Bending the Foundation Beam on Elastic Base by Two Reaction Coefficient of Winkler’s Subgrade

Abstract

A new method for analysis of counter beams is presented in the paper. The analysis has taken into account their stiffness EI, Winkler’s space with modulus of subgrade reaction k and equality deformities of the foundation beam with the ground. The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k 2 outside the force zone r , while under the force P exists the modulus of the subgrade reaction k , up to the definition of minimum bending moments. The exponential function k 2 (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 k 2 are explicitly determined, introducing in the calculation initial and calculation soil displacement w si successively. At the end of the paper, it presented numerical example in which the influence of k and k 2 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.