Sensitivity Analysis of Geometrically Imperfect Single-storey Steel Frame Structure - A Comparison of Two Loading Modes

• Autorzy: Jindra Daniel , Kala Zdeněk , Kala Jiří

Identyfikatory

DOI

10.29227/IM-2024-02-20

Warianty tytułu

PL

Analiza wrażliwości geometrycznie niedoskonałej jednopiętrowej konstrukcji szkieletowej ze stali – porównanie dwóch trybów obciążenia

• Konferencja: 9th World Multidisciplinary Congress on Civil Engineering, Architecture, and Urban Planning - WMCCAU 2024 : 2-6.09.2024
• Języki publikacji: EN

Abstrakty

EN

In this study, two methods to numerically analyse a single-storey vertically loaded steel frame structure with initial geometrical imperfections are compared. The first method is deterministic, where the initial imperfections, sway of the frame and local bow imperfections of the columns are based on the corresponding European standard to design steel structures, Eurocode 3 (EC3). The second, probabilistic method, where the imperfections are defined by the random stochastic parameters is using the first order reliability method (FORM) along with numerous numerical finite element analyses in order to estimate the ultimate resistance of the structure. In this FORM method, the statistical values of these input imperfections are derived from the European standard for allowed erection and manufacturer tolerances, and these data corresponds with the experimentally measured imperfections on real structures. Material parameters, as Young’s modulus and yield stress are also considered as stochastic variables. Design ultimate resistance based on EC3 is compared with the 0.1% quantile of the stochastic ultimate resistance of the FORM method. In general, assumptions of the deterministic EC3 approach are sometimes considered as overly conservative. The main objective of this study is to verify and evaluate these assumptions by comparison with more precise probabilistic method. Moreover, for both methods (EC3 and FORM), the resistance is determined under two loading modes, one by increasing of the force load, the other by prescribed displacement. The loading conditions of these two loading modes are applied analogically to each other, hence similar resistances for the corresponding method are expected. However, this assumption needs to be verified within the probabilistic analysis conditions, what is the secondary objective of this paper.

Słowa kluczowe

EN

single-storey steel frame; initial geometric imperfection; erection tolerances; correlations; first order reliability method; geometrically nonlinear analysis

PL

jednopiętrowa rama stalowa; początkowa niedoskonałość geometryczna; tolerancje montażu; korelacje; metoda niezawodności pierwszego rzędu; analiza geometrycznie nieliniowa

• Wydawca: Polskie Towarzystwo Przeróbki Kopalin
• Czasopismo: Inżynieria Mineralna
• Rocznik: 2024
• Tom: Vol. 1, no. 2
• Strony: art. no. 20
• Opis fizyczny: Bibliogr. 30 poz., tab., wykr., zdj.

Twórcy

autor

Jindra Daniel

• Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Veveří 331/95, 602 00 Brno, Czech Republic

• https://orcid.org/0000-0002-9512-2558

autor

Kala Zdeněk

• Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Veveří 331/95, 602 00 Brno, Czech Republic

• https://orcid.org/0000-0002-6873-3855

autor

Kala Jiří

• Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Veveří 331/95, 602 00 Brno, Czech Republic

