Analytical Solution for Piles Supporting Combined Lateral Loads

Analytical solutions of normalized maximum deflection and normalized maximum moment for laterally loaded long piles in homogeneous elastoplastic soil under combined loads are presented in this paper. Both the normalized deflection surface and normalized moment surface are continuous and increasing constantly with normalized applied force and moment with various slopes. It shows that the normalized applied force and moment have different contributions to the deflection and moment. In general, the variation of normalized moment surface is relatively moderate compared to normalized maximum deflection. Due to the nonlinear effect, the deflections and moments using superposition approach will be on the unsafe side. The analytical solutions can be used for any elastic materials, any type of soil, and any shapes of pile cross section. Above all, the analytical solutions may be easily applied to calculate the maximum deflection or moment of lateral long piles subject to combined loads accurately using a calculator.