DOI: https://doi.org/10.15587/1729-4061.2019.155469

### Construction of an algorithm for the selection of rigid stops in steel concrete beams

Anatoliy Petrov, Mykhailo Pavliuchenkov, Alexander Nanka, Andriy Paliy

#### Abstract

Calculation of steel-concrete beams is performed with a rigid connection between concrete and a steel strip. This is possible if one installs hard stops that prevent the displacement of the strip with respect to concrete. The force acting on the stop, the number of hard stops and their pitch, are determined through the rotation angles between two adjacent stops. To determine the efforts that act on hard stops, as well as a step, one must first find a rotation angle between two cross-sections within the beams. The rotation angles of cross-sections are derived using a graph-analytical method. Calculation for the deformations of reinforced-concrete and steel-concrete beams is performed based on the reduced rigidities of cross-sections.

When one chooses a step for hard stops and their number, it is necessary to strive for the optimization of a structure of steel-concrete beams. Optimization implies that the maximum stresses in a steel strip are equal to its limiting value while the effort acting in stops, and the step of stops, are the same. In order for the efforts in each stop to be the same, one must fabricate a zero section less than the others.

In the course of our study we have developed an algorithm for selecting the number, a step of hard stops, and the efforts in them. The choice is based on the assigned characteristics of materials used, the acting external load, the length of a beam, known size of the cross-section of concrete and a steel strip. In this case, efforts in all stops are identical, the step of stops is constant except for the zero section, maximum effort in the steel strip, occurring in the middle of the span, does not exceed the boundary value obtained in the calculation. The reported algorithm makes it possible to calculate hard stops at the assigned value for efforts that act on them under existing load

#### Keywords

steel-concrete beam; hard stop; step between stops; effort in a stop; steel sheet; reduced rigidity; graph-analytical method

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#### References

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TKP EN 1994-1-1-2009 (02250). Evrokod 4: Proektirovanie stalezhelezobetonnyh konstrukciy. Ch. 1-1. Obshchie pravila i pravila dlya zdaniy (2010). Minsk: Minstroyarhitektury, 95.

DSTU B V.2.6-216:2016. Rozrakhunok i konstruiuvannia ziednuvalnykh elementiv stale zalizobetonnykh konstruktsiy (2016). Kyiv, 40.

Hsiao, P.-C., Lehman, D. E., Roeder, C. W. (2012). Improved analytical model for special concentrically braced frames. Journal of Constructional Steel Research, 73, 80–94. doi: https://doi.org/10.1016/j.jcsr.2012.01.010

Mahmoud, A. M. (2016). Finite element modeling of steel concrete beam considering double composite action. Ain Shams Engineering Journal, 7 (1), 73–88. doi: https://doi.org/10.1016/j.asej.2015.03.012

Luan, N. K., Bakhshi, H., Ronagh, H. R., Barkhordari, M. A. (2011). Analytical solutions for the in-plane behavior of composite steel/concrete beams with partial shear interaction. Asian Journal of Civil Engineering, 12 (6), 751–771.

Medvedev, V. N., Semeniuk, S. D. (2016). Durability and deformability of braced bending elements with external sheet reinforcement. Magazine of Civil Engineering, 3, 3–15. doi: https://doi.org/10.5862/mce.63.1

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Bobalo, T. V., Blikharskyi, Z. Ya., Ilnytskyi, B. M., Kramarchuk, A. P. (2011). Osoblyvosti roboty stalebetonnykh balok armovanykh sterzhnevoiu vysokomitsnoiu armaturoiu riznykh klasiv. Visnyk NU «Lvivska politekhnika», 697, 35–48.

Vahnenko, P. F., Hilobok, V. G., Andreyko, N. T., Yarovoy, M. L. (1987). Raschet i konstruirovanie chastey zhilyh i obshchestvennyh zdaniy. Kyiv, 423.

Petrov, A. N., Kobzeva, E. N., Krasyuk, A. G. (2015). Vybor optimal'nyh po stoimosti parametrov stalebetonnyh balok. Materialy III mizhnarodnoi naukovo-praktychnoi konferentsiyi. Kharkiv-Krasnyi Lyman, 330–336.

Darkov, A. V., Shpiro, G. S. (1975). Soprotivlenie materialov. Moscow: Vysshaya shkola, 654.

Kruhmalev, A. V. (2010). The strainstress state of steel reinforced concrete beams. Vestnik DNUZHT: Nauka i progress transporta, 143–145.

