Abstract
Analytical methods cannot find the exact solution for inelastic lateral torsional buckling. This study aims to develop innovative solutions by creating closed-form equations. A series of numerical studies (ANSYS) have been conducted for buckling load calculation on European I-section cantilever beams reinforced with transverse stiffener plates at different intervals. Formulations were developed using two methods to estimate the found load values more practically. Multiple linear regression analysis and multigene genetic programming methods were used to obtain these formulations. According to the error statistics, the multigene genetic programming method gave more accurate results than the multiple linear regression analysis methods in buckling load estimation. The estimates obtained from the multigene genetic programming method and the numerical results calculated in the ANSYS program were found to be compatible with each other. The scientific novelty brought by the research is to develop more original formulations for cantilever beams instead of using the buckling load calculation described for simply supported beams in the specifications. The scientific difference is that the developed formulations can calculate in a way that can consider the contribution of transverse stiffeners to the buckling load. This study will show that formulations designed with computer technologies can be an alternative calculation method for estimating the lateral buckling load according to the transverse stiffener plate spacing for European I-section cantilever steel beams.
Similar content being viewed by others
Change history
05 December 2022
A Correction to this paper has been published: https://doi.org/10.1007/s13369-022-07518-6
Abbreviations
- a :
-
The transverse stiffener plate spacing
- L :
-
Cantilever beam length
- h :
-
The depth of cantilever beam section
- Aw :
-
The cross-section area of cantilever beam section
- d :
-
Web height of the beam profile
- tw :
-
Web thickness of the beam profile
- C = G.J :
-
Torsional stiffness
- C 1 = E.C w :
-
Warping stiffness
- JD:
-
The torsion constant of the profile section with a transverse stiffener plate
References
Timoshenko, S.P.; Gere, J.M.: Theory of Elastic Stability. In: Courier Corporation. Courier Corporation (2009)
Demirhan, A.L.; Eroğlu, H.E.; Mutlu, E.O.; Yılmaz, T.; Anil, Ö.: Experimental and numerical evaluation of inelastic lateral-torsional buckling of I-section cantilevers. J. Constr. Steel Res. (2020). https://doi.org/10.1016/j.jcsr.2020.105991
Özbaşaran, H.: Finite differences approach for calculating elastic lateral torsional buckling moment of cantilever I sections. Anadolu Üniversitesi Bilim Ve Teknol. Derg. A-Uygulamalı Bilim. ve Mühendislik. 14, 143–152 (2013)
Vigil, J.: Structural steel design: a practice-oriented approach (2014)
Andrade, A.; Camotim, D.: Lateral-torsional buckling of singly symmetric tapered beams: theory and applications. J. Eng. Mech. 131, 586–597 (2005). https://doi.org/10.1061/(asce)0733-9399(2005)131:6(586)
Dowswell, B.: Lateral-torsional buckling of wide flange cantilever beams. Eng. J. Am. Inst. Steel Constr. 40, 85–91 (2004)
Andrade, A.; Camotim, D.; Dinis, P.B.: Lateral-torsional buckling of singly symmetric web-tapered thin-walled I-beams: 1D model vs. shell FEA. Comput. Struct. 85, 1343–1359 (2007). https://doi.org/10.1016/j.compstruc.2006.08.079
Yuan, W.B.; Kim, B.; Chen, C.Y.: Lateral-torsional buckling of steel web tapered tee-section cantilevers. J. Constr. Steel Res. 87, 31–37 (2013). https://doi.org/10.1016/j.jcsr.2013.03.026
