剪切变形对基桩P-Δ效应的影响
P-Δ effect analysis of pile and bearing with shear deformation

给出了小剪切变形下的基桩P-Δ效应和大剪切变形下支座P-Δ效应计算的杆单元刚度矩阵方程。假定杆单元弯曲变形位移函数为三次幂函数，剪切变形函数为线性函数，根据有限元法一般原理，推导了一种同时计入竖向力径向剪切分力剪切变形和水平力剪切变形的P-Δ效应杆单元刚度方程，推导了一种仅计入竖向力径向剪切分力剪切变形而忽略水平力剪切变形的P-Δ效应杆单元刚度方程，推导了一种仅计入水平力剪切变形而忽略竖向力径向剪切分力剪切变形的P-Δ效应杆单元刚度方程。计入水平力剪切变形而忽略竖向力径向剪切分力剪切变形的P-Δ效应杆单元可良好的模拟支座在大剪切变形下的偏心工作特性，能实时计入其偏心弯矩影响，为实时计入支座偏心特性的结构动静力分析提供了理论支撑。最后通过自编MATLAB程序进行算例分析，结果表明，计入支座大剪切变下的P-Δ效应后，基桩内力位移和地基土压力均显著增大。基桩自身剪切变形对桩身内力位移和地基土压力影响较小，可以忽略。
Finite pole element method is presented for P-Δ effect analysis of pile and bearing while shear deformation is well considered. It is assumed that horizontal displacement of the pole element has a longitudinally cubic power function and the shear displacement has a longitudinally linear function, the P-Δ effect pole element rigid equation considering the shear deformation produced by lateral load and the radial component of vertical load, is derived. The P-Δ effect pole element rigid equation considering the shear deformation only produced by lateral load is derived in the paper. The P-Δ effect pole element rigid equation considering the shear deformation only produced by the radial component of vertical load, is derived in the paper. And the P-Δ effect pole element considering the shear deformation only produced by lateral load can simulate the bearing working eccentrically well in real-time. Matlab process of finite pole element method for P-Δ effect analysis of pile and bearing is edited, and case analysis is done, and the theory and the method is proved good. Finally conclusions are drawn as follows:(i) the P-Δ effect analysis result of pile will increase obviously while the eccentric bending moment of the bearing is well considered; (ii) the deformation has little effect on the P-Δ effect analysis result of the pile and bearing.