Development of the Theory of Computation of Pivotally-Connected Beams on an Elastic Foundation Taking into Account Their Physical Nonlinearity

https://doi.org/10.35579/2076-6033-2019-11-01

ABSTRACT

This work presents a brief review of the literature on the theory and technique of computation of pivotally-connected structures on a linearly-elastic foundation. The authors refer to the works of B.G.Korenev, G.Ya.Popov, I.A.Simvulidi, R.V.Serebryany and A.G.Yuryev, in which investigations for calculating the pivotally-connected beams and slabs on an elastic foundation are performed using different approaches.

From the analysis of the scientific and normative literature on the subject under consideration, a conclusion can be made that there is no common approach to solution of this problem, which would hold for any pivotally connected structures being in contact with any elastic foundation model under the action of an arbitrary external load.

Besides, when designing the load carrying members of pavements of motor roads of various purposes in the Republic of Belarus, a number of branch-specific normative documents, where the pavements with the load carrying member and interconnection of members over the track length are considered separately in unconnected setting, is used.

In this work, a universal approach for computation of pivotally-connected beams on an elastic foundation in the linear setting and taking into account the physical nonlinearity of the beam material is proposed. This approach is based on a mixed method of structural mechanics and implemented in different foundations taking into account the Zhemochkin’s relations for the functions of influences of an elastic medium.

The following hypotheses and assumptions of the linear theory of elasticity and structural mechanics are taken into consideration: only normal stresses act at the contact of the beam with the foundation; for beams the hypotheses of the flexural theory; the pivot joints are cylindrical and the distribution of the contact stresses over the beam width is uniform.

The physical nonlinearity of the beam material is taken into consideration through the variable rigidity of the Zhemochkin’s areas. Namely: after determining the forces in the Zhemochkin’s bonds at the contact of every beam with an elastic foundation as a result of the linear computation, the values of bending moments in each section of every beam are determined by the structural mechanics methods. From the calculated values of the moments, the tangential rigidity for each Zhemochkin’s area on the beam is determined using the formula of the “moment-curvature” dependence for the beam sections are determines as hyperbolic tangent.

In the results of nonlinear computation, the stress-strain behaviour of the system of pivotally-connected beams on an elastic foundation is investigated as it was made earlier in the linear setting: distribution of contact stresses under the beams, internal forces in the beams and pivot joints as well as elastic foundation settlements.

The proposed approach is implemented numerically with the use of the Mathematica 10.4 mathematical package. The computation example for three pivotally-connected beams on the Winkler foundation taking into account their physical nonlinearity.

Keywords: pivotally-connected beams, mixed method, Zhemochkin’s bonds, Winkler foundation, nonlinear computation, “moment curvature” dependence, contact tension, elastic foundation settlements.

For citation: Bosakov S., Kozunova O. Development of the Theory of Computation of Pivotally-Connected Beams on an Elastic Foundation Taking into Account Their Physical Nonlinearity. Contemporary Issues of Concrete and Reinforced Concrete: Collected Research Papers. Minsk. Institute BelNIIS. Vol. 11. 2019. pp. 11–24.

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