Calculation of buckling loads of IPE-section bending members based on optimization of analytical formulations

Yıl 2024, Cilt: 42 Sayı: 4, 973 - 987, 01.08.2024

Ahmet Özbayrak , Mohammed Kamal Ali Hatice Çıtakoğlu

Öz

The critical lateral buckling load of cantilever beams with IPE cross-section was calculated using analytical closed-form equations and numerical finite element analyses within the scope of the research. The equations suggested in the specifications for simply supported beams were used to calculate the buckling load of cantilever beams. The rationality of the values calculated due to this is not fully known. In the research, a single loading was made to the shear center at the free end of the cantilever beam. Cantilever length and section height were kept variable. As a result, it has been determined that there are partial differences in the analysis result obtained from the elastic stability theory and finite element method. Accordingly, the results obtained from ANSYS and SAP2000 analyses confirm each other. On the other hand, the results obtained using the formulation of Timoshenko and Gere, the calculation results made according to the AISC and DCCPSS regulations, and the results obtained from the LTBeam program confirm each other. However, it differs from the FEA analysis due to the cantilever beam length’s shortening and the section height increase. Thus, to obtain accurate and reliable results in the buckling load calculation of cantilever beams, the equations used in analytical calculations were optimized according to finite element analysis (FEA) results. As a result of the study conducted according to the error criteria, it was determined that the updated equa-tion results gave similar results to the FEA results.

Anahtar Kelimeler

Analytical Calculation, Buckling Load, Calibration, Cantilever Beam, Finite Element Method