Lu, L.W.; Shen, S.Z.; Shen, Z.Y.; Hu, X.R.: Stability of steel members (1983)
Zhang, L.; Tong, G.S.: Elastic flexural–torsional buckling of thin-walled cantilevers. Thin-Walled Struct. 46, 27–37 (2008). https://doi.org/10.1016/j.tws.2007.08.011
Andrade, A.; Camotim, D.; Providência e Costa, P.: On the evaluation of elastic critical moments in doubly and singly symmetric I-section cantilevers. J. Constr. Steel Res. 63, 894–908 (2007). https://doi.org/10.1016/j.jcsr.2006.08.015
Samanta, A.; Kumar, A.: Distortional buckling in braced-cantilever I-beams. Thin-Walled Struct. 46, 637–645 (2008). https://doi.org/10.1016/j.tws.2007.12.004
Khanh, T.D.; Tuyen, N.M.; Cuong, B.H.: Effects of end-plate on the critical moment of I-section cantilever beam with free end restrained laterally. J. Sci. Technol. Civ. Eng. HUCE 15, 102–109 (2021). https://doi.org/10.31814/STCE.NUCE2021-15(1)-09
Piotrowski, R.; Szychowski, A.: Lateral torsional buckling of steel beams elastically restrained at the support nodes. Appl. Sci. 9(9), 2019 (1944). https://doi.org/10.3390/APP9091944
Piotrowski, R.; Szychowski, A.: Lateral–torsional buckling of beams elastically restrained against warping at supports. Arch. Civ. Eng. 61, 155–174 (2015). https://doi.org/10.1515/ACE-2015-0042
Hassanien, M.; Bahaa, M.; Sobhy, H.; Hassan, A.; Inoue, J.: Effect of vertical web stiffeners on lateral torsional buckling behavior of cantilever steel I-beams. J. Appl. Mech. 7, 233–246 (2004). https://doi.org/10.2208/journalam.7.233
Cường, B.H.: Ảnh hưởng của sườn đầu dầm đến mômen tới hạn của dầm công xôn tiết diện chữ I. Tạp chí Khoa học Công nghệ Xây dựng 13, 20–27 (2019). https://doi.org/10.31814/STCE.NUCE2019-13(5V)-03
Jáger, B.; Dunai, L.: Nonlinear imperfect analysis of corrugated web beams subjected to lateral–torsional buckling. Eng. Struct. (2021). https://doi.org/10.1016/J.ENGSTRUCT.2021.112888
Jáger, B.; Dunai, L.; Kövesdi, B.: Lateral-torsional buckling strength of corrugated web girders: experimental study. Structures 43, 1275–1290 (2022). https://doi.org/10.1016/J.ISTRUC.2022.07.053
Qiao, P.; Zou, G.; Davalos, J.F.: Flexural–torsional buckling of fiber-reinforced plastic composite cantilever I-beams. Compos. Struct. 60, 205–217 (2003). https://doi.org/10.1016/S0263-8223(02)00304-5
Pinarbasi, S.: Lateral torsional buckling of rectangular beams using variational iteration method. Sci. Res. Essays 6, 1445–1457 (2011). https://doi.org/10.5897/SRE11.032
Kalkan, İ.; Ertenli, M.F.; Baş, S.: Petek Kirişlerde Yanal Stabilite Sorunun İncelenmesi ve Karşılaştırmalı Sonuçlar. In: 6. ÇELİK YAPILAR SEMPOZYUMU (2015)
Yilmaz, T.; Kirac, N.: Analytical and parametric investigations on lateral torsional buckling of European IPE and IPN beams. Int. J. Steel Struct. 17, 695–709 (2017). https://doi.org/10.1007/s13296-017-6024-6
Zhang, W.F.; Liu, Y.C.; Hou, G.L.; Chen, K.S.; Ji, J.; Deng, Y.; Deng, S.L.: Lateral-torsional buckling analysis of cantilever beam with tip lateral elastic brace under uniform and concentrated load. Int. J. Steel Struct. 16, 1161–1173 (2016). https://doi.org/10.1007/s13296-016-0052-5
Ozbasaran, H.; Aydin, R.; Dogan, M.: An alternative design procedure for lateral-torsional buckling of cantilever I-beams. Thin-Walled Struct. 90, 235–242 (2015). https://doi.org/10.1016/j.tws.2015.01.021
Gillich, G.R.; Maia, N.M.M.; Wahab, M.A.; Tufisi, C.; Korka, Z.I.; Gillich, N.; Pop, M.V.: Damage detection on a beam with multiple cracks: a simplified method based on relative frequency shifts. Sensors 21, 5215 (2021). https://doi.org/10.3390/S21155215
