Computational Approach for Collapse Assessment of Concentrically Braced Frames in Seismic Regions
Publication: Journal of Structural Engineering
Volume 140, Issue 8
Abstract
This paper proposes a computational approach for the collapse assessment of concentrically braced frames (CBFs) subjected to earthquakes. Empirical formulations for modeling the postbuckling behavior and fracture of three main steel brace shapes that are commonly used in CBFs are developed. These formulations are based on extensive calibrations of a fiber-based steel brace model with available information from a recently developed steel brace database. As part of the same computational approach, the representation of strength and stiffness deterioration associated with plastic hinging in steel columns and gusset-plate beam-to-column connections is considered. Through a case study of a 12-story Special Concentrically Braced Frame (SCBF), the influence of classical damping on the collapse capacity of CBFs is investigated. It is demonstrated that when SCBFs attain a negative stiffness during an earthquake, their collapse capacity can be significantly overestimated, if viscous damping is based on a commonly employed Rayleigh assumption with initial stiffness approximation. It is shown that sidesway collapse of CBFs should be traced based on a combination of criteria that associate large story drift ratios and the story shear resistance of a CBF at the corresponding story drift ratios.
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Acknowledgments
This study is based on work supported by the National Science and Engineering Research Council of Canada (NSERC) under the Discovery Grant Program. Partial funding was provided by the McGill University Summer Undergraduate Research in Engineering (S.U.R.E) program to support Mr. Gabriel Martin, who contributed to the development of the steel brace database, which is briefly discussed in this paper. This financial support is gratefully acknowledged. The authors would like to sincerely thank Professor Ben Fell (Sacramento State), Dr. Patzi Uriz (Exponent Failure Analysis) and Professor Steven Mahin (University of California at Berkeley) for their willingness to share their experimental data to assemble part of the steel brace database discussed in the paper. Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of sponsors.
References
Abramson, M., Audet, C., Chrissis, J., and Walston, J. (2009). “Mesh adaptive direct search algorithms for mixed variable optimization.” Opt. Lett., 3(1), 35–47.
Aguero, A., Izvernari, C., and Tremblay, R. (2006). “Modelling of the seismic response of concentrically braced steel frames using the Opensees analysis environment.” Int. J. Adv. Steel Constr., 2(3), 242–274.
AIJ. (1995). Reconnaissance report on damage to steel building structures observed from the 1995 Hyogoken-Nanbu (Hanshin/Awaji) earthquake, Steel Committee of Kinki Branch, Architectural Institute of Japan, Tokyo, Japan.
AISC. (2005). “Seismic provisions for structural steel buildings, including supplement No. 1.” American Institute of Steel Construction (AISC), Chicago.
AISC. (2010a). “Seismic provisions for structural steel buildings.”, American Institute of Steel Construction (AISC), Chicago.
AISC. (2010b). “Specification for structural steel buildings.”, American Institute of Steel Construction (AISC), Chicago.
Baker, J. W. (2011). “Conditional mean spectrum: Tool for ground-motion selection.” J. Struct. Eng., 322–331.
Charney, F. (2008). “Unintended consequences of modeling damping in structures.” J. Struct. Eng., 581–592.
Chatterjee, S., Hadi, A. S., and Price, B. (2000). Regression analysis by example, 3rd Ed., Wiley, New York.
Coleman, J., and Spacone, E. (2001). “Localization issues in force-based frame elements.” J. Struct. Eng., 1257–1265.
Cornell, C. A., and Krawinkler, H. (2000). “Progress and challenges in seismic performance assessment.” PEER Center News, 3(2), 1–4.
De Souza, R. M. (2000). “Force-based finite element for large displacement inelastic analysis of frames.” Ph.D. dissertation, Univ. of California at Berkeley, Berkeley, CA.
Eads, L., Miranda, E., Krawinkler, H., and Lignos, D. G. (2013). “An efficient method for estimating the collapse risk of structures in seismic regions.” Earthquake Eng. Struct. Dynam., 42(1), 25–41.
Fell, B. V., Kanvinde, A. M., Deierlein, G. G., and Myers, A. T. (2009). “Experimental investigation of inelastic cyclic buckling and fracture of steel braces.” J. Struct. Eng., 19–32.
FEMA P695. (2009). “Quantification of building seismic performance factors.”, Federal Emergency Management Agency, Washington, DC.
Filippou, F. C., Popov, E. P., and Bertero, V. V. (1983). “Effects of bond deterioration on hysteretic behavior of reinforced concrete joints.”, Univ. of California at Berkeley, CA.
