Simulating Local Buckling-Induced Softening in Steel Members Using an Equivalent Nonlocal Material Model in Displacement-Based Fiber Elements
Publication: Journal of Structural Engineering
Volume 144, Issue 10
Abstract
Fiber-based elements are commonly used to simulate steel beam–columns because of their ability to capture interactions and spread of plasticity. However, when mechanisms such as local buckling result in effective softening at the fiber scale, conventional fiber models exhibit mesh dependence. To address this, a two-dimensional (2D) nonlocal fiber-based beam–column model is developed and implemented numerically. The model focuses on hot-rolled wide flange sections (W-sections) that exhibit local buckling-induced softening when subjected to combinations of axial compression and flexure. The formulation upscales a previously developed nonlocal formulation for single-fiber buckling to the full frame element. The formulation incorporates a physical length scale associated with local buckling along with an effective softening constitutive relationship at the fiber level. To support these aspects of the model, 43 continuum finite element (CFE) test problems are constructed. These test problems examine a range of parameters, including the axial load, cross section, and moment gradient. The implemented formulation is validated against CFE models as well as physical steel beam–column experiments that exhibit local buckling-nduced softening. The formulation successfully predicts postpeak response for these validation cases in a mesh-independent manner, while also capturing the effects of P-M interactions and moment gradient. To enable convenient generalization, guidelines for calibration and selection of the model parameters are provided. Limitations are discussed along with areas for future development.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The work was supported by the National Science Foundation (Grant No. CMMI 1434300) and graduate fellowships from the University of California, Davis. The findings and opinions presented in this paper are entirely those of the authors.
References
AISC. 2016. Seismic provisions for structural steel buildings. AISC 341-16. Chicago: AISC.
Armstrong, P. J., and C. O. Frederick. 1966. A mathematical representation of the multiaxial Bauschinger effect. Berkeley, CA: Berkeley Nuclear Laboratories.
ASCE. 2014. Seismic evaluation and retrofit of existing buildings. ASCE 41-13. Reston, VA: ASCE.
Bazant, Z. 1976. “Instability, ductility, and size effect in strain-softening concrete.” J. Eng. Mech. 102 (2): 331–344.
Bazant, Z. P., and M. Jirasek. 2002. “Nonlocal integral formulations of plasticity and damage: Survey of progress.” J. Eng. Mech. 128 (11): 1119–1149. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:11(1119).
Bazant, Z. P., and B. H. Oh. 1983. “Crack band theory for fracture of concrete.” Mat. Struct. 16 (3): 155–177. https://doi.org/10.1007/BF02486267.
Bazant, Z. P., and J. Planas. 1998. Fracture and size effect in concrete and other quasibrittle materials. Boca Raton, FL: CRC Press.
Coleman, J., and E. Spacone. 2001. “Localization issues in force-based frame elements.” J. Struct. Eng. 127 (11): 1257–1265. https://doi.org/10.1061/(ASCE)0733-9445(2001)127:11(1257).
Computers and Structures. 2016. ETABS: Integrated building design software: Users guide. Berkeley, CA: Computers and Structures.
Dides, M. A., and J. C. De la Llera. 2005. “A comparative study of concentrated plasticity models in dynamic analysis of building structures.” Earthquake Eng. Struct. Dyn. 34 (8): 1005–1026. https://doi.org/10.1002/eqe.468.
di Prisco, M., and J. Mazars. 1996. “Crush-crack: A nonlocal damage model for concrete.” Mech. Cohesive Frictional Mater. 1 (4): 321–347. https://doi.org/10.1002/(SICI)1099-1484(199610)1:4%3C321::AID-CFM17%3E3.0.CO;2-2.
Elkady, A., and D. G. Lignos. 2012. “Dynamic stability of deep slender steel columns as part of special MRFs designed in seismic regions: Finite element modeling.” In Proc., First Int. Conf. on Performance-Based and Life-Cycle Structural Engineering (PLSE). Hong Kong.
