# THE NEW HYPOTHESIS ANGULAR DEFORMATION AND FILLING OF DIAGRAMS IN BENDING WITH TORSION IN REINFORCED CONCRETE STRUCTURES

### Abstract

*The authors considered a simple method for constructing bend-torsion functionals by grid methods. ** **Analysis of the diagrams of angular deformations and shear stresses made it possible to develop a new hypothesis of angular deformations. The consequences of the hypothesis were in the form of expressions from the analysis of diagrams.* *The authors also obtained functionals for determining angular deformations, bending and torque moments from the compressed area of concrete and reinforcement. The projection ratios helped to determine the shear and normal stresses through deformations using diagrams. The filling of the diagrams was in the form of expressions using functionals.* *The authors recorded expressions for determining the filling of the diagrams, as well as the total bending and torque moments**.*

### References

2. Lessig N.N., Rullay L.K. (1972). General principles for calculating the torsional flexural strength of reinforced concrete bars. Theory of reinforced concrete dedicated to the 75th anniversary of the birth of A.A. Gvozdev, p.43-49.

3. Zalesov A.S., Khozyainov B.P. (1991). Strength of reinforced concrete elements in torsion and bending. Proceedings of universities in chapter Construction and architecture, no. 1, p.1-4.

4. Arzamastsev S.A., Rodevich V.V. (2015). To the calculation of reinforced concrete elements for bending with torsion. Proceedings of higher educational institutions. Building, vol. 681. no. 9, p. 99-109.

5. Ilker Kalkan, Saruhan Kartal. (2017). Torsional Rigidities of Reinforced Concrete Beams Subjected to Elastic Lateral Torsional Buckling. International Journal of Civil and Environmental Engineering, vol. 11, no.7, p. 969-972.

6. G. Klein, G. Lucier, S. Rizkalla, P. Zia and H. Gleich. (2013) Torsion simplified: a failure plane model for design of spandrel beams. ACI Concrete International Journal, p. 1-19

7. Karpenko N.I. (1970). Determination of deformations of rod-shaped reinforced concrete box-shaped elements with torsional cracks. Cross-sectoral construction issues. "Domestic Experience", no. 10, p. 39-42

8. Karpenko N.I., Elagin E.G. (1970). Deformations of reinforced concrete tubular elements subjected to torsion after cracking. Concrete and reinforced concrete, no. 3, p. 3-12.

9. Karpenko N.I. (1972). To the calculation of deformations of reinforced concrete rods with cracks in bending with torsion. Theory of reinforced concrete dedicated to the 75th anniversary of the birth of A.A. Gvozdev, p. 50-59.

10. Karpenko N.I. (1976). The theory of deformation of reinforced concrete with cracks. Stroyizdat, Moscow.

11. Karpenko N.I. (1996). General models of reinforced concrete mechanics. Stroyizdat, Moscow.

12. Travush V.I., Karpenko N.I., Kolchunov V.I., Kaprielov S.S., Demyanov A.I., Konorev A.V. (2018) The results of experimental studies of structures square and box sections in torsion with bending. Building and Reconstruction, vol. 80, no. 6, p. 32-43.

13. Travush V.I., Karpenko N.I., Kolchunov Vl. I., Kaprielov S.S., Demyanov A.I., Bulkin S.A., Moskovtseva V.S. (2020). Results of experimental studies of high-strength fiber reinforced concrete beams with round cross-sections under combined bending and torsion. Structural mechanics of engineering structures and structures, vol. 16, no. 4. p. 290-297, DOI:10.22363/1815-5235-2020-16-4-290-297.

14. Travush V.I., Karpenko N.I., Kolchunov Vl. I., Kaprielov S.S., Demyanov A.I., Konorev A.V. (2019). Main results of experimental studies of reinforced concrete structures of high-strength concrete b100 round and circular cross sections in torsion with bending. Structural Mechanics of Engineering Constructions and Buildings, vol. 15, no. 1. p. 51-61. DOI:10.22363/1815-5235-2019-15-1-51-61

15. Demyanov A.I., Salnikov A.S., Kolchunov Vl. I. (2017). The experimental studies of reinforced concrete constructions in torsion with bending and the analysis of their results. Building and Reconstruction, vol. 72, no. 4, p. 17–26.

16. Demyanov A.I., Kolchunov V.I., Pokusaev A.A. (2017). Experimental studies of the deformation of reinforced concrete structures during torsion with bending. Structural Mechanics of Engineering Constructions and Buildings, no. 6, p. 37–44, DOI:10.22363/1815-5235-2017-6-37-44

17. Kolchunov V.I., Kolchunov Vl. I., Fedorova N.V. (2018). Deformation models of reinforced concrete under special influences. Industrial and civil construction, no. 8, p. 54-60.

18. Kolchunov Vl. I., Fedorov V.S. (2020). Conceptual Hierarchy of Models in the Theory of Resistance of Building Structures. Industrial and Civil Engineering, no. 8. p. 16–23, DOI: 10.33622 / 0869-7019.2020.08.16-23.

19. Fedorov, V. S., Kolchunov Vl. I., Pokusaev A.A., Naumov N.V. (2019). Design models of deformation of reinforced concrete structures with spatial cracks. Scientific journal of construction and architecture, vol. 56, no. 4, p. 11-28.

20. Bondarenko V.М., Kolchunov V.I. (2004). Design models of the power resistance of reinforced concrete. Publishing house ABC, Moscow.

21. Velyuzhsky Yu.V., Golyshev A.B., Kolchunov Vl.I., Klyueva N.V., Lisitsin B.M., Mashkov I.L., Yakovenko I.A. (2014). A reference guide to structural mechanics. Volume II. Publishing house ABC, Moscow.

22. Timoshenko SP, Goodyer J. Theory of elasticity. - M .: Nauka, 1975 .- 576 p.