Shear lag and transverse shear in beams have been studied separately so far. The research on shear lag has taken cross-sectional deformation into account since its early stage. On the other hand, most of the research on transverse shear has devoted itself to determine the shear correction factor and has rarely considered the cross-sectional deformation. The authors have developed a beam theory that explicitly takes into account the cross-sectional deformation of transverse shear. On the basis of this theory, this paper proposes a beam theory that can take into account the cross-sectional deformations due to shear lag and transverse shear in a unified manner. A numerical method for determining the cross-sectional parameters required for the proposed beam theory is presented and comparison of solutions of the proposed theory with finite element solutions using continuum elements confirms the validity of the proposed beam theory.

 The finite element method (FEM) is commonly used to verify seismic performance in the design of various facilities, such as buildings with pile foundations and sheet pile quay walls in Japan. It is very important to conduct validation and verification of numerical analysis. Although validations of numerical analysis is usually conducted, it is very difficult to conduct verification of non-linear problem. We did verification of modeling of pile end resistance by using FLIP ROSE. We conducted the simulation of monotonic loading test and cyclic loading test of a pile. The pile penetration was represented as the enforced displacement and the enforced load at the pile head nodes. The load-settlement relationship of enforced displacement did not agree with that of enforced load when the effective confining pressure of ground elements at the pile tip goes zero. However, when the ground nodal points within the pile diameter are constrained not to occur tensile stress, the load-settlement relationship of enforced displacement agreed well with that of enforced load. Finally, we could confirm the verification of modeling of pile end resistance using FLIP ROSE.