Bending the Foundation Beam on an Elastic base by Two Winkler's Subgrade Reaction Coefficients

A new method for analysis of counter beams is presented in This chapter. Beam on elastic foundation have been analysed, most usually, based on the Winkler’s model in which the soil is replaced by a bed of elastic springs. The compressive resistance of soil against the beam deflection is quantified in terms of spring constant k [force/length2/length], which is a frequent occurrence in the Euler-Bernoulli beam theory. The stiffness EI, Winkler's space with modulus of subgrade reaction k, and equality deformities of the foundation beam with the ground were all considered in the analysis. The solution is discovered through numerical analysis of the Winkler's model, with variation of different moduli of the subgrade reaction k2 outside the force zone r, while the modulus of the subgrade reaction k exists under the force P, up to the definition of minimum bending moments. The exponential function k2(r), as the geometric position of the minimum moments is approximately assumed. From the potential energy conditions of the reciprocity of displacement and reaction, the width of the zone r and the modulus of the subgrade reaction k2 is explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. It is well-known that the error in shear force and moment distribution can become significant in the case of foundation beams with small length-to-depth ratio subjected to closely spaced discrete column loads, as well as in the case of flanged beams and beams with sandwich-like cross-section. It is concluded that numerical example in which the influence of k and k2 values on bending moments of the counter beam is analyzed. The essential idea of this paper is to decrease the quantity of the reinforcement in the foundations, beams, i.e. to obtain a cost-efficient foundation construction.