(1. Department of Civil Engineering of Tianjin Institute of Urban Constrution, Tianjin 300384, China; 2. School of Civil Engineering of Henan Polytechnic University, Jiaozuo, Henan 454000, China; 3. School of Civil Engineering of Southwest Jiaotong University, Chengdu 610031, China)
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.
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