Sharifi, Y.; Tohidi, S.: Lateral–torsional buckling capacity assessment of web opening steel girders by artificial neural networks: elastic investigation. Front. Struct. Civ. Eng. 8, 167–177 (2014). https://doi.org/10.1007/s11709-014-0236-z
Onchis, D.M.; Gillich, G.R.: Stable and explainable deep learning damage prediction for prismatic cantilever steel beam. Comput. Ind. 125, 103359 (2021). https://doi.org/10.1016/J.COMPIND.2020.103359
Kamane, S.K.; Patil, N.K.; Patagundi, B.R.: Prediction of twisting performance of steel I beam bonded exteriorly with fiber reinforced polymer sheet by using neural network. Mater. Today Proc. 43, 514–519 (2021). https://doi.org/10.1016/J.MATPR.2020.12.026
Nguyen, T.-A.; Ly, H.-B.; Tran, V.Q.: Investigation of ANN architecture for predicting load-carrying capacity of castellated steel beams. Complexity (2021). https://doi.org/10.1155/2021/6697923
Limbachiya, V.; Shamass, R.: Application of artificial neural networks for web-post shear resistance of cellular steel beams. Thin-Walled Struct. (2021). https://doi.org/10.1016/J.TWS.2020.107414
Graciano, C.; Kurtoglu, A.E.; Casanova, E.: Machine learning approach for predicting the patch load resistance of slender austenitic stainless steel girders. Structures 30, 198–205 (2021). https://doi.org/10.1016/J.ISTRUC.2021.01.012
Nguyen, Q.H.; Ly, H.B.; Le, T.T.; Nguyen, T.A.; Phan, V.H.; Tran, V.Q.; Pham, B.T.: Parametric investigation of particle swarm optimization to improve the performance of the adaptive neuro-fuzzy inference system in determining the buckling capacity of circular opening steel beams. Materials (2020). https://doi.org/10.3390/ma13102210
Hosseinpour, M.; Rossi, A.; Sander Clemente de Souza, A.; Sharifi, Y.: New predictive equations for LDB strength assessment of steel–concrete composite beams. Eng. Struct. (2022). https://doi.org/10.1016/J.ENGSTRUCT.2022.114121
Mohanty, N.; Suvendu, S.K.; Mishra, U.K.; Sahu, S.K.: Experimental and computational analysis of free in-plane vibration of curved beams. J. Vib. Eng. Technol. 1, 3 (2022). https://doi.org/10.1007/s42417-022-00670-1
Neves, M.; Basaglia, C.; Camotim, D.: Stiffening optimisation of conventional cold-formed steel cross-sections based on a multi-objective genetic algorithm and using generalised beam theory. Thin-Walled Struct. (2022). https://doi.org/10.1016/J.TWS.2022.109713
Laman, M.; Uncuoglu, E.: Prediction of the moment capacity of pier foundations in clay using neural networks. Kuwait J. Sci. Eng. 36, 33–52 (2009)
Altun, F.; Dirikgil, T.: The prediction of prismatic beam behaviours with polypropylene fiber addition under high temperature effect through ANN, ANFIS and fuzzy genetic models. Compos. Part B Eng. 52, 362–371 (2013). https://doi.org/10.1016/j.compositesb.2013.04.015
Citakoglu, H.: Comparison of artificial intelligence techniques via empirical equations for prediction of solar radiation. Comput. Electron. Agric. 118, 28–37 (2015). https://doi.org/10.1016/j.compag.2015.08.020
Bayram, S.; Al-Jibouri, S.: Efficacy of estimation methods in forecasting building projects’ costs. J. Constr. Eng. Manag. 142, 05016012 (2016). https://doi.org/10.1061/(asce)co.1943-7862.0001183
Citakoglu, H.: Comparison of artificial intelligence techniques for prediction of soil temperatures in Turkey. Theor. Appl. Climatol. 130, 545–556 (2017). https://doi.org/10.1007/s00704-016-1914-7
Limbachiya, V.; Shamass, R.: Application of artificial neural networks for web-post shear resistance of cellular steel beams. Thin-Walled Struct. 161, 107414 (2021). https://doi.org/10.1016/j.tws.2020.107414
