Solution of Contact Problem for Supporting Node of Beam Hinged Plate

The paper considers a solution of contact problem for hinged supporting node of beam floor slab (coating). The main goal is to determine a stress state of the area where a plate rests on the wall. In this case, a number of problems are solved: construction of reactive pressure diagrams in the area of direct plate and wall contact, clarification of the calculated plate span, influence of contact zone size on a value of maximum bending moment in the middle of the plate, determination of contact area at various indices of flexibility and comparison of the obtained results with the known solution of rigid stamp and elastic quarter-plane interaction. The calculation has been carried out by the Zhemochkin method, its implementation for the given task corresponds to a mixed method of structural mechanics. As an illustration, the calculation has been performed on a concentrated load applied in the middle of the plate span. In the course of the study, it has been established that when a reinforced concrete slab rests on concrete and brick walls, the contact zone reduces itself to two Zhemochkin sections. When a flexibility index is decreased that corresponds to slab support on a less rigid base, the contact area is increased, and that, in its turn, has an influence on an increase of the calculated slab span and the bending moment in the middle of the slab. In the case of an absolutely rigid plate support (flexibility index is equal to zero), the contact stresses reach their maximum value at the point of plate edge contact and elastic quarter-plane. The nature of the diagram is confirmed by an analytical dependence of contact stress distribution obtained by Aleksandrov V. M. when solving a problem of pressing a rigid stamp into an edge of an elastic wedge.

1. Alexandrov V. M., Romalis B. L. (1986) Contact Problems in Mechanical Engineering. Moscow, Mashinostroyenie Publ. 176 (in Russian).

2. Alexandrov V. M., Pozharsky D. A. (1998) Nonclassical Spatial Mechanics Problems for Contact Interaction of Elastic Solids. Moscow, Faktorial Publ. 288 (in Russian).

3. Alexandrov V. M., Pozharsky D. A. (2006) Plane Contact Problem for Split Flexible Wedge. Izvestiya Vuzov. SeveroKavkazskii Region. Estestvennye Nauki University = News North-Caucasian Region Natural Sciences Series, (6), 27–30 (in Russian).

4. Bosakov S. V. (2002) Statistical Calculations of Plates on Elastic Foundation. Minsk, Belarusian National Technical University. 128 (in Russian).

5. Gorbunov-Posadov M. I., Malikova T. A., Solomin V. I. (1984) Calculation of Structures on Elastic Foundation. 3th ed. Moscow, Stroyizdat Publ. 680 (in Russian).

6. Zhemochkin B. N., Sinitsyn A. P. (1962) Practical Methods for Calculations of Foundation Beams and Plates on Elastic Foundation. 2nd ed. Moscow, Gosstroyizdat Publ. 240 (in Russian).

7. Klepikov S. N. (1967) Calculation of Structures on Elastic Foundation. Kiev, Budivelnik Publ. 184 (in Russian).

8. Korenev B. G. (1954) Calculation Problems for Beams and Plates on Elastic Foundation. Moscow, Gosstroyizdat Publ. 231 (in Russian).

9. Galin L. A. ed. (1976) Development of Theory for Contact Problem in the USSR. Moscow, Nauka Publ. 496 (in Russian).

10. Dmitrieva K. V. (2010) Contact Problem for Punch on Flexible Wedge with Free Edges. Vestnik BNTU, (4), 24–29 (in Russian).

11. Dmitrieva K. V. (2017) Calculation of Non-Linear-Elastic Flexible Wall in Elastic Foundation. Minsk, Belarusian National Technical University. 26 (in Russian).

12. Kulagina M. F., Ivanov E. G. (2009) Solution of First Main Problem of Elasticity Theory for Wedge in PowerLaw Series. Izvestiya Tul'skogo Gosudarstvennogo Universiteta = Izvestiya Tula State University, (2), 127–138 (in Russian).

13. Mitrofanov B. P. (1964) Action of Normal Concentrated Force on Elastic Rectangular Wedge of Infinite Extent. Izvestiya Tomskogo Politekhnicheskogo Instituta [Proceedings of Tomsk Polytechnical Institute], 114, 112–114 (in Russian).

14. Molchanov A. A., Pozharsky D. A. (2011) Generalization of the Galin Contact Problem and Punch Inter-Action. Vestnik Nizhegorodskogo Universiteta im. N. I. Lobachevskogo = Vestnik of Lobachevsky University of Nizhni Novgorod, (4–4), 1636–1638 (in Russian).

15. Pestrenin V. M., Pestrenina I. V., Landik L. V. (2014) Non-Standard Problems for Uniform Elements of Structures with Specific Features in the Form of Wedges under Conditions of Plane Problem. Vestnik Tomskogo Gosudarstvennogo Universiteta = Tomsk State University Journal, 27 (1), 95–109 (in Russian).

16. Pozharsky D. A., Lartseva N. A. (2007) On Stress Calculation in 3D-Flexible Wedge. Izvestiya Vuzov. SeveroKavkazskii Region. Estestvennye Nauki University = News North-Caucasian Region Natural Sciences Series, (2), 31–32 (in Russian).

17. Gersevanov Research Institute of Bases and Underground Structures (NIIOSP) of USSR State Committee for Construction (1985)Recommendations on Calculation of Settlement and Displacement of Rectangular Foundation on Wedge-Type Base. Moscow. 29 (in Russian).

18. Alexandrov A. V., Potapov V. D., Derzhavin B. P. (2000) Resistance of Materials. Moscow, Vysshaya Shkola Publ. 560 (in Russian).

19. TKP [Technical Code of Common Practice] EN 1992-1-1– 2009*. Eurocode 2. Designing of Reinforced Concrete Structures. Part 1-1. General Rules and Rules for Assignments. Minsk, Publishing House of Ministry of Architecture and Construction, 2010. 191 (in Russian).

20. Rak N. A., Danilenko I. V., Smekh V. I., Shcherbak S. B. (2012) Calculation and Designing of Assembled Reinforced Structures for Multi-Storey Half-Timbered Building. Minsk, Belarusian National Technical University. 96 (in Russian).

21. TKP [Technical Code of Common Practice] 45-1.03-314– 2018. Installation of Building Structures, Buildings and Facilities. Basic Requirements. Minsk, Publishing House of Ministry of Architecture and Construction, 2018. 124 (in Russian).