Kaynakça

• REFERENCES
• [1] Trahair NS. Steel cantilever strength by inelastic lateral buckling. J Constr Steel Res 2010;66:993–999. [CrossRef]
• [2] American Institute of Steel Construction. Specification for structural steel buildings. Chicago: American Institute of Steel Construction; 2011.
• [3] Turkish Republic – Ministry of Envirounment and Urbanization. Çelik yapıların tasarım, hesap ve yapım esaslarına dair yönetmelikte değişiklik yapılmasına dair yönetmelik. Available at: https://www.resmigazete.gov.tr/eskiler/2018/02/20180215M1-4.htm. Accessed on Jun 12, 2024.
• [4] Chen WF, Atsuta T. Theory of beam-columns: Space behavior and design. McGraw-Hill, New York: J. Ross Publishing; 1977.
• [5] Chen WF. Structural stability: Theory and implementation. 1st ed. New York: Prentice Hall; 1987.
• [6] Timoshenko SP, Gere JM, Prager W. Theory of elastic stability, second edition. J Appl Mech 1962;29:220–221. [CrossRef]
• [7] Trahair NS. Inelastic lateral buckling of steel cantilevers. Eng Struct 2020;208:109918. [CrossRef]
• [8] ANSYS. ANSYS Help. Release 145 Copyr 2012.
• [9] Sapfire. SAP2000 Structural analysis and design. Available at: https://www.csiamerica.com/products/sap2000. Accessed on Jun 26, 2024.
• [10] Gonenli C, Das O. Effect of crack location on buckling and dynamic stability in plate frame structures. J Braz Soc Mech Sci Eng 2021;43:311. [CrossRef]
• [11] Demirhan AL, Eroğlu HE, Mutlu EO, Yılmaz T, Anil Ö. Experimental and numerical evaluation of inelastic lateral-torsional buckling of I-section cantilevers. J Constr Steel Res 2020;168:105991. [CrossRef]
• [12] Samanta A, Kumar A. Distortional buckling in braced-cantilever I-beams. Thin-Walled Struct 2008;46:637–645. [CrossRef]
• [13] Ozbasaran H, Aydin R, Dogan M. An alternative design procedure for lateral-torsional buckling of cantilever I-beams. Thin-Walled Struct 2015;90:235–242. [CrossRef]
• [14] Ma M, McNatt T, Hays B, Hunter S. Elastic lateral distortional buckling analysis of cantilever I-beams. Ships Offshore Struct 2013;8:261–269. [CrossRef]
• [15] Andrade A, e Costa PP, Camotim DRZ. Elastic lateral-torsional buckling of restrained web-tapered I-beams. Comput Struct 2010;88:1179–1196. [CrossRef]
• [16] Zhang WF, Liu YC, Hou GL, Chen KS, Ji J, Deng Y, et al. Lateral-torsional buckling analysis of cantilever beam with tip lateral elastic brace under uniform and concentrated load. Int J Steel Struct 2016;16:1161–1173. [CrossRef]
• [17] Winatama Kurniawan C, Mahendran M. Elastic lateral buckling of cantilever litesteel beams under transverse loading. Int J Steel Struct 2011;11:395–407. [CrossRef]
• [18] Yılmaz T, Kiraç N. Analytical and parametric investigations on lateral torsional buckling of European IPE and IPN beams. Int J Steel Struct 2017;17:695–709. [CrossRef]
• [19] Prombut P, Anakpotchanakul C. Deflection of composite cantilever beams with a constant I-cross section. IOP Conf Ser Mater Sci Eng 2019;501:012025. [CrossRef]
• [20] Ozbasaran H, Yilmaz T. Shape optimization of tapered I-beams with lateral-torsional buckling, deflection and stress constraints. J Constr Steel Res 2018;143:119–130. [CrossRef]
• [21] Rahami H, Kaveh A, Glolipour Y. Sizing, geometry and topology optimization of trusses via force method and genetic algorithm. Eng Struct 2008;30:2360–2369. [CrossRef]
• [22] Camp CV, Bichon BJ, Stovali SP. Design of steel frames using ant colony optimization. J Struct Eng 2005;131:369–379. [CrossRef]
• [23] Hayalioglu MS, Degertekin SO. Design of non-linear steel frames for stress and displacement constraints with semi-rigid connections via genetic optimization. Struct Multidiscip Optim 2004;27:259–271. [CrossRef]
• [24] Lagaros ND, Papadrakakis M. Robust seismic design optimization of steel structures. Struct Multidiscip Optim 2007;33:457–469. [CrossRef]
• [25] Lagaros ND, Papadrakakis M. Seismic design of RC structures: A critical assessment in the framework of multi‐objective optimization. Earthq Eng Struct Dyn 2007;36:1623–1639. [CrossRef]
• [26] Yassami M, Ashtari P. Using fuzzy genetic algorithm for the weight optimization of steel frames with semi-rigid connections. Int J Steel Struct 2014;15:63–73. [CrossRef]
• [27] Dehghani S, Fathizadeh SF, Vosoughi AR, Farsangi EN, Yang TY, Hajirasouliha I. Development of a novel cost-effective toggle-brace-curved damper (TBCD) for mid-rise steel structures using multi-objective NSGA II optimization technique. Struct Multidiscip Optim 2020;63:661–688. [CrossRef]
• [28] Prendes-Gero MB, Bello-García A, del Coz-Díaz JJ, Suárez-Domínguez FJ, Gero MBP. Optimization of steel structures with one genetic algorithm according to three international building codes. Rev Constr 2018;17:47–59. [CrossRef]
• [29] Kaveh A, Moghanni RM, Javadi S. Optimum design of large steel skeletal structures using chaotic firefly optimization algorithm based on the Gaussian map. Struct Multidiscip Optim 2019;60:879–894. [CrossRef]
• [30] Perelmuter A, Yurchenko V. Parametric optimization of steel shell towers of high-power wind turbines. Procedia Eng 2013;57:895–905. [CrossRef]
• [31] Shaqfa M, Orban Z. Modified parameter-setting-free harmony search (PSFHS) algorithm for optimizing the design of reinforced concrete beams. Struct Multidiscip Optim 2019;60:999–1019. [CrossRef]
• [32] Omkar SN, Khandelwal R, Ananth TVS, Naik GN GS. Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures. Expert Syst Appl 2009;36:11312– 11322. [CrossRef]
• [33] Barraza M, Bojórquez E, Fernández-González E, Reyes-Salazar A. Multi-objective optimization of structural steel buildings under earthquake loads using NSGA-II and PSO. Design Optim Appl Civil Eng 2017;21:488–500. [CrossRef]
• [34] Błachut J, Magnucki K. Strength, stability, and optimization of pressure vessels: Review of selected problems. Appl Mech Rev 2008;61:060801. [CrossRef]