Aytek, A.; Kişi, Ö.: A genetic programming approach to suspended sediment modelling. J. Hydrol. 351, 288–298 (2008). https://doi.org/10.1016/j.jhydrol.2007.12.005
Danandeh Mehr, A.; Kahya, E.; Olyaie, E.: Streamflow prediction using linear genetic programming in comparison with a neuro-wavelet technique. J. Hydrol. 505, 240–249 (2013). https://doi.org/10.1016/j.jhydrol.2013.10.003
Searson, D.P.; Leahy, D.E.; Willis, M.J.: GPTIPS: an open source genetic programming toolbox for multigene symbolic regression. In: Proceedings of the International multiconference of engineers and computer scientists (2010)
Kumar, B.; Jha, A.; Deshpande, V.; Sreenivasulu, G.: Regression model for sediment transport problems using multi-gene symbolic genetic programming. Comput. Electron. Agric. 103, 82–90 (2014). https://doi.org/10.1016/j.compag.2014.02.010
Muduli, P.K.; Das, S.K.: CPT-based seismic liquefaction potential evaluation using multi-gene genetic programming approach. Indian Geotech. J. 44, 86–93 (2014). https://doi.org/10.1007/s40098-013-0048-4
Cobaner, M.; Babayigit, B.; Dogan, A.: Estimation of groundwater levels with surface observations via genetic programming. J. Am. Water Works Assoc. 108, E335–E348 (2016). https://doi.org/10.5942/jawwa.2016.108.0078
Citakoglu, H.; Babayigit, B.; Haktanir, N.A.: Solar radiation prediction using multi-gene genetic programming approach. Theor. Appl. Climatol. 142, 885–897 (2020). https://doi.org/10.1007/s00704-020-03356-4
Ferreira, F.P.V.; Shamass, R.; Limbachiya, V.; Tsavdaridis, K.D.; Martins, C.H.: Lateral–torsional buckling resistance prediction model for steel cellular beams generated by artificial neural networks (ANN). Thin-Walled Struct. 170, 108592 (2022). https://doi.org/10.1016/J.TWS.2021.108592
Sharifi, Y.; Moghbeli, A.; Hosseinpour, M.; Sharifi, H.: Neural networks for lateral torsional buckling strength assessment of cellular steel I-beams. Adv. Struct. Eng. 22, 2192–2202 (2019). https://doi.org/10.1177/1369433219836176
Abambres, M.; Rajana, K.; Tsavdaridis, K.D.; Ribeiro, T.P.: Neural network-based formula for the buckling load prediction of I-section cellular steel beams. Computers (2019). https://doi.org/10.3390/COMPUTERS8010002
Hosseinpour, M.; Moghbeli, A.; Sharifi, Y.: Evaluation of lateral-distortional buckling strength of castellated steel beams using regression models. Innov. Infrastruct. Solut. 6, 1–13 (2021). https://doi.org/10.1007/S41062-021-00510-3/FIGURES/10
Moghbeli, A.; Sharifi, Y.: New predictive equations for lateral-distortional buckling capacity assessment of cellular steel beams. Structures 29, 911–923 (2021). https://doi.org/10.1016/J.ISTRUC.2020.12.004
D’Aniello, M.; Güneyisi, E.M.; Landolfo, R.; Mermerdaş, K.: Predictive models of the flexural overstrength factor for steel thin-walled circular hollow section beams. Thin-Walled Struct. 94, 67–78 (2015). https://doi.org/10.1016/J.TWS.2015.03.020
Trahair, N.S.: Steel cantilever strength by inelastic lateral buckling. J. Constr. Steel Res. 66, 993–999 (2010). https://doi.org/10.1016/J.JCSR.2010.02.007
AISC (American Institute of Steel Construction).: Specification for structural steel buildings. Chicago (2010)
Ansys Inc.: mechanical user’s guide (2013)
Alpar, R.: Uygulamalı çok değişkenli istatistiksel yöntemlere giriş-I (1997)
Koza, J.R.: Genetic programming: on the programming of computers by means of natural selection. Stat. Comput. 4, 87–112 (1994)
Gandomi, A.H.; Alavi, A.H.: A new multi-gene genetic programming approach to nonlinear system modeling. Part I: materials and structural engineering problems. Neural Comput. Appl. 21, 171–187 (2012). https://doi.org/10.1007/s00521-011-0734-z
