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基于传统文克尔弹性地基梁理论,考虑梁土间的摩阻效应、梁的纵横向变形耦合及变形的几何非线性,建立出相应的弹性地基梁挠曲变形控制微分方程。引入Galerkin法,导出了对称荷载作用下有限长梁的挠曲变形、转角、剪力及弯矩的非线性解析解。在此基础上,分析探讨了外加荷载、地基梁刚度、梁与土体之间的水平摩阻力、竖向地基反力系数等因素对地基梁位移及内力的影响。分析结果表明:水平摩阻力并不影响地基梁位移及内力的整体变化发展趋势,但将导致地基梁位移及内力值的降低,且水平摩阻力越大,其对地基梁位移及内力的影响也就越大,此外,当地基梁抗弯刚度越大,水平摩阻力对梁位移及内力的影响反而越小。
Based on the traditional Wenkell elastic foundation beam theory, considering the friction effect between the beam and the soil, the coupling between the longitudinal and transverse deformation of the beam and the geometric nonlinearity of the deformation, a corresponding governing differential equation for the deflection of the elastic foundation beam is established. The Galerkin method is introduced to derive the nonlinear analytical solutions of the flexural deformation, corner, shear and moment of a finite length beam under the symmetrical load. On this basis, the influences of external load, stiffness of foundation beam, horizontal friction between beam and soil, vertical reaction coefficient of foundation and other factors on displacement and internal force of foundation beam are analyzed. The results show that the horizontal frictional resistance does not affect the trend of overall displacement of foundation girder and internal force, but it will lead to the displacement of foundation girder and the decrease of internal force, and the greater the horizontal frictional resistance, the greater the effect on the displacement and internal force of foundation girder The greater the flexural rigidity of the local girder, the smaller the influence of the horizontal frictional resistance on beam displacement and internal force.