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 k2 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 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 are explicitly determined, introducing in the calculation initial and calculation soil displacement wsi successively. At the end of the paper, it presented 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.
Highlights
IntroductionThe second parameter introduced the interaction between adjacent springs, in addition to the first parameter from the ordinary Winkler’s model [15]
The solution is found by using the numerical analysis of the Winkler’s model, with variation of different moduli of the subgrade reaction k2 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 analysis is based on variational principles of mechanics and an approximate numerical-graphical solution, in which a rational soil-displacement field, influence zone r and subgrade reaction modulus k2 are obtained
Summary
The second parameter introduced the interaction between adjacent springs, in addition to the first parameter from the ordinary Winkler’s model [15]. This procedure is proposed in [13] for homogenous elastic semi space. The proposed model of soil has two soil characteristics, k (characterising displacement of the elastic base under pressure) and t (and describing behaviour of the subgrade during sliding and base “distribution properties”). In order to eliminated the bearing soil reaction as a variable in the problem solution of beam on elastic foundation, the simplified continuum. The change of k values does not significantly affect this difference
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