Simulating Cyclic Local Buckling–Induced Softening in Steel Beam-Columns Using a Nonlocal Material Model in Displacement-Based Fiber Elements
Publication: Journal of Structural Engineering
Volume 146, Issue 1
Abstract
Steel beam-columns subjected to cyclic loading (such as during earthquakes) may exhibit local buckling, which results in effective cross-sectional softening and localization of deformation. These phenomena are critical from the standpoint of performance and collapse assessment. Fiber-based elements are attractive for simulating beam-column response because they capture P-M interactions and the spread of plasticity and can be generalized to different cross sections from material-level calibrations. However, conventional fiber models typically employ softening constitutive material laws to represent local buckling. Without a regularizing length scale, this results in a nonelliptic boundary-value problem, leading to severe mesh dependence. A two-dimensional nonlocal fiber-based beam-column model is presented to address this issue for steel wide-flange sections subject to combinations of axial and cyclic lateral loads. The methodology includes the following elements: (1) a constitutive material model that is able to represent inelastic cyclic local buckling, (2) a nonlocal strain formulation that incorporates a physically based length scale, and (3) suggested practices for input selection and parameter calibration. Forty-two continuum finite-element models (encompassing a range of parameters including cross section, axial load ratio, moment gradient, and loading history) are constructed to inform as well as validate the presented methodology. The methodology simulates various aspects (load-deformation response, localized deformation, and column axial shortening) with accuracy and without mesh dependence. This is in contrast to conventional fiber models that exhibit severe mesh dependence. Limitations are discussed.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This work was supported by the National Science Foundation (Grant No. CMMI 1434300), as well as graduate fellowships from the University of California at 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. Chicago: AISC.
Armstrong, P. J., and C. O. Frederick. 1966. A mathematical represenation of the multiaxial Bauschinger effect. Berkeley, UK: Berkeley Nuclear Laboratories, Research and Development Dept.
ASCE. 2017. Minimum design loads for buildings and other structures. ASCE/SEI-7. Reston, VA: ASCE.
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).
Chaboche, K. D. V., V. Dang, and G. Codier. 1979. “Modelization of the strain moment effect on the cyclic hardening of 316 stainless steel.” In Proc., Structural Mechanics in Reactor Technology—SmiRT 5, L11. Raleigh, NC: International Association for Structural Mechanics in Reactor Technology.
Chen, C.-H., W.-C. Lai, P. Cordova, G. G. Deierlein, and K. C. Tsai. 2004. “Pseudo-dynamic testing of a full-scale RCS frame: Part 1—Design, construction, and testing.” In Proc., 13th World Conf. on Earthquake Engineering. Vancouver, BC: International Association for Earthquake Engineering.
Clark, P., K. Frank, H. Krawinkler, and R. Shaw. 1997. Protocol for fabrication, inspection, testing, and documentation of beam-column connection tests and other experimental specimens. Washington, DC: FEMA.
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).
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.
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.
Elkady, A., and D. G. Lignos. 2018a. “Full-scale testing of deep wide-flange steel columns under multiaxis cyclic loading: Loading sequence, boundary effects, and lateral stability bracing force demands.” J. Struct. Eng. 144 (2): 04017189. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001937.
Elkady, A., and D. G. Lignos. 2018b. “Improved seismic design and nonlinear modeling recommendations for wide-flange steel columns.” J. Struct. Eng. 144 (9): 04018162. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002166.
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. 2009. Quantification of building seismic performance factors. FEMA-P695. Washington, DC: FEMA.
Hibbitt, D., B. Karlsson, and P. Sorensen. 2013. Abaqus/CAE user’s guide, ABAQUS 6.11. Providence, RI: Dassault Systèmes Simulia.
Ibarra, L. F., and H. Krawinkler. 2005. Global collapse of frame structures under seismic excitations. Stanford, CA: Stanford Univ.
Ibarra, L. G., R. 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.
Inamasu, H., D. Lignos, and A. M. Kanvinde. 2018. “Effect of column base flexibility on earthquake induced residual deformation of steel columns.” In Proc., 9th Int. Conf. on the Behavior of Steel Structures in Seismic Areas STESSA 2018. Christchurch, New Zealand: Steel Construction New Zealand Incorporated.
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.
Kasai, K., T. Nam, and B. Maison. 2016. “Structural collapse correlative analysis using phenomenological fiber hinge elements to simulate two-directional column deteriorations.” Earthquake Eng. Struct. Dyn. 45 (10): 1581–1601. https://doi.org/10.1002/eqe.2742.
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.
Kolwankar, S. S., A. M. Kanvinde, M. Kenawy, D. G. Lignos, and S. Kunnath. 2018. “Simulating local buckling-induced softening in steel members using an equivalent nonlocal material model in displacement-based fiber elements.” J. Struct. Eng. 144 (10): 04018192. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002189.
LATBSDC (Los Angeles Tall Building Structural Design Council). 2017. “An alternative procedure for seismic analysis and design of tall buildings located in the Los Angeles region, 2017 edition.” Accessed March 20, 2018. http://www.tallbuildings.org/.
