Vibration reliability of steel beams prestressed by drawing

Introduction. Vibrations of building structures and mechanism parts were analyzed. The need to investigate the oscillation processes and vibration reliability of steel beams prestressed by web drawing was formulated. The subject of study is structural steel. The object of study is bimetallic steel beam prestressed without rods.

Materials and methods. The scientific inquiry is based on the basics of structural mechanics of buildings and structures: superposition principle, differential equation of deflection curve of a bar, energy method, and methods of determination of stress-strain state of prestressed steel bars.

Results. A comparative analysis of vibration reliability of non-prestressed beams and prestressed structures of equal bearing capacity was performed. Rotations of the beam supporting nodes loaded by prestressing forces and external impacts were determined by integration of differential equation of deflection curve of a split bar. The support moments in rigid supporting nodes of structures were determined on the basis of superposition principle. The developed methods of stressed condition of prestressed bars are the basis for determination of normal stresses in the sections of beams under study. The resultant stresses were obtained by algebraic addition of prestresses and stresses from external loads. Dynamic parameters of bearing capacity of beams were determined on the basis of works by I.M. Rabinovich and V.A. Kiselev. The oscillation circular frequency of conventional and prestressed beams was established, analytical expressions for determination of angular velocity of prestressed bending elements were formulated, and the dynamic deflections and factors of structures were determined. It is found that the circular frequency of prestressed beams hinged in supporting nodes compared to the circular frequency of conventional beams decreases by a factor of 1.4 and by a factor of 5.6 in beams with rigid supports. Angular velocity decreases by a factor of 1.4 (hinge supports) and 6.8 (rigid supports), respectively. The deflections of prestressed beams are reduced by a factor of 1,87: 11,9. There is a significant reduction in the stressed condition of prestressed structures.

Conclusions. A hinged traditional beam under external and vibration loads in limit state is in the material yield zone and does not meet the first and second limit state conditions. These structures have the lowest vibration reliability. Prestressed structures are more reliable. With rigid supporting nodes, the moments of prestressing forces coincide with the supporting moments and produce hogging with the vector opposite to the external load deflection vector. In the limit state, total deflections are less than the external load deflections. Stresses in the structure decrease. Since load moments and beam deflections are initial parameters for dealing with dynamic strength tasks, we may state that prestressed beams with rigid supporting nodes have an increased vibration reliability.

1. Maslennikov A. M., Sukhoterin M. V. et al. Sravnitel’nyy analiz opredeleniya chastot sobstvennykh kolebaniy pryamougol’nykh paneley s zashchemlennymi svobodnymi krayami [Comparative analysis of determining the natural vibration frequencies of rectangular panels with clamped free edges]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2022; No. 2(91): 45-57. (in Russ.)

2. Rosenzweig L. M. Metod vychisleniya chastot sobstvennykh kolebaniy uprugikh sterzhney pryamym integrirovaniyem differentsial’nogo uravneniya izgiba [Method for calculating the natural frequencies of elastic rods by direct integration of the Kagan differential equation of bending]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2019; 1(72): 61-66. (in Russ.)

3. Sokolov V. G., Dmitriev A. V. Kolebaniya podzemnykh tonkostennykh magistral’nykh truboprovodov s uchetom vnutrennego davleniya i prodol’noy sily. [ Free vibrations of underground rectilinear thinwalled sections of gas pipelines]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2019; 2 (73): 29-34. (in Russ.)

4. Nesterova O. P. Osobennosti rascheta sooruzheniy s dinamicheskimi gasitelyami kolebaniy po akselerogrammam proyektnykh zemletryaseniy. [Features of calculation of structures with dynamic vibration dampers based on accelerograms of design earthquakes]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2019; 2(73): 48-53. (in Russ.)

5. Sokolov V. G., Ogorodnikova Yu. V. Kolebaniya podzemnykh tonkostennykh magistral’nykh truboprovodov s uchetom vnutrennego davleniya i prodol’noy sily. [Oscillations of underground thin-walled main pipelines taking into account internal pressure and longitudinal force]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2019; 5 (76): 105112. (in Russ.)

6. Nguyen H. H. Opredeleniye chastot svobodnykh kolebaniy pologikh obolochek na pryamougol’nom plane i sravneniye analiticheskikh i chislennykh rezul’tatov [Determination of the frequencies of free vibrations of shallow shells on a rectangular plan and comparison of analytical and numerical results]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2014; 1(42): 44-48. (in Russ.)

7. Bereznev A.V. Vliyaniye vnutrennego rabochego davleniya na chastoty svobodnykh kolebaniy krivolineynykh uchastkov polietilenovykh truboprovodov [Influence of internal working pressure on the frequencies of free vibrations of curved sections of polyethylene pipelines]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2015; (50): 101-104. (in Russ.)

