考虑纵向摩阻时弹性地基梁的弯曲

The bending of beam on the elastic foundation considering longitudinal frictional resistances

考虑地基纵向摩擦力的影响,建立了广义Winkler型地基梁的平衡方程.假定纵向摩擦力与梁底面的纵向位移成正比,引入广义剪力,得到梁的位移型平衡方程.将位移及荷载展开为带附加项的Fourier级数,利用平衡方程和边界条件对弹性地基梁的一般弯曲进行分析.分析表明,梁的位移和内力均受到纵向摩擦力的影响,并且随着纵向反力系数和梁截面高度的增大而增大;梁的最大挠度、转角、弯矩及剪力随着地基纵向反力系数的增大而减小;梁的轴向位移和轴力则随着地基纵向反力系数的增大而增大.

The equilibrium equations of beam on the general Winkler elastic foundation are established considering longitudinal friction.Assuming that the longitudinal friction is proportional to the beam’s base longitudinal displacement,the equations of equilibrium in the forms of displacement can be obtained after introducing ageneral shearing force.By expanding the displacements and loads to Fourier series with additional terms,the bending problems of elastic foundation beam are analyzed by using the equilibrium equations and boundary conditions.The results indicate that the beam’s displacements and internal forces are related to the longitudinal friction and the influences of friction are magnified with the longitudinal force coefficient and height of cross-section of beam.As the longitudinal force coefficient increased,the maximums of deflection,slope,bending moment and shear force decreased but the maximums of axial displacement and axial force increased.