Elastic Lateral Torsional Buckling of I-Beams Strengthened While under Loading
Publication: Journal of Structural Engineering
Volume 149, Issue 1
Abstract
The present study investigates the elastic lateral torsional buckling resistance for steel I-beams that are strengthened with steel cover plates while being subjected to loading. A variational principle was developed for the problem by accounting for the full sequence of prestrengthening load application, strengthening process, poststrengthening load application, up to the buckling response. The variational principle was then used to develop a finite-element formulation for the problem leading to a quadratic eigenvalue problem. The formulation successfully captures the effects of prestrengthening loads, the beneficial effects due to prebuckling deformation, and the interactions between both effects. The study documents the benefit of providing transverse stiffeners to maximize the critical moment capacity attained when cover plates are used for strengthening. The study determines the locations of cover plates that would maximize the gain in critical moments in strengthening scenarios where only part of the beam span is to be strengthened. A systematic parametric study was developed to characterize the gain in elastic critical moment strength attained by cover plate strengthening and associated prebuckling deformation effects, in terms of dimensionless parameters that characterize the effects of prestrengthening load magnitude, beam span, cross-sectional geometry, length of cover plates, and cover plate cross section. Other parameters investigated include the distributions of prestrengthening and poststrengthening loading.
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Data Availability Statement
Some or all data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
The authors gratefully acknowledge scholarship support from the University of Ottawa to the first author and further research funding from the Natural Science and Engineering Research Council of Canada (NSERC) to the second author.
References
AISC. 2016. Specification for structural steel buildings. ANSI/AISC 360-16. Chicago: AISC.
Andrade, A., and D. Camotim. 2004. “Lateral-torsional buckling of prismatic and tapered thin-walled open beams: Assessing the influence of pre-buckling deflections.” Steel Compos. Struct. 4 (4): 281–301. https://doi.org/10.12989/scs.2004.4.4.281.
Arizou, R., and M. Mohareb. 2021. “Design considerations for distortional lateral buckling.” J. Struct. Eng. 147 (12): 04021203. https://doi.org/10.1061/(ASCE)ST.1943-541X.0003167.
Arizou, R., and M. Mohareb. 2022. “Finite element formulation for distortional lateral buckling of I-beams.” Eng. Struct. 262 (Jul): 114265. https://doi.org/10.1016/j.engstruct.2022.114265.
Barsoum, R. S., and R. H. Gallagher. 1970. “Finite element analysis of torsional and torsional–flexural stability problems.” Int. J. Numer. Methods Eng. 2 (3): 335–352. https://doi.org/10.1002/nme.1620020304.
CSA (Canadian Standards Association). 2019. Design of steel structures. CSA S16:19. Toronto: CSA.
Erkmen, R. E., and M. M. Attard. 2011. “Lateral–torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects.” Int. J. Mech. Sci. 53 (10): 918–925. https://doi.org/10.1016/j.ijmecsci.2011.08.006.
Gellin, S., and G. C. Lee. 1988. “Finite elements available for the analysis of non-curved thin-walled structures.” In Finite element analysis of thin-walled structures, 1–30. Amsterdam, Netherlands: Elsevier Applied Science.
Gjelsvik, A. 1981. The theory of thin-walled bars. New York: Wiley.
Hsu, W. T., D. M. Lue, and Y. F. Chen. 2012. “Design aid for moment strength of built-up crane runway girders.” Int. J. Steel Struct. 12 (3): 403–417. https://doi.org/10.1007/s13296-012-3009-3.
Hsu, W. T., D. M. Lue, and B. T. Hsiao. 2009. “Numerical approach for torsion properties of built-up runway girders.” J. Appl. Sci. Eng. 12 (4): 381–389. https://doi.org/10.6180/jase.2009.12.4.02.
Iranpour, A., and M. Mohareb. 2022. “Elastic lateral torsional buckling resistance for continuous beams using artificial neural networks.” In Proc., CSCE 2022 Annual Conf. Whistler, BC, Canada: Canadian Society for Civil Engineering.
Liu, Y., and L. Gannon. 2009a. “Experimental behavior and strength of steel beams strengthened while under load.” J. Constr. Steel Res. 65 (6): 1346–1354. https://doi.org/10.1016/j.jcsr.2009.01.008.
Liu, Y., and L. Gannon. 2009b. “Finite element study of steel beams reinforced while under load.” Eng. Struct. 31 (11): 2630–2642. https://doi.org/10.1016/j.engstruct.2009.06.011.
MacCrimmon, R. 2009. Guide for the design of crane-supporting steel structures. Edmonton, AB, Canada: Canadian Institute of Steel Construction.
Machado, S. P., and V. H. Cortínez. 2005. “Lateral buckling of thin-walled composite bisymmetric beams with prebuckling and shear deformation.” Eng. Struct. 27 (8): 1185–1196. https://doi.org/10.1016/j.engstruct.2005.02.018.
