*DUAN Jing-min1,2 , QIAN Yong-jiu3

Based on the minimum potential principle, three generalized displacement functions are applied to establish the governing differential equations of the U-shaped beams considering the shear deformation, shear lag effect and self-equilibrium condition for shear lag warping stress. Given corresponding natural boundary conditions, the closed-form solutions of generalized displacements are obtained. This paper proposes an approach to analyzing mechanical characteristics of U-shaped beams generally used in structure engineering, and the contribution of shear deformation, shear lag effect and self-equilibrium condition to the deflection and stress of the U-shaped beam is discussed. The calculation examples compare the finite element solutions with the analytical solutions and the validity of the proposed approach is verified.