Gugerli, H., and Goel, S. C. (1982). “Inelastic cyclic behavior of steel bracing members.”, Dept. of Civil Engineering, Univ. of Michigan, Ann Arbor, MI.
Haselton, C. B., Baker, J. W., Liel, A. B., and Deierlein, G. G. (2011). “Accounting for ground-motion spectral shape characteristics in structural collapse assessment through an adjustment for Epsilon.” J. Struct. Eng., 332–344.
Haselton, C. B., and Deierlein, G. G. (2006). “Assessing seismic collapse safety of modern reinforced concrete moment frame buildings.”, Stanford Univ., Stanford, CA.
Higginbotham, A. B. (1973). “The inelastic cyclic behavior of axially-loaded steel members.” Ph.D. dissertation, Dept. of Civil Engineering, Univ. of Michigan, Ann Arbor, MI.
Hines, E. M., Appel, M. E., and Cheever, P. J. (2009). “Collapse performance of low-ductility chevron braced steel frames in moderate seismic regions.” Eng. J., (3), 149–180.
Hsiao, P. C., Lehman, D. E., and Roeder, C. W. (2013). “A model to simulate special concentrically braced frames beyond fracture.” Earthquake Eng. Struct. Dynam., 42(2), 183–200.
Hsiao, P. C., Lehman, D. E., and Roeder, C. W. (2012a). “Improved analytical model for special concentrically braced frames.” J. Constr. Steel Res., 73(3), 80–84.
Huang, Y., and Mahin, S. A. (2010). “Simulating the inelastic seismic behavior of steel braced frames including the effects of low-cycle fatigue.”, Univ. of California at Berkeley, CA.
Ibarra, L. F., Medina, R., and Krawinkler, H. (2002). “Collapse assessment of deteriorating SDOF systems.” Proc., 12th European Conf. on Earthq. Eng, Elsevier Science, London.
Ibarra, L. F., Medina, R. A., and Krawinkler, H. (2005). “Hysteretic models that incorporate strength and stiffness deterioration.” Earthquake Eng. Struct. Dynam., 34(12), 1489–1511.
Ikeda, K., and Mahin, S. A. (1986). “Cyclic response of steel braces.” J. Struct. Eng., 342–361.
Ikeda, K., Mahin, S. A., and Dermizakis, S. N. (1984). “Phenomenological modeling of steel braces under cyclic loading.”, Earthquake Engineering Research Center (EERC), Univ. of California, Berkeley, CA.
Jin, J., and El-Tawil, S. (2003). “Inelastic cyclic model for steel braces.” J. Eng. Mech., 548–557.
Karamanci, E., and Lignos, D. G. (2013). “Collapse assessment and performance-based evaluation techniques for concentrically braced frames designed in seismic regions.” M.S. thesis, Dept. of Civil Engineering and Applied Mechanics, McGill Univ., Montreal, QC.
Krawinkler, H. (1978). “Shear in beam-column joints in seismic design of steel frames.” Eng. J., 15(3), 82–91.
Krawinkler, H., and Miranda, E. (2006). “Performance-based earthquake engineering.” Chapter 9, Earthquake engineering: From engineering seismology to performance-based engineering, 1st Ed., Y. Borzognia and V. Bertero, eds., CRC, Boca Raton, FL, 9-1–9-59.
Krishnan, S. (2010). “The modified elastofiber element for steel slender column and brace modeling.” J. Struct. Eng., 1350–1366.
Lai, J. (2012). “Experimental and analytical studies on the seismic behavior of conventional and hybrid braced frames.” Ph.D. dissertation, Univ. of California at Berkeley, CA.
Lee, K., and Bruneau, M. (2005). “Energy dissipation of compression members in concentrically braced frames: Review of experimental data.” J. Struct. Eng., 552–559.
Leger, P., and Dussault, S. (1992). “Seismic-energy dissipation in MDOF structures.” J. Struct. Eng., 1251–1269.
Lehman, D. E., Roeder, C. W., Herman, D., Johnson, S., and Kotulka, B. (2008). “Improved seismic performance of gusset plate connections.” J. Struct. Eng., 890–901.
Lignos, D. G., Hikino, T., Matsuoka, Y., and Nakashima, M. (2013). “Collapse assessment of steel moment frames based on E-Defense full-scale shake table collapse tests.” J. Struct. Eng., 120–132.
Lignos, D. G., and Karamanci, E. (2013). “Drift-Based and dual-parameter fragility curves for concentrically braced frames in seismic regions.” J. Construct. Steel Res., 90, 209–220.
