桩基承台梁受力分析的幂级数解答

Power series solutions force analysis of girder grillage supported by piles

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。

By treating the girder grillage supported by piles as a finite beam resting on an elastic foundation, regarding the vertical pile and the surrounding soil as springs with different rigidities, and with consideration of the interaction between the pile and the surrounding soil, a differential control equation for the capping beam is established on the base of the Winkler elastic foundation model. The semi analytical power series solutions for the vertical displacement, rotation, bending moment and shearing force of the capping beam under arbitrary loads such as concentrated load, added moment and distributed load are presented. The validity of the presented solutions is verified by the existing rigid-bar method and Newmark method. On the base of that, the influence factors such as the diversity of pile bearing capacity, the reaction of the surrounding soil, the diameter of pile and the load spreading properties on the behavior of the girder grillage supported by piles are discussed. The results indicate that the above factors significantly affect the behavior of the girder grillage supported by piles, with consideration of these above factors, the vertical deformation, bending moment and support reaction on the top of pile of the beam are different from that without consideration of these factors. So in the real engineering design of the capping pile beam, all those influence factors should be taken into account.