Improvement of Calculation Technique for Flexible Orthotropic Plates on Elastic Base. Part 2. Calculation Results

The proposed paper is a continuation of the author's theoretical work presented earlier in the development of the theory and methodology for calculating flexible orthotropic reinforced concrete plates on an elastic foundation, taking into account the physical nonlinearity of the plate material. The paper presents numerical results of elastic and nonlinear calculations of an isolated rectangular orthotropic plate on an elastic foundation, modeled by an elastic homogeneous isotropic layer rigidly connected to a non-deformable foundation under the action of an external static load, taking into account the own weight of the reinforced concrete plate. The change in its stiffness at the time of cracking and further active opening of cracks has been taken into account in the calculation of the structure under study. The nonlinear calculation of the studied structure takes into account the change in its rigidity at the time of cracking and further active crack opening. The calculation of a flexible orthotropic plate on an elastic foundation in a nonlinear formulation is performed iteratively by the method of B. N. Zhemochkin. A mixed method of structural mechanics has been used to determine the coefficients of canonical equations and free terms. At the first iteration, the reinforced concrete plate is calculated as linearly elastic, homogeneous, and orthotropic; at the subsequent ones – as linearly elastic, inhomogeneous, and orthotropic at each Zhemochkin site. Camber plates with a clamped normal in the primary system of mixed method due to the action of a concentrated force are determined by the Ritz method when the deflections were represented as a power polynomial in a new original expression that has been proposed for the first time in the Part 1 of the paper. The solution algorithm has been implemented using the Wolfram Mathematica 11.3 computer program. Numerical and graphical results of elastic and non-linear calculations of sediment concrete road plate, contact stresses and bending moment diagrams on the plate are presented in the paper.

1. Kozunova O. V. (2022) Improvement of Calculation Technique for Flexible Orthotropic Plates on Elastic Base. Part 1: Calculation Theory. Nauka i Tekhnika = Science & Technique, 21 (3), 211–221. https://doi.org/10.21122/2227-1031-2022-21-3-211-221 (in Russian).

2. Alexandrov A. V., Potapov V. D. (2002) Fundamentals of the Theory of Elasticity and Plasticity. 2nd еd. Moscow, Vysshaya Shkola Publ. 400 (in Russian).

3. Rzhanitsyn R. A. (1991) Structural Mechanics. Moscow, Vysshaya Shkola Publ. 439 (in Russian).

4. Zhemochkin B. N., Sinitsyn A. P. (1962) Practical Methods for Calculating Foundation Beams and Slabs on an Elastic Foundation. 2nd еd. Moscow, Gosstroiizdat Publ. 240 (in Russian).

5. Solomin V. I., Shmatkov S. B. (1986) Calculation Methods and Optimal Design of Reinforced Concrete Foundation Structures. Moscow, Gosstroiizdat Publ. 208 (in Russian).

6. Bosakov S. V. (2002) Static Calculations of Slabs on an Elastic Foundation. Minsk, Belarusian National Technical University. 128 (in Russian).

7. Bosakov S. V. (2006) The Ritz Method in Contact Problems of Elasticity Theory. Brest, Brest State Technical University. 107 (in Russian).

8. SP [Construction Rules 52-103–2007]. Code of Practice for Design and Construction. Reinforced Concrete Monolithic Structures of Buildings. Moscow, Research and Development Center “Construction” – Scientific Research, Design and Technological Institute of Concrete and Reinforced Concrete named after A. A. Gvozdev, 2007. 22 (in Russian).

9. SP [Construction Rules] 63.13330.2018. Code of Practice. Concrete and Reinforced Concrete Structures. Basic Provisions. Moscow, Research and Development Center “Construction” – Scientific Research, Design and Technological Institute of Concrete and Reinforced Concrete named after A. A. Gvozdev, 2018. 168 (in Russian).

10. Guidance Manual. Flat Beamless Reinforced Concrete Floors. Design Rules. Moscow, Research and Development Center “Construction” – Scientific Research, Design and Technological Institute of Concrete and Reinforced Concrete named after A. A. Gvozdev, 2017. 158 (in Russian).

11. Gorbunov-Posadov M. I., Malikova T. A., Solomin V. I. (1984) Calculation of Structures on an Elastic Foundation. 3rd еd. Moscow, Stroiizdat Publ. 680 (in Russian).