• https://orcid.org/0000-0002-8250-8515

Bibliografia

• 1. W. Liu, K.J.R. Rasmussen, H. Zhang, Y. Xie, Q. Liu, L. Dai, “Probabilistic study and numerical modelling of initial geometric imperfections for 3D steel frames in advanced structural analysis,” Structures 57 (2023) 105190.
• 2. J. Melcher, “Classification of structural steel members initial imperfections,” In: Proc. of structural stability research council, Lehigh University, Bethlehem; 1980.
• 3. Z. Kala, “Sensitivity assessment of steel members under compression,” Eng. Struct. 31 (2009), 1344–1348.
• 4. European Committee for Standardization. Part 1-1: General rules— General rules and rules for buildings. In EN 1993-1-1:2005 Eurocode 3—Design of Steel Structures; European Committee for Standardization: Brussels, Belgium, 2005.
• 5. J.Y.R. Liew, D.W. White, W.F. Chen, “Notional-load plastic-hinge method for frame design,” J. Struct. Eng ASCE 120, 1434–1454 (1994).
• 6. J.X. Gu, S.L. Chan, “Second-order analysis and design of steel structures allowing for member and frame imperfections,” Int. Journal Numer. Methods Eng 62, 601–15 (2005).
• 7. Z.P. Bažant, Y. Xiang, “Postcritical imperfection-sensitive buckling and optimal bracing of large regular frames,” J. Struct. Eng. 123, 513–522 (1997).
• 8. A. Agüero, I. Baláž, Y. Koleková, P. Martin, “Assessment of in-Plane Behavior of Metal Compressed Members with Equivalent Geometrical Imperfection,” Appl. Sci. 10, 8174 (2020).
• 9. A.R. Alvarenga, R.A.M Silveria, “Second-order plastic-zone analysis of steel frames – part II: effects of initial geometric imperfection and residual stress,” Lat. Am. J. Solids Struct. 6, 323–42 (2009).
• 10. S. Shayan, K.J.R. Rasmussen, H. Zhang, “On the modelling of initial geometric imperfections of steel frames in advanced analysis,” J. Constr. Steel Res. 98, 167–177 (2014).
• 11. Z. Kala, “Strain Energy and Entropy Based Scaling of Buckling Modes,” Entropy 25, 1630 (2023).
• 12. S.E. Kim, “Practical advanced analysis for steel frame design,” Ph.D. thesis, West Lafayette, IN: Purdue University; 1996.
• 13. Z. Kala and J. Vales, “Imperfection sensitivity analysis of steel columns at ultimate limit state,” Arch. Civ. Mech. Eng. 18, 1207–1218 (2018).
• 14. A. Machowski, I. Tylek, “Random equivalent initial bow and tilt in steel frame,” Adv. Steel Constr. 8, 383–397 (2012).
• 15. Y. Ding, X. Song, H.T. Zhu, “Probabilistic progressive collapse analysis of steel-concrete composite floor systems,” J. Constr. Steel Res. 129, 129–140 (2017).
• 16. European Committee for Standardization, EN 1990:2002+A1:2005 (E), Eurocode 0: Basis of structural design, in: CEN, Brussels, Belgium, 2005.
• 17. M.H. Faber, Statistics and Probability Theory: In pursuit of Engineering Decision Support, (Springer Publishing Company, Dordrecht, 2012), pp. 192.
• 18. Y.G. Zhao, T. Ono, “A general procedure for first/second-order reliability method (FORM/SORM),” Struct. Saf. 21, 95–112 (1999).
• 19. British Standard Institution (BSI): BS EN 1090-2:2018: Execution of steel structures and aluminium structures Part 2: Technical requirements for steel structures.
• 20. J. Lindner, R. Gietzelt, “Imperfektionsannahmen für Stützenschiefstellungen (Assumptions for imperfections for outof-plumb of columns),” Stahlbau 53, 97–102 (1984).
• 21. Z. Kala, “Sensitivity analysis in probabilistic structural design: A comparison of selected techniques,” Sustainability 12, 4788 (2020).
• 22. Z. Kala, “New importance measures based on failure probability in global sensitivity analysis of reliability,” Mathematics 9, 2425 (2021).
• 23. Cross-Section Properties, www.staticstools.eu/en/ Accessed 27 Oct. 2023.
• 24. Ansys, Inc, ANSYS 20.0, Ansys, Inc., Canonsburg, PA, USA, 2019.
• 25. D.E. Hungtington, C.S. Lyrintzis, “Improvements to and limitations of Latin hypercube sampling,” Probab. Eng. Mech. 13(4), 245–253 (1998).
• 26. GmbH Dynardo, OptiSLang Software Manual: Methods for Multi-Disciplinary Optimization and Robustness Analysis, Weimar (2018).
• 27. Z. Kala, J. Vales, “Sensitivity assessment and lateral-torsional buckling design of I-beams using solid finite elements,” J Constr Steel Res 139, 110–122 (2017).
• 28. D. Jindra, Z. Kala, J. Kala, “Flexural buckling of stainless steel CHS columns: Reliability analysis utilizing FEM simulations,” J Constr Steel Res 188, 107002 (2022).
• 29. D. Jindra, Z. Kala, J. Kala, “Buckling curves of stainless steel CHS members: Current state and proposed provisions,” J Constr Steel Res 198, 107521 (2022).
• 30. D. Jindra, Z. Kala, J. Kala, “Ultimate Load Capacity of Multi-Story Steel Frame Structures with Geometrical Imperfections: A Comparative Study of Two Methods,” in Modern Building Materials, Structures and Techniques. MBMST 2023, Lecture Notes in Civil Engineering, vol 392, edited by J.A.O. Barros, G. Kaklauskas, E.K. Zavadskas (Springer, Cham. 2023)

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki i promocja sportu (2025).