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将桩基承台梁视为置于弹性地基上的有限长梁,将竖向桩体及承台梁下桩间土体视为刚度不同的弹簧系列,基于Winkler弹性地基梁理论,推导出考虑桩土共同工作的承台梁竖向位移控制微分方程,并给出其幂级数半解析解,进而导得了在集中荷载、外加弯矩及分布荷载共同作用下桩基承台梁的竖向位移、转角、弯矩及剪力的计算公式。最后通过与链杆法、Newmark法的比较,验证了本文幂级数解答的正确性。在此基础上,探讨分析了基桩差异性、承台梁下土体作用、桩径及荷载形式等因素对桩基承台梁受力变形的影响。研究表明:当考虑上述因素影响时,桩基承台梁的竖向变形、弯矩及桩顶反力均发生不同程度的变化,因此,在实际的设计计算中应予以考虑。
Considering the pile foundation girder as a finite long beam placed on the elastic foundation, the soil between the vertical pile and the pile under the caisson girder is regarded as a series of springs with different rigidities. Based on the Winkler elastic foundation beam theory, The vertical displacement control differential equations of pile cap girder and pile soil working together are presented, and the semi-analytical solutions of power series are given. Then, under the combined action of concentrated load, applied bending moment and distributed load, the vertical Displacement, corner, bending moment and shear formula. Finally, through the comparison with the chain method and the Newmark method, the correctness of the power series solution in this paper is verified. On this basis, the paper analyzes the influence of pile foundation difference, foundation soil under pile cap, pile diameter and load form on the bearing deformation of pile foundation. The results show that when considering the above factors, the vertical deformation, bending moment and pile top reaction of the pile cap platform girder vary in varying degrees. Therefore, it should be considered in the actual design and calculation.