Nash, J.E.; Sutcliffe, J.V.: River flow forecasting through conceptual models part I. A discussion of principles. J. Hydrol. 10, 282–290 (1970). https://doi.org/10.1016/0022-1694(70)90255-6
Willmott, C.J.; Robeson, S.M.; Matsuura, K.: A refined index of model performance. Int. J. Climatol. 32, 2088–2094 (2012). https://doi.org/10.1002/joc.2419
Gandomi, A.H.; Roke, D.A.: Assessment of artificial neural network and genetic programming as predictive tools. Adv. Eng. Softw. 88, 63–72 (2015). https://doi.org/10.1016/j.advengsoft.2015.05.007
Republic of Turkey Ministry of Environment and Urbanization: (DCCPSS 2016) Regulation on Design, Calculation and Construction Principles of Steel Structures (2016)
Özbayrak, A.: Estimation of design bending moments of RC flat slabs under earthquake effect by ANN analysis. Nigde Omer Halisdemir Univ. J. Eng. Sci. 8, 979–991 (2019). https://doi.org/10.28948/NGUMUH.523939
Citakoglu, H.: Comparison of multiple learning artificial intelligence models for estimation of long-term monthly temperatures in Turkey. Arab. J. Geosci. (2021). https://doi.org/10.1007/S12517-021-08484-3
Başakın, E.E.; Ekmekcioğlu, Ö.; Çıtakoğlu, H.; Özger, M.: A new insight to the wind speed forecasting: robust multi-stage ensemble soft computing approach based on pre-processing uncertainty assessment. Neural Comput. Appl. 34, 783–812 (2022). https://doi.org/10.1007/S00521-021-06424-6
Citakoglu, H.; Demir, V.: Developing numerical equality to regional intensity–duration–frequency curves using evolutionary algorithms and multi-gene genetic programming. Acta Geophys. (2022). https://doi.org/10.1007/S11600-022-00883-8
Uncuoglu, E.; Citakoglu, H.; Latifoglu, L., et al.: Comparison of neural network, Gaussian regression, support vector machine, long short-term memory, multi-gene genetic programming, and M5 Trees. Elsevier, Hoboken (2022)
Citakoglu, H.; Coşkun, Ö.: Comparison of hybrid machine learning methods for the prediction of short-term meteorological droughts of Sakarya Meteorological Station in Turkey. Environ. Sci. Pollut. Res. (2022). https://doi.org/10.1007/S11356-022-21083-3
Demir, V.; Citakoglu, H.: Forecasting of solar radiation using different machine learning approaches. Neural Comput. Appl. (2022). https://doi.org/10.1007/S00521-022-07841-X
Demir, V.; Yaseen, Z.M.: Neurocomputing intelligence models for lakes water level forecasting: a comprehensive review. Neural Comput. Appl. (2022). https://doi.org/10.1007/S00521-022-07699-Z
Demir, V.: Enhancing monthly lake levels forecasting using heuristic regression techniques with periodicity data component: application of Lake Michigan. Theor. Appl. Climatol. 148, 915–929 (2022). https://doi.org/10.1007/S00704-022-03982-0
Funding
No funds, grants, or other support was received.
Author information
Authors and Affiliations
Contributions
All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by AÖ, MKA and HÇ. The first draft of the manuscript was written by AÖ and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Ethics approval
This article does not contain any studies with human participants or animals performed by any of the authors.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Özbayrak, A., Ali, M.K. & Çıtakoğlu, H. Buckling Load Estimation Using Multiple Linear Regression Analysis and Multigene Genetic Programming Method in Cantilever Beams with Transverse Stiffeners. Arab J Sci Eng 48, 5347–5370 (2023). https://doi.org/10.1007/s13369-022-07445-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13369-022-07445-6