• [35] Meddaikar YM, Irisarri FX, Abdalla MM. Laminate optimization of blended composite structures using a modified Shepard’s method and stacking sequence tables. Struct Multidiscip Optim 2017;55:535– 546. [CrossRef]
• [36] Cho HK. Optimization of laminated composite cylindrical shells to maximize resistance to buckling and failure when subjected to axial and torsional loads. Int J Precis Eng Manuf 2018;19:85–95. [CrossRef]
• [37] Msabawy A Mohammad F. Practical analysis procedures of steel portal frames having different connections rigidities using modified stiffness matrix and end-fixity factor concept. IOP Conf Ser Mater Sci Eng 2019;518:022037. [CrossRef]
• [38] Kirsch U. A unified reanalysis approach for structural analysis, design, and optimization. Struct Multidiscip Optim 2003;25:67–85. [CrossRef]
• [39] Msabawy A, Mohammad F. Continuous sizing optimization of cold-formed steel portal frames with semi-rigid joints using generalized reduced gradient algorithm. Mater Today Proc 2021;42:2290–2300. [CrossRef]
• [40] Taki T. Optimization of flat Z-stiffened panel subjected to compression. Trans Japan Soc Aero Space Sci 2019;62:44–54. [CrossRef]
• [41] Vosoughi AR. A developed hybrid method for crack identification of beams. Smart Struct Syst 2015;16:401–414. [CrossRef]
• [42] Le LM, Ly H-B, Pham BT, Le VM, Pham TA, Nguyen D-H, et al. Hybrid artificial intelligence approaches for predicting buckling damage of steel columns under axial compression. Materials (Basel) 2019;12:1670. [CrossRef]
• [43] Jung ID, Shin DS, Kim D, Lee J, Lee MS, Son HJ, et al. Artificial intelligence for the prediction of tensile properties by using microstructural parameters in high strength steels. Materialia 2020;11:100699. [CrossRef]
• [44] Cuong-Le T, Nghia-Nguyen T, Khatir S, Trong-Nguyen P, Mirjalili S, Nguyen KD. An efficient approach for damage identification based on improved machine learning using PSO-SVM. Eng Comput 2022;38:3069–3084. [CrossRef]
• [45] Daş O, Bağci Daş D. İzotropik plakaların regressif topluluk öğrenmesi kullanarak serbest titreşim analizi. Eur J Sci Technol 2022:428–434. [CrossRef]
• [46] Özbayrak A, Ali MK, 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 2023;48:5347–5370. [CrossRef] [47] Sharifi Y, Tohidi S. Lateral-torsional buckling capacity assessment of web opening steel girders by artificial neural networks - Elastic investigation. Front Struct Civ Eng 2014;8:167–177. [CrossRef]
• [48] Onchis DM, Gillich GR. Stable and explainable deep learning damage prediction for prismatic cantilever steel beam. Comput Ind 2021;125:103359. [CrossRef]
• [49] Kamane SK, Patil NK, Patagundi BR. Prediction of twisting performance of steel I beam bonded exteriorly with fiber reinforced polymer sheet by using neural network. Mater Today Proc 2021;43:514–519. [CrossRef]
• [50] Nguyen TA, Ly HB, Tran VQ. Investigation of ANN architecture for predicting load-carrying capacity of castellated steel beams 2021;6697923. [CrossRef]
• [51] Limbachiya V, Shamass R. Application of artificial neural networks for web-post shear resistance of cellular steel beams. Thin Walled Struct 2021;161:107414. [CrossRef]
• [52] Hosseinpour M, Rossi A, de Souza ASC, Sharifi Y. New predictive equations for LDB strength assessment of steel–concrete composite beams. Eng Struct 2022;258:114121. [CrossRef]
• [53] Mohanty N, Sasmal SK, Uttam, Mishra UK, Sahu SK. Experimental and computational analysis of free in-plane vibration of curved beams. J Vib Eng Technol 2022;11:1777–1796. [CrossRef]
• [54] 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;179:109713. [CrossRef]
• [55] Galéa Y. ) LTBeam Version 1.0. 11. CTICM Fr 2012.
• [56] Access Steel. NCCI: Elastic critical moment for lateral torsional buckling. Available at: https://www.steelconstruction.info/images/0/0f/SN003b.pdf. Accessed Jun 26, 2024.
• [57] ECCS. Rules for Member Stability in EN 1993-1-1: Background documentation and design guidelines. Available at: https://store.steelconstruct.com/site/index.php? module=store&target=publicStore&id_category=13&id=19. Accessed Jun 26, 2024.
• [58] Karunanithi N, Grenney WJ, Whitley D, Bovee K. Neural networks for river flow prediction. J Comput Civ Eng 1994;8:201–220. [CrossRef]
• [59] Citakoglu H. Comparison of artificial intelligence techniques for prediction of soil temperatures in Turkey. Theor Appl Climatol 2017;130:545–556. [CrossRef]
• [60] Nash JE, Sutcliffe JV. River flow forecasting through conceptual models part I - A discussion of principles. J Hydrol 1970;10:282–290. [CrossRef]
• [61] Graciano C, Kurtoglu AE, Casanova E. Machine learning approach for predicting the patch load resistance of slender austenitic stainless steel girders. Structures 2021;30:198–205. [CrossRef]
• [62] Ferreira FPV, Shamass R, Limbachiya V, Tsavdaridis KD, Martins CH. Lateral–torsional buckling resistance prediction model for steel cellular beams generated by Artificial Neural Networks (ANN). Thin Walled Struct 2022;170:108592. [CrossRef]
• [63] Sharifi Y, Moghbeli A, Hosseinpour M, Sharifi H. Neural networks for lateral torsional buckling strength assessment of cellular steel I-beams. 2019;22:2192–2202. [CrossRef]
• [64] Abambres M, Rajana K, Tsavdaridis KD, Ribeiro TP. Neural network-based formula for the buckling load prediction of I-section cellular steel beams. Computers 2019;8:2. [CrossRef]
• [65] Moghbeli A, Sharifi Y. New predictive equations for lateral-distortional buckling capacity assessment of cellular steel beams. Structures 2021;29:911–923. [CrossRef]
• [66] Hosseinpour M, Moghbeli A, Sharifi Y. Evaluation of lateral-distortional buckling strength of castellated steel beams using regression models. Innov Infrastruct Solut 2021;6:142.