Lignos, D. G., Karamanci, E., and Martin, G. (2012). “A steel database for modeling post-buckling behavior and fracture of concentrically braced frames under earthquakes.” Proc., 15th World Conf. of Earthquake Engineering, (15WCEE), Lisboa, Portugal.
Lignos, D. G., and Krawinkler, H. (2011). “Deterioration modeling of steel components in support of collapse prediction of steel moment frames under earthquake loading.” J. Struct. Eng., 1291–1302.
Lignos, D. G., and Krawinkler, H. (2012). “Sidesway collapse of deteriorating structural systems under seismic excitations.”, Stanford Univ., Stanford, CA.
Lignos, D. G., and Krawinkler, H. (2013). “Development and utilization of structural component databases for performance-based earthquake engineering.” J. Struct. Eng., 1382–1394.
Lignos, D. G., Krawinkler, H., and Whittaker, A. S. (2011). “Prediction and validation of sidesway collapse of two scale models of a 4-story steel moment frame.” Earthquake Eng. Struct. Dynam., 40(7), 1215–1228.
Liu, J., and Astaneh-Asl, A. (2000). “Cyclic testing of simple connections including effects of slab.” J. Struct. Eng., 32–39.
Liu, J., and Astaneh-Asl, A. (2004). “Moment-rotation parameters for composite shear tab connections.” J. Struct. Eng., 1371–1380.
Luco, N., and Bazzurro, P. (2007). “Does amplitude of ground motion records result in biased nonlinear structural drift responses?” Earthquake Eng. Struct. Dynam., 36(13), 1813–1835.
MacRae, G. A., Carr, A. J., and Walpole, W. R. (1990). “The seismic response of steel frames.”, Dept. of Civil Engineering, Univ. of Canterbury, Christchurch, New Zealand.
Manson, S. S. (1965). “Fatigue: A complex subject—some simple approximations.” Exp. Mech., 5(4), 193–226.
MATLAB Version 7.10.0 (R2010a) [Computer software]. Natick, MA, The Mathworks Inc.
McKenna, F. (1997). “Object oriented finite element programming frameworks for analysis, algorithms and parallel computing.” Ph.D. dissertation, Univ. of California at Berkeley, CA.
Medina, R., and Krawinkler, H. (2003). “Seismic demands for nondeteriorating frame structures and their dependence on ground motions.”, Stanford Univ., Stanford, CA.
Menegotto, M., and Pinto, P. E. (1973). “Method of analysis for cyclically loaded reinforced concrete plane frames including changes in geometry and non-elastic behavior of elements under combined normal force and bending.” Proc., IABSE Symposium on Resistance and Ultimate Deformability of Structures Acted on by Well Defined Repeated Loads, 15–22.
Nam, T. T., and Kasai, K. (2011). “Dynamic analysis of a full-scale four-story steel building experimented to collapse by strong ground motions.” Proc., 8CUEE Conf., Center for Urban Earthquake Engineering (CUEE), Tokyo, Japan.
Neuenhofer, A., and Filippou, F. C. (1997). “Evaluation of nonlinear frame finite-element models.” J. Struct. Eng., 958–966.
Newell, J., and Uang, C. M. (2006). “Cyclic behavior of steel columns with combined high axial load and drift demand.”, Dept. of Structural Engineering, Univ. of California, San Diego.
NIST. (2010). “Evaluation of the FEMA P-695 methodology for quantification of building seismic performance factors, GCR 10-917-8.” NEHRP consultants Joint Venture for the National Institute of Standards and Technology, Gaithersburg, MD.
Okazaki, T., Lignos, D. G., Hikino, T., and Kajiwara, K. (2013a). “Dynamic response of a chevron concentrically braced frames.” J. Struct. Eng., 515–525.
Okazaki, T., Lignos, D. G., Midorikawa, M., Ricles, J. M., and Love, J. (2013b). “Damage to steel buildings observed after the 2011 Tohoku-Oki earthquake.” Earthquake Spectra, 29(S1), 219–243.
OpenSees [Computer software]. McKenna.
PEER/ATC. (2010). “Modeling and acceptance criteria for seismic design and analysis of tall buildings.”, Applied Technology Council in cooperation with the Pacific Earthquake Engineering Research Center, Redwood City, CA.
Scott, M. H., and Ryan, K. L. (2013). “Moment-rotation behavior of force-based plastic hinge elements.” Earthquake Spectra, 29(2), 597–607.
Spacone, E., Filippou, F. C., and Taucer, F. F. (1996). “Fiber beam-column model for nonlinear analysis of R/C frames, part I: Formulation.” Earthquake Eng. Struct. