Phenomenological Hysteretic Model for Steel Braces Including Inelastic Postbuckling and Low-Cycle Fatigue Prediction
Publication: Journal of Structural Engineering
Volume 145, Issue 6
Abstract
This study presents a simple yet efficient phenomenological hysteretic model for hollow circular steel (HCS) braces without a middle connection in concentrically braced frames (CBFs). The model is calibrated on the basis of the available experimental results and on a series of numerical simulations by finite-element (FE) models, which are validated by existing experiments. The Miner linear cumulative damage theory based on the Coffin-Manson expression is used to represent the low-cycle fatigue deterioration of a brace subjected to cyclic loading. Furthermore, the cumulative yielding strength degradation is considered by a simplified formulation, which is defined as the cumulative fatigue damage. Comparisons of the hysteretic responses obtained by the proposed model with the results of the FE models show that this model can capture several failure modes of a brace during inelastic cyclic behaviors, such as yielding, inelastic postbuckling, strength degradation, and fracture due to low-cycle fatigue, as well as the fracture point. The cumulative dissipated energy of a brace is well-predicted by the model. In addition, this model takes much less computing time than the FE model and is therefore suitable for structural analyses. The model should be further examined to more precisely consider the effect of the local buckling of a brace with different cross-sectional geometries.
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 Natural Science Foundation of China (Grant No. 51078166). Any opinions, findings, and conclusions expressed in this paper are those of authors and do not necessarily reflect the views of those acknowledged here.
References
AISC. 2016. Seismic provision for structural steel buildings. ANSI/AISC 341. Chicago: AISC.
Asgarian, B., A. A. Aghakouchack, and R. G. Bea. 2005. “Inelastic postbuckling and cyclic behavior of tubular braces.” J. Offshore Mech. Arct. Eng. 127 (3): 256–262. https://doi.org/10.1115/1.1904637.
Black, R. G., W. A. Wenger, and E. P. Popov. 1980. Inelastic buckling of steel struts under cyclic load reversals. Berkeley, CA: Earthquake Engineering Research Center.
Brown, J., and S. K. Kunnath. 2000. Low-cycle fatigue behavior of longitudinal reinforcement in reinforced concrete bridge columns. Buffalo, NY: Multidisciplinary Center for Earthquake Engineering Research.
Chen, C. H., and H. K. Hu. 2017. “Evaluation of loading sequences on testing capacity of concentrically braced frame structures.” J. Constr. Steel Res. 130 (11): 1–11. https://doi.org/10.1016/j.jcsr.2016.11.017.
Coffin, L. F., Jr. 1954. “A study of the effects of cyclic thermal stresses on a ductile metal.” Trans. Am. Soc. Mech. Eng. 76: 931–950.
Davaran, A., and N. E. Far. 2009. “An inelastic model for low cycle fatigue prediction in steel braces.” J. Constr. Steel Res. 65 (3): 523–530. https://doi.org/10.1016/j.jcsr.2008.07.027.
Dicleli, M., and E. E. Calik. 2008. “Physical theory hysteretic model for steel braces.” J. Struct. Eng. 134 (7): 1215–1228. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:7(1215).
Dodd, L. L., and J. I. Restrepo-Posada. 1995. “Model for predicting cyclic behavior of reinforcing steel.” J. Struct. Eng. 121 (3): 433–445. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:3(433).
Downing, S. D., and D. F. Socie. 1982. “Simple rainflow counting algorithms.” Int. J. Fatigue 4 (1): 31–40. https://doi.org/10.1016/0142-1123(82)90018-4.
Fell, B. V. 2008. “Large-scale testing and simulation of earthquake-induced ultra low cycle fatigue in bracing members subjected to cyclic inelastic buckling.” Ph.D. thesis, Dept. of Civil and Environment Engineering, Univ. of California Davis.
Fukuta, T., I. Nishiyama, H. Yamanouchi, and B. Kato. 1989. “Seismic performance of steel frames with inverted V braces.” J. Struct. Eng. 115 (8): 2016–2028. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:8(2016).
Goggins, J. M., B. M. Broderick, A. Y. Elghazouli, and A. S. Lucas. 2005. “Experimental cyclic response of cold-formed hollow steel bracing members.” Eng. Struct. 27 (7): 977–989. https://doi.org/10.1016/j.engstruct.2004.11.017.
Haddad, M. 2015. “Concentric tubular steel braces subjected to seismic loading: Finite element modeling.” J. Constr. Steel Res. 104 (10): 155–166. https://doi.org/10.1016/j.jcsr.2014.10.013.
Hibbitt, H., B. Karlsson, and P. Sorensen. 2011. Abaqus analysis user’s manual version 6.10. Providence, RI: Dassault Systèmes Simulia.
Hill, C. D., G. E. Blandford, and S. T. Wang. 1989. “Post-buckling analysis of steel space trusses.” J. Struct. Eng. 115 (4): 900–919. https://doi.org/10.1061/(ASCE)0733-9445(1989)115:4(900).
Hooputra, H., H. Gese, H. Dell, and H. Werner. 2004. “A comprehensive failure model for crashworthiness simulation of aluminium extrusions.” Int. J. Crashworthiness 9 (5): 449–464. https://doi.org/10.1533/ijcr.2004.0289.
Hsiao, P. C., D. E. Lehman, and C. W. Roeder. 2013. “A model to simulate special concentrically braced frames beyond brace fracture.” Earthquake Eng. Struct. Dyn. 42 (2): 183–200. https://doi.org/10.1002/eqe.2202.
