2) Compared with the commonly used traditional shear-lag theory, the shear lag effect of U-shaped girder has no coupling relationship with the elementary beam theory, and its calculation accuracy is significantly improved. (3) The shear lag effect not only affects the normal stress of the bottom slab of U-shaped girders, but also on its web, which cannot be ignored. (4) If the cross-sectional dimensions of U-shaped girder is determined, its shear lag stress contribution to web and bottom slab is not affected by the span. (5) The method in this paper is a guide for the design of trapezoidal U-shaped reinforcement and prestressing tendons, and this in turn will improve its durability.
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