Elkady, A., and D. G. Lignos. 2015. “Analytical investigation of the cyclic behavior and plastic hinge formation in deep wide-flange steel beam-columns.” Bull. Earthquake Eng. 13 (4): 1097–1118. https://doi.org/10.1007/s10518-014-9640-y.
Engelen, R. A. B., M. G. D. Geers, and F. P. T. Baaijens. 2003. “Nonlocal implicit gradient enhanced elasto-plasticity for the modeling of softening behavior.” Int. J. Plast. 19 (4): 403–433. https://doi.org/10.1016/S0749-6419(01)00042-0.
Fell, B. V., A. M. Kanvinde, and G. G. Deierlein. 2010. Large-scale testing and simulation of earthquake induced ultra low cycle fatigue in bracing members subjected to cyclic inelastic buckling. Stanford, CA: Stanford Univ.
FEMA. 2012. Seismic performance assessment of buildings. FEMA P-58. Washington, DC: FEMA.
Fogarty, J., and S. El-Tawil. 2015. “Collapse resistance of steel columns under combined axial and lateral loading.” J. Struct. Eng. 142 (1): 04015091. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001350.
Hamburger, R. O., H. Krawinkler, J. O. Malley, and S. M. Adan. 2009. Seismic design of steel special moment frames: A guide for practicing engineers. Gaithersburg, MD: NIST.
Hartloper, A., and D. Lignos. 2017. “Updates to the ASCE-41-13 provisions for the nonlinear modeling of steel wide-flange columns for performance-based earthquake engineering.” In Proc., Eurosteel 2017, Copenhagen, Denmark.
Ibarra, L. F., and H. Krawinkler. 2005. Global collapse of frame structures under seismic excitations. Stanford, CA: Stanford Univ.
Ibarra, L. F., R. A. Medina, and H. Krawinkler. 2005. “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dyn. 34 (12): 1489–1511. https://doi.org/10.1002/eqe.495.
Ikeda, K., and S. A. Mahin. 1986. “Cyclic response of steel braces.” J. Struct. Eng. 112 (2): 342–361. https://doi.org/10.1061/(ASCE)0733-9445(1986)112:2(342).
Jirásek, M., and B. Patzak. 2002. “Consistent tangent stiffness for nonlocal damage models.” Comput. Struct. 80 (14–15): 1279–1293. https://doi.org/10.1016/S0045-7949(02)00078-0.
Jirásek, M., and S. Rolshoven. 2003. “Comparison of integral-type nonlocal plasticity models for strain-softening materials.” Int. J. Eng. Sci. 41 (13–14): 1553–1602. https://doi.org/10.1016/S0020-7225(03)00027-2.
Khaloo, A. R., and S. Tariverdilo. 2002. “Localization analysis of reinforced concrete members and softening behavior.” J. Struct. Eng. 128 (9): 1148–1157. https://doi.org/10.1061/(ASCE)0733-9445(2002)128:9(1148).
Khaloo, A. R., and S. Tariverdilo. 2003. “Localization analysis in softening RC frame structures.” Earthquake Eng. Struct. Dyn. 32 (2): 207–227. https://doi.org/10.1002/eqe.220.
Kolwankar, S. S., A. M. Kanvinde, M. Kenawy, and S. Kunnath. 2017. “A uniaxial nonlocal formulation for geometric nonlinearity-induced necking and buckling localization in a steel bar.” J. Struct. Eng. 143 (9): 04017091. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001827.
Krawinkler, H., M. Zohrei, B. Lashkari-Irvani, N. G. Cofie, and H. Hadidi-Tamjed. 1983. Recommendations for experimental studies on the seismic behavior of steel components and materials. Stanford, CA: Stanford Univ.
Lay, M. G. 1965. Some studies of flange local buckling in wide flange shapes. Bethlehem, PA: Lehigh Univ.