Lignos, D. G., T. Hikino, Y. Matsuoka, and M. Nakashima. 2013. “Collapse assessment of steel moment frames based on e-defense full-scale shake table collapse tests.” J. Struct. Eng. 139 (1): 120–132. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000608.
Lignos, D. G., and H. Krawinkler. 2013. “Development and utilization of structural component databases for performance-based earthquake engineering.” J. Struct. Eng. 139 (8): 1382–1394. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000646.
Lignos, D. G., H. Krawinkler, and A. Whittaker. 2011. “Prediction and validation of sidesway collapse of two scale models of a 4-story steel moment frame.” Earthquake Eng. Struct. Dyn. 40 (7): 807–825. https://doi.org/10.1002/eqe.1061.
McKenna, F., G. L. Fenves, M. H. Scott, and B. Jeremic. 2012. Open system for earthquake engineering simulation (OpenSees). Berkeley, CA: Pacific Earthquake Engineering Research Center, Univ. of California.
Newell, J. D., and C. M. Uang. 2008. “Cyclic behavior of steel wide-flange columns subjected to large drift.” J. Struct. Eng. 134 (8): 1334–1342. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:8(1334).
PEER (Pacific Earthquake Engineering Research Center). 2010. Guidelines for the performance-based seismic design of tall buildings. Berkeley, CA: PEER.
Rahnama, M., and H. Krawinkler. 1993. Effects of soft soil and hysteresis model on seismic demands. Stanford, CA: John A. Blume Earthquake Engineering Center, Stanford Univ.
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.
Salehi, M., and P. Sideris. 2018. “A finite-strain gradient-inelastic beam theory and a corresponding force-based frame element formulation.” Int. J. Numer. Methods Eng. 116 (6): 380–411. https://doi.org/10.1002/nme.5929.
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. Kanvinde, and G. G. Deierlein. 2017b. “Calibration of continuum cyclic constitutive models for structural steel using particle swarm optimization.” J. Eng. Mech. 143 (5): 04017012. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001214.
Smith, C. M., A. M. Kanvinde, and G. G. Deierlein. 2017a. “A local criterion for ductile fracture under low-triaxiality axisymmetric stress states.” Eng. Fract. Mech. 169 (Jan): 321–335. https://doi.org/10.1016/j.engfracmech.2016.10.011.
Sousa, A. C., and D. G. Lignos. 2017. On the inverse problem of classic nonlinear plasticity models—An application to cyclically loaded structural steels. Lausanne, Switzerland: Resilient Steel Structures Laboratory, École Polytechnique Fédérale de Lausanne.
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.
Suzuki, Y. 2019. “Earthquake-induced collapse of steel moment resisting frames with conventional and high performance steel columns.” Ph.D. dissertation, Dept. of Civil Engineering, McGill Univ.
Suzuki, Y., and D. G. Lignos. 2014. “Development of loading protocols for experimental testing of steel columns subjected to combined high axial load and lateral drift demands near collapse.” In Proc., 10th National Conf. on Earthquake Engineering. Anchorage, AK: Earthquake Engineering Research Institute.
Suzuki, Y., and D. G. Lignos. 2015. “Large scale collapse experiments of wide-flange steel beam-columns.” In Proc., 8th Int. Conf. on Behavior of Steel Structures in Seismic Areas (STESSA). Shanghai, China: Tongji Univ.
Suzuki, Y., and D. G. Lignos. 2018. “Fiber-based model for earthquake induced collapse simulation of steel frame buildings.” In Proc., 11th US National Conf. on Earthquake Engineering. Oakland, CA: Earthquake Engineering Research Institute.
Uang, C.-M., G. Ozkula, and J. Harris. 2015. “Observations from cyclic tests on deep slender wide-flange steel beam-column members.” In Proc., Structural Stability Research Council. Chicago, IL: Structural Stability Research Council.
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 non-local strain measure for softening plasticity.” In Proc., Localization and Bifurcation Theory for Soil and Rocks, 89–100. Rotterdam, Nethrelands: A.A. Balkema.
Voce, E. 1948. “The relationship between stress and strain for homogenous deformation.” J. Inst. Met. 74: 537–562.
Wu, S., and X. Wang. 2008. “Comparison of boundary conditions of gradient elasticity and gradient plasticity.” In Proc., Inaugural Int. Conf. of the Engineering Mechanics Institute. Minneapolis, MN: Univ. of Minnesota.
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.
Yang, Y.-B., and L.-J. Leu. 1991. “Force recovery procedures in nonlinear analysis.” Comput. Struct. 41 (6): 1255–1261. https://doi.org/10.1016/0045-7949(91)90262-K.
Zhang, G., and K. Khandelwal. 2016. “Modeling of nonlocal damage-plasticity in beams using isogeometric analysis.” Comput. Struct. 165 (Mar): 76–95. https://doi.org/10.1016/j.compstruc.2015.12.006.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 146 • Issue 1 • January 2020
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jul 26, 2018
Accepted: Apr 25, 2019
Published online: Oct 29, 2019
Published in print: Jan 1, 2020
Discussion open until: Mar 29, 2020
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.