DOI QR코드

DOI QR Code

Simulating large scale structural members by using Buckingham theorem: Case study

  • Muaid A. Shhatha (Department of Civil Engineering, University of Kufa)
  • 투고 : 2020.05.18
  • 심사 : 2023.04.13
  • 발행 : 2023.04.25

초록

Scaling and similitude large scale structural member to small scale model is considered the most important matter for the experimental tests because of the difficulty in controlling, lack of capacities and expenses, furthermore that most of MSc and PhD students suffering from choosing the suitable specimen before starting their experimental study. The current study adopts to take large scale slab with opening as a case study of structural member where the slab is squared with central squared opening, the boundary condition is fixed from all sides, the load represents by four concentrated force in four corners of opening, as well as, the study adopts Buckingham theorem which has been used for scaling, all the parameters of the problem have been formed in dimensionless groups, the main groups have been connected by a relations, those relations are represented by force, maximum stress and maximum displacement. Finite element method by ANSYS R18.1 has been used for analyzing and forming relations for the large scale member. Prediction analysis has been computed for three small scale models by depending on the formed relations of the large scale member. It is found that Buckingham theorem is considered suitable way for creating relations among the parameters for any structural problem then making similitude and scaling the large scale members to small scale members. Finally, verification between the prediction and theoretical results has been done, it is observed that the maximum deviation between them is not more than 2.4%.

키워드

참고문헌

  1. Altunisik, A.C., Kalkan, E. and Basaga, H.B. (2018), "Structural response relationship between scaled and prototype concrete load bearing systems using similarity requirements", Comput. Concr., 21(4), 385-397. https://doi.org/10.12989/cac.2018.21.4.385
  2. Bhattacharya, S., Demirci, H.E., Nikitas, G., Prakhya, G.K.V., Lombardi, D., Alexander, N.A., Aleem, M., Amani, S. and Mylonakis, G. (2021), "Physical modeling of interaction problems in geotechnical engineering", Model. Geotech. Eng., 205-256. https://doi.org/10.1016/B978-0-12-821205-9.00017-4
  3. Chiou, J.S., Jheng, Y.W. and Hung, H.H. (2019), "Numerical simulation of bridge piers with spread footings under earthquake excitation", Earthq. Struct., 16(6), 691-704. https://doi.org/10.12989/eas.2019.16.6.691
  4. Cho, U. and Wood, K. (1997), "Empirical similitude method for the functional test with rapid prototypes", Proceedings of the 1997 International Solid Freeform Fabrication Symposium.
  5. Kim, S. and Choi, S.W. (2016), "Experimental and analytical investigation based on 1/2 scale model for a cleanroom unit module consisting of steel section and reinforced concrete", Adv. Mater. Sci. Eng., 2016, 6920725. https://doi.org/10.1155/2016/6920725
  6. Kline, S.J. (2011), Similitude and Approximation Theory, McGraw-Hill, U.S.A.
  7. Kossakowski, P.G. (2017), "A combined experimental and numerical method for structural response assessment applied to cable-stayed footbridges", Adv. Comput. Des., 2(3), 143-163. https://doi.org/10.12989/acd.2017.2.3.143
  8. Kossakowski, P.G. and Uzarska, I. (2019), "Numerical modeling of an orthotropic RC slab band system using the Barcelona model", Adv. Comput. Des., 4(3), 211-221. https://doi.org/10.12989/acd.2019.4.3.211
  9. Langhaar, H.L. (1971), Dimensional Analysis and Theory of Models, John Wiley & Sons, U.S.A.
  10. Li, J. (2023), "Computational continuum modelling to analysis the dynamic and static stability of a cantilever nano-scale system", Adv. Comput. Des., 8(1), 77-96. https://doi.org/10.12989/acd.2023.8.1.077
  11. Moradi, G., Abdolmaleki, A. and Soltani, P. (2019), "Small-and large-scale analysis of bearing capacity and load-settlement behavior of rock-soil slopes reinforced with geogrid-box method", Geomech. Eng., 18(3), 315-328. https://doi.org/10.12989/gae.2019.18.3.315
  12. Phatak, D.R. and Dhonde, H.B. (2003), "Dimensional analysis of reinforced concrete beams subjected to pure torsion", J. Struct. Eng., 129(11), 1559-1563. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:11(1559)
  13. Russo, L., Sorrentino, M., Polverino, P. and Pianese, C. (2017), "Application of buckingham π theorem for scaling-up oriented fast modelling of proton exchange membrane fuel cell impedance", J. Power Sources, 353, 277-286. https://doi.org/10.1016/j-jpowsour.2017.03.116
  14. Salmani, F. and Mahpeykar, M.R. (2019), "Dimensional analysis for estimating wetness terms of condensing steam using dry flow data", J. Therm. Anal. Calorim., 137(6), 2121-2134. https://doi.org/10.1007/s10973-019-08108-9
  15. Salmani, F., Amiri Rad, E. and Mahpeykar, M.R. (2022), "Investigation effects of roughness in wet steam flow with Buckingham Pi-theorem", J. Therm. Anal. Calorim., 1-11. https://doi.org/10.1007/s10973-020-10526-z
  16. Salmani, F., Mahpeykar, M.R. and Rad, E.A. (2019), "Estimating heat release due to a phase change of high-pressure condensing steam using the Buckingham Pi theorem", Eur. Phys. J. Plus, 134(1), 48. https://doi.org/10.1140/epjp/i2019-12416-6
  17. Shehadeh, M., Shennawy, Y. and El-Gamal, H. (2015), "Similitude and scaling of large structural elements", Alexandria Eng. J., 54(2), 147-154. https://doi.org/10.1016/j.aej.2015.01.005.
  18. Simitses, G.J., Starnes, J.H. and Rezaeepazhand, J. (2002), "Structural similitude and scaling laws for plates and shells: A review", Adv. Mech. Plates Shells, 88, 295-310. https://doi.org/10.1007/0-306-46954-5_19.
  19. Tanimoto, S. (2006), "Dimensional analysis and physical laws", arXiv Preprint Physics, 0609117. https://doi.org/10.48550/arXiv.physics/0609117