8. Chernov Yu. T. Proyektirovaniye zdaniy i sooruzheniy, podvergayushchikhsya dinamicheskim vozdeystviyam. [Design of buildings and structures subject to dynamic influences]. Promyshlennoye i grazhdanskoye stroitel’stvo. 2018; 4: 73-77. (in Russ.)

9. Turkov A.V., Vetrova O.A, Marfin K.V. Progiby i chastoty sobstvennykh kolebaniy sistem perekrestnykh ferm na kvadratnom plane s razlichnymi skhemami operaniya [Deflections and natural oscillation frequencies of cross-truss systems on a square plan with various support schemes]. Promyshlennoye i grazhdanskoye stroitel’stvo. 2018; 11: 42–45. (in Russ.)

10. Mkrtychev O. R., Bulushev. Veroyatnostnyy analiz raboty ploskoy stal’noy ramy pri seysmicheskom vozdeystvii. [Probabilistic analysis of the operation of a flat steel frame under seismic influence]. Promyshlennoye i grazhdanskoye stroitel’stvo. 2020; 5: 45-50. (in Russ.)

11. Gusev B.V., Saurin V.V. O modelirovanii izgibnykh kolebaniy balok peremennogo poperechnogo secheniya [On modeling of bending vibrations of beams of variable cross-section]. Industrial and Civil Construction. 2020; 11: 94-98. (in Russ.)

12. Zedgenizov V.G., Faizov S.Kh. Impact of force application point in two-mass oscillation system on its energy efficiency. The Russian Automobile and Highway Industry Journal. 2023;20(1):12-23. (In Russ.) https://doi.org/10.26518/2071-7296-2023-20-1-12-23

13. Korytov M.S., Shcherbakov V.S., Belyakov V.E. Fluctuations of the cargo transported by lifting crane: simulation and analysis. The Russian Automobile and Highway Industry Journal. 2019;16(5):526533. (In Russ.) https://doi.org/10.26518/2071-72962019-5-526-533

14. Sukharev R.Y., Tanskiy V.V. Influence analysis of the attachment coordinates relating to the cargo oscillations on the pipe laying crane’s boom. The Russian Automobile and Highway Industry Journal. 2018;15(2):199-206. (In Russ.) https://doi.org/10.26518/2071-7296-2018-2-199-206

15. Kravchuk V. A. Svobodnyye kolebaniya stal’nykh balok, predvaritel’no napryazhennykh vytyazhkoy stenki [Free vibrations of steel beams prestressed by drawing the wall]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2020; 6(83): 97-103. (in Russ.)

16. Kravchuk V.A. Dinamicheskiye parametry nesushchey sposobnosti stal’nykh balok, predvaritel’no napryazhennykh vytyazhkoy tonkoy stenki pri zhestkom zakreplenii ikh na oporakh. [Dynamic parameters of the load-bearing capacity of steel beams prestressed by stretching a thin wall when rigidly fastened to supports]. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2021; 6 (89): 72-77. (in Russ)

17. Kravchuk V. A., Kravchuk E. V. Rabota tonkostennykh stal’nykh sterzhney, predvaritel’no napryazhennykh vytyazhkoy stenki, pri sluchaynykh dinamicheskikh vozdeystviyakh. Vestnik Grazhdanskikh Inzhenerov – Bulletin of Civil Engineers. 2022; 6(95):10-20. (in Russ.)

18. Song S., Qian Y., Liu J., Xie X., Wu G. Time-variant fragility analysis of the bridge system considering time-varying dependence among typical component seismic demands. Earthquake Engineering and Engineering Vibration. 2019; Vol. 18. Issue 2: 363-377.

19. Du Y., Hao J., Yu J., Yu H., Deng B., Lv D., Liang Z. Seismic performance of a repaired thin steel plate shear wall structure. Journal of Constructional Steel Research. 2018; 151: 194-203

20. Jalali S. A., Darvishan E. Seismic demand assessment of self-centering steel plate shear walls. Journal of Constructional Steel Research. 2019; 162: 105738

21. Mu Z., Yang Y. Experimental and numerical study on seismic behavior of obliquely stiffened steel plate shear walls with openings. Thin-Walled Structures. 2020; 146: 106457

22. Zhong S. C., Oyadiji S. O. Analytical predictions of natural frequencies of cracked simply supported beams with a stationary roving mass. Journal of Sound and Vibration. 2008; 311 (1-2): 328-352. DOI: 10.1016/j.jsv.2007.09.00923

23. Lien T. V., Duc N. T., Khiem N. T. Free and forced vibration analysis of multiple cracked FGM multi span continuous beams using dynamic stiffness method. Latin American Journal of Solids and Structures. 2019; 16 (2): 1-26. DOI: 10.1590/1679-78255242

24. Kravchuk V. A. Stal’nyye sterzhni, predvaritel’no napryazhennyye bez zatyazhek [Steel rods, prestressed without tightening.] Moscow, ASV, 2015. 550 p. (in Russ.)