Abstract:
Considering the shear deformation effect of crossed foundation beams, and using the relationship between the load and deformation of an infinite length Timoshenko beam on Winkler foundation acted by a concentrated load and a moment, the cantilevering coefficients of a semi-infinite length Timoshenko beam on Winkler foundation acted by a concentrated load and a moment were derived. When the shear stiffness of a Timoshenko beam became into infinite, the cantilevering coefficients can be degenerated into those of an Euler beam without considering the shear deformation effect. Thus, the present formula was very general. The influence of shear deformation effect on the cantilevering coefficient of a concentrated load was great, and of concentrated moment was little. For those of the crossed foundations with dense nodes, large sectional dimensions, and sensitive to deflection, the shear deformation effect must be considered. According to static equilibrium conditions and deformation compatibility, the general formulae of nodal load distribution of a crossed foundation beam with cantilever were established, which can incorporate both the shear deformation effect and concentrated load & moment at the same time. Examples show that although the concentrated moment acted on the crossed foundation is small, but it can change the load distribution along the x, y axis. The larger of the concentrated moment, the more apparent of the influence. Considering the shear deformation effect, nodal load distribution becomes more uniform by calculations.