Mohri, F., N. Damil, and M. Potier-Ferry. 2012. “Pre-buckling deflection effects on stability of thin-walled beams with open sections.” Steel Compos. Struct. 13 (1): 71–89. https://doi.org/10.12989/scs.2012.13.1.071.
Mohri, F., and M. Potier-Ferry. 2006. “Effects of load height application and pre-buckling deflections on lateral buckling of thin-walled beams.” Steel Compos. Struct. 6 (5): 401. https://doi.org/10.12989/scs.2006.6.5.401.
Pezeshky, P., and M. Mohareb. 2018. “Distortional lateral torsional buckling of beam-columns including pre-buckling deformation effects.” Comput. Struct. 209 (Oct): 93–116. https://doi.org/10.1016/j.compstruc.2018.08.010.
Pezeshky, P., A. Sahraei, F. Rong, S. Sasibut, and M. Mohareb. 2020. “Generalization of the Vlasov theory for lateral torsional buckling analysis of built-up monosymmetric assemblies.” Eng. Struct. 221 (Oct): 111055. https://doi.org/10.1016/j.engstruct.2020.111055.
Pham, P. V., M. Mohareb, and A. Fam. 2017. “Elastic analysis of steel beams strengthened with GFRP plates including preexisting loading effects.” J. Struct. Eng. 143 (12): 04017163. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001904.
Pi, Y. L., and N. S. Trahair. 1992a. “Prebuckling deflections and lateral buckling. I: Theory.” J. Struct. Eng. 118 (11): 2949–2966. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:11(2949).
Pi, Y. L., and N. S. Trahair. 1992b. “Prebuckling deflections and lateral buckling. II: Applications.” J. Struct. Eng. 118 (11): 2967–2985. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:11(2967).
Pi, Y. L., N. S. Trahair, and S. Rajasekaran. 1992. “Energy equation for beam lateral buckling.” J. Struct. Eng. 118 (6): 1462–1479. https://doi.org/10.1061/(ASCE)0733-9445(1992)118:6(1462).
Reichenbach, M. C., Y. Liu, T. A. Helwig, and M. D. Engelhardt. 2020. “Lateral-torsional buckling of singly symmetric I-girders with stepped flanges.” J. Struct. Eng. 146 (10): 04020203. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002780.
Roberts, T. M., and Z. G. Azizian. 1983. “Instability of thin walled bars.” J. Eng. Mech. 109 (3): 781–794. https://doi.org/10.1061/(ASCE)0733-9399(1983)109:3(781).
Sahraei, A., P. Pezeshky, and M. Mohareb. 2017. “Lateral torsional buckling analysis and design of steel beams with continuous spans.” In Proc., 6th Int. Conf. on Engineering Mechanics and Materials. Vancouver, BC, Canada: Canadian Society for Civil Engineering.
Sahraei, A., P. Pezeshky, M. Mohareb, and G. Doudak. 2018. “Simplified expressions for elastic lateral torsional buckling of wooden beams.” Eng. Struct. 174 (Nov): 229–241. https://doi.org/10.1016/j.engstruct.2018.07.042.
SIMULIA. 2020. Abaqus/CAE user’s manual. Providence, RI: Dassault Systemes.
Trahair, N. 1993. Flexural-torsional buckling of structures. Boca Raton, FL: CRC Press.
Trahair, N. S., and S. T. Woolcock. 1973. “Effect of major axis curvature on I-beam stability.” J. Eng. Mech. Div. 99 (1): 85–98. https://doi.org/10.1061/JMCEA3.0001731.
Vacharajittiphan, P., S. Woolcock, and N. S. Trahair. 1974. “Effect of in-plane deformation on lateral buckling.” J. Struct. Mech. 3 (1): 29–60. https://doi.org/10.1080/03601217408907255.
Vlasov, V. 1961. Thin-walled elastic beams. Jerusalem, Israel: Israel Program for Scientific Translations.
Wang, Y.-Q., L. Zong, R.-X. Zhu, X.-Y. Liu, and Y.-J. Shi. 2015. “Behavior of I-section steel beam welding reinforced while under load.” J. Constr. Steel Res. 106 (Mar): 278–288. https://doi.org/10.1016/j.jcsr.2014.12.020.
Wu, L., and M. Mohareb. 2011. “Buckling of shear deformable thin-walled members—I. Variational principle and analytical solutions.” Thin-Walled Struct. 49 (1): 197–207. https://doi.org/10.1016/j.tws.2010.09.025.
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Published In
Journal of Structural Engineering
Volume 149 • Issue 1 • January 2023
Copyright
© 2022 American Society of Civil Engineers.
History
Received: Jan 30, 2022
Accepted: Jun 8, 2022
Published online: Oct 17, 2022
Published in print: Jan 1, 2023
Discussion open until: Mar 17, 2023
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Cited by
- Amin Iranpour, Magdi Mohareb, Design Expressions for Elastic Lateral Torsional Buckling Capacity of I-Beams Strengthened While under Loading, Journal of Structural Engineering, 10.1061/JSENDH.STENG-12203, 149, 7, (2023).