Ikeda, K., S. A. Mahin, and S. N. Dermitzakis. 1984. Phenomenological modeling of steel braces under cyclic loading. Berkeley, CA: Earthquake Engineering Research Center.
Jin, J., and S. El-Tawil. 2003. “Inelastic cyclic model for steel braces.” J. Eng. Mech. 129 (5): 548–557. https://doi.org/10.1061/(ASCE)0733-9399(2003)129:5(548).
Kanvinde, A. M., and G. G. Deierlein. 2006. “The void growth model and the stress modified critical strain model to predict ductile fracture in structural steels.” J. Struct. Eng. 132 (12): 1907–1918. https://doi.org/10.1061/(ASCE)0733-9445(2006)132:12(1907).
Karamanci, E., and D. G. Lignos. 2014. “Computational approach for collapse assessment of concentrically braced frames in seismic regions.” J. Struct. Eng. 140 (8): A4014019. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001011.
Kashani, M. M., L. N. Lowes, A. J. Crewe, and N. A. Alexander. 2015. “Phenomenological hysteretic model for corroded reinforcing bars including inelastic buckling and low-cycle fatigue degradation.” Comput. Struct. 156 (4): 58–71. https://doi.org/10.1016/j.compstruc.2015.04.005.
Krawinkler, H. 1992. Guidelines for cyclic seismic testing of components of steel structures. Vol. 24. Redwood City, CA: Applied Technology Council.
Krishnan, S. 2010. “Modified elastofiber element for steel slender column and brace modeling.” J. Struct. Eng. 136 (11): 1350–1366. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000238.
Kunnath, S. K., Y. Heo, and J. F. Mohle. 2009. “Nonlinear uniaxial material model for reinforcing steel bars.” J. Struct. Eng. 135 (4): 335–343. https://doi.org/10.1061/(ASCE)0733-9445(2009)135:4(335).
Lignos, D., and E. Karamanci. 2013. “Predictive equations for modelling cyclic buckling and fracture of steel braces.” In Proc., 10th Int. Conf. on Urban Earthquake Engineering, 105–107. Pathum Thani, Thailand: Asian Institute of Thailand.
Maison, B. F., and E. P. Popov. 1980. “Cyclic response prediction for braced steel frames.” J. Struct. Div. 106 (7): 1401–1416.
Manson, S. S. 1965. “Fatigue: A complex subject—Some simple approximations.” Exp. Mech. 5 (4): 193–226. https://doi.org/10.1007/BF02321056.
Miner, M. A. 1945. “Cumulative damage in fatigue.” J. Appl. Mech. 12 (3): A159–A164.
Prota, A., F. De Cicco, and E. Cosenza. 2009. “Cyclic behavior of smooth steel reinforcing bars: Experimental analysis and modeling issues.” J. Earthquake Eng. 13 (4): 500–519. https://doi.org/10.1080/13632460902837686.
Remennikov, A. M., and W. R. Walpole. 1997. “Modelling the inelastic cyclic behaviour of a bracing member for work-hardening material.” Int. J. Solids Struct. 34 (27): 3491–3515. https://doi.org/10.1016/S0020-7683(96)00212-0.
Roeder, C. W., E. J. Lumpkin, and D. E. Lehman. 2011. “A balanced design procedure for special concentrically braced frame connections.” J. Constr. Steel Res. 67 (11): 1760–1772. https://doi.org/10.1016/j.jcsr.2011.04.016.
Shaback, B., and T. Brown. 2003. “Behaviour of square hollow structural steel braces with end connection.” Can. J. Civ. Eng. 30 (4): 745–753. https://doi.org/10.1139/l03-028.
Thai, H. T., and S. E. Kim. 2011. “Nonlinear inelastic time-history analysis of truss structures.” J. Constr. Steel Res. 67 (12): 1966–1972. https://doi.org/10.1016/j.jcsr.2011.06.015.
Tremblay, R., M. H. Archambault, and A. Filiatrault. 2003. “Seismic response of concentrically braced steel frames made with rectangular hollow bracing members.” J. Struct. Eng. 129 (12): 1626–1636. https://doi.org/10.1061/(ASCE)0733-9445(2003)129:12(1626).
Uriz, P. 2005. “Towards earthquake resistant design of concentrically braced steel buildings.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley.
Uriz, P., F. C. Filippou, and S. A. Mahin. 2008. “Model for cyclic inelastic buckling of steel braces.” J. Struct. Eng. 134 (4): 619–628. https://doi.org/10.1061/(ASCE)0733-9445(2008)134:4(619).
Zayas, V. A., E. P. Popov, and S. A. Mahin. 1980. Cyclic inelastic buckling of tubular steel braces. Berkeley, CA: Univ. of California, Earthquake Engineering Research Center.
Zheng, H. D., and J. Fan. 2018. “Analysis of the progressive collapse of space truss structures during earthquakes based on a physical theory hysteretic model.” Thin Walled Struct. 123 (10): 70–81. https://doi.org/10.1016/j.tws.2017.10.051.
Zheng, H. D., J. Fan, and X. H. Long. 2017. “Analysis of the seismic collapse of a high-rise power transmission tower structure.” J. Constr. Steel Res. 134 (3): 180–193. https://doi.org/10.1016/j.jcsr.2017.03.005.
Ziegler, H. 1959. “A modification of Prager’s hardening rule.” Q. Appl. Math. 17 (1): 55–65. https://doi.org/10.1090/qam/104405.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 145 • Issue 6 • June 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: May 8, 2018
Accepted: Oct 25, 2018
Published online: Mar 18, 2019
Published in print: Jun 1, 2019
Discussion open until: Aug 18, 2019
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.