#### GOST Style Citations

Experimental and numerical study on static behavior of elastic concrete-steel composite beams / Xing Y., Han Q., Xu J., Guo Q., Wang Y. // Journal of Constructional Steel Research. 2016. Vol. 123. P. 79–92. doi: https://doi.org/10.1016/j.jcsr.2016.04.023

Sudhir P. P., Keshav K. S. Tests of steel fibre reinforced concrete beams under predominant torsion // Journal of Building Engineering. 2016. Vol. 6. Р. 157–162. doi: https://doi.org/10.1016/j.jobe.2016.02.004

DBN V.2.6-160:2010. Stalezalizobetonni konstruktsiyi. Kyiv: Minrehionbud Ukrainy, 2011. 93 p.

TKP EN 1994-1-1-2009 (02250). Evrokod 4: Proektirovanie stalezhelezobetonnyh konstrukciy. Ch. 1-1. Obshchie pravila i pravila dlya zdaniy. Minsk: Minstroyarhitektury, 2010. 95 p.

DSTU B V.2.6-216:2016. Rozrakhunok i konstruiuvannia ziednuvalnykh elementiv stale zalizobetonnykh konstruktsiy. Kyiv, 2016. 40 p.

Hsiao P.-C., Lehman D. E., Roeder C. W. Improved analytical model for special concentrically braced frames // Journal of Constructional Steel Research. 2012. Vol. 73. P. 80–94. doi: https://doi.org/10.1016/j.jcsr.2012.01.010

Mahmoud A. M. Finite element modeling of steel concrete beam considering double composite action // Ain Shams Engineering Journal. 2016. Vol. 7, Issue 1. P. 73–88. doi: https://doi.org/10.1016/j.asej.2015.03.012

Analytical solutions for the in-plane behavior of composite steel/concrete beams with partial shear interaction / Luan N. K., Bakhshi H., Ronagh H. R., Barkhordari M. A. // Asian Journal of Civil Engineering. 2011. Vol. 12, Issue 6. P. 751–771.

Medvedev V. N., Semeniuk S. D. Durability and deformability of braced bending elements with external sheet reinforcement // Magazine of Civil Engineering. 2016. Issue 3. P. 3–15. doi: https://doi.org/10.5862/mce.63.1

Zamaliev F. S. Numerical and full-scale experiments of prestressed hybrid reinforced concrete-steel beams // Vestnik MGSU. 2018. Vol. 13, Issue 3. P. 309–321. doi: https://doi.org/10.22227/1997-0935.2018.3.309-321

Rahmanov A. D., Solov'ev N. P., Pozdeev V. M. Computer modeling for investigating the stress-strainstate of beams with hybrid reinforcement // Vestnik MGSU. 2014. Issue 1. P. 187–195.

Utkin V. A. Regulirovanie polozheniya neytral'noy osi pri proektirovanii secheniy stalezhelezobetonnyh balok // Vestnik SibADI. 2010. Issue 4 (18). P. 55–60.

Storozhenko L. I., Lapenko O. I., Horb O. H. Konstruktsiyi zalizobetonnykh perekryttiv po profilnomu nastylu iz zabezpechenniam sumisnoi roboty betonu i stali za dopomohoiu skleiuvannia // Visnyk NU «Lvivska politekhnika». 2010. Issue 662. P. 360–365.

Mel'man V. A., Torkatyuk V. I., Zolotova N. M. Ispol'zovanie akrilovyh kleev dlya soedineniya betonnyh i zhelezobetonnyh konstrukciy // Kommunal'noe hozyaystvo gorodov. 2003. Issue 51. P. 61–68.

Storozhenko L. I., Krupchenko O. A. Stalezalizobetonni balky iz zalizobetonnym verkhnim poiasom // Visnyk NU «Lvivska politekhnika». 2010. Issue 662. P. 354–360.

Osoblyvosti roboty stalebetonnykh balok armovanykh sterzhnevoiu vysokomitsnoiu armaturoiu riznykh klasiv / Bobalo T. V., Blikharskyi Z. Ya., Ilnytskyi B. M., Kramarchuk A. P. // Visnyk NU «Lvivska politekhnika». 2011. Issue 697. P. 35–48.

Raschet i konstruirovanie chastey zhilyh i obshchestvennyh zdaniy / Vahnenko P. F., Hilobok V. G., Andreyko N. T., Yarovoy M. L. Kyiv, 1987. 423 p.

Petrov A. N., Kobzeva E. N., Krasyuk A. G. Vybor optimal'nyh po stoimosti parametrov stalebetonnyh balok // Materialy III mizhnarodnoi naukovo-praktychnoi konferentsiyi. Kharkiv-Krasnyi Lyman, 2015. P. 330–336.

Darkov A. V., Shpiro G. S. Soprotivlenie materialov. Moscow: Vysshaya shkola, 1975. 654 p.

Kruhmalev A. V. The strainstress state of steel reinforced concrete beams // Vestnik DNUZHT: Nauka i progress transporta. 2010. P. 143–145.

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Copyright (c) 2019 Anatoliy Petrov, Mykhailo Pavliuchenkov, Alexander Nanka, Andriy Paliy