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.