纵横弯曲桩计算的综合刚度和双参数法的有限差分解

 为提高外露段较长的桩在横向和竖向荷载共同作用下变形和内力的计算精度和效率，基于综合刚度原理和双参数法推导可考虑桩的纵横弯曲，即计及竖向荷载(包括桩顶竖向力及桩身自重和桩侧摩阻力)对弯曲变形影响的有限差分解，采用MATLAB程序语言编制相应的计算程序。与模型试验数据或现有方法工程实例计算结果的比较验证了该法的可靠性，同时还表明该方法比基于相同原理的杆系有限元法更方便快捷。研究结果表明：对于外露长度和桩顶竖向荷载较大的桩，重力二阶效应是不容忽视的，且竖向荷载不仅会增大桩身弯矩，还会导致桩身剪力的增大，现有方法未体现其对剪力的影响，是偏于不安全的，在纵横弯曲桩的设计计算中应引起重视。

Finite difference solution based on composite stiffness and bi-parameter method for calculating vertical and horizontal bending piles

To improve the accuracy and effectiveness in calculating the deformations and internal forces of piles with large exposure lengths under horizontal and vertical loads，a finite difference solution was established based on the composite stiffness principle and the bi-parameter method. A computation program was compiled by means of MATLAB. The reliability of this approach was verified through comparisons with the measured data from model tests or the calculated results of an engineering example with the existing methods. The comparisons showed that the approach was more convenient and faster than the link finite element method based on the same principle. It was also showed that，for piles with large exposure lengths under vertical loads，the gravity second-order effect must not be ignored and the vertical loads increased not only the bending moments of piles but also the shear forces. The influence of vertical loads on shear forces was not reflected in the current methods，which tended to be unsafe and should be noted in design calculations of vertical and horizontal bending piles.