Lee, K., and B. Stojadinovic. 1996. “A plastic collapse method for evaluating rotation capacity of full-restrained steel moment connections.” Theor. Appl. Mech. 35 (1–3): 191–214. https://doi.org/10.2298/TAM0803191L.
Lignos, D., J. Cravero, and A. Elkady. 2016. “Experimental investigation of the hysteretic behavior of wide-flange steel columns under high axial load and lateral drift demands.” In Proc., 11th Pacific Steel Conf. Shanghai, China.
Newell, J. D., and C. M. Uang. 2006. Cyclic behavior of steel columns with combined high axial load and drift demand. San Diego: Univ. of California.
NIST. 2010. Nonlinear structural analysis for seismic design. Gaithersburg, MD: NIST.
Pugh, J. S., L. N. Lowes, and D. E. Lehman. 2015. “Nonlinear line-element modeling of flexural reinforced concrete walls.” Eng. Struct. 104: 174–192. https://doi.org/10.1016/j.engstruct.2015.08.037.
Salehi, M., and P. Sideris. 2017. “Refined gradient inelastic flexibility-based formulation for members subjected to arbitrary loading.” J. Eng. Mech. 143 (9): 04017090. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001288.
Shuttle, D. A., and I. M. Smith. 1988. “Numerical simulation of shear band formation in soils.” Int. J. Numer. Anal. Methods Geomech. 12 (6): 611–626. https://doi.org/10.1002/nag.1610120604.
Sideris, P., and M. Salehi. 2016. “A gradient inelastic flexibility-based frame element simulation.” J. Eng. Mech. 142 (7): 04016039. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001083.
Smith, C. M., A. M. Kanvinde, and G. G. Deierlein. 2017. “A local criterion for ductile fracture under low-triaxiality axisymmetric stress states.” Eng. Fract. Mech. 169: 321–335. https://doi.org/10.1016/j.engfracmech.2016.10.011.
Spacone, E., and F. C. Filippou. 1996. “Fibre-beam column model for nonlinear analysis of R/C frames. Part I: Formulation.” Earthquake Eng. Struct. Dyn. 25 (7): 711–725. https://doi.org/10.1002/(SICI)1096-9845(199607)25:7%3C711::AID-EQE576%3E3.0.CO;2-9.
Torabian, S., and B. W. Schafer. 2014. “Role of local slenderness in the rotation capacity of structural steel members.” J. Constr. Steel Res. 95: 32–43. https://doi.org/10.1016/j.jcsr.2013.11.016.
Valipour, H., and S. Foster. 2009. “Nonlocal damage formulation for a flexibility-based frame element.” J. Struct. Eng. 135 (10): 1213–1221. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000054.
Vermeer, P. A., and R. B. J. Brinkgreve. 1994. “A new effective nonlocal strain measure for softening plasticity.” In Proc., Localization and bifurcation theory for soil and rocks, 89–100. Rotterdam, Netherlands: Balkema.
Wu, S., and X. Wang. 2010. “Mesh dependence and nonlocal regularization of one-dimensional strain softening plasticity.” J. Eng. Mech. 136 (11): 1354–1365. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000184.
Yu, C., and B. W. Schafer. 2006. “Simulation of cold-formed steel beams in local and distortional buckling with applications to the direct strength method.” J. Constr. Steel Res. 63 (5): 581–590. https://doi.org/10.1016/j.jcsr.2006.07.008.
Zhang, G., and K. Khandelwal. 2016. “Modeling of nonlocal damage-plasticity in beams using isogeometric analysis.” Comput. Struct. 165: 76–95. https://doi.org/10.1016/j.compstruc.2015.12.006.
Information & Authors
Information
Published In
Copyright
©2018 American Society of Civil Engineers.
History
Received: Oct 9, 2017
Accepted: May 3, 2018
Published online: Jul 31, 2018
Published in print: Oct 1, 2018
Discussion open until: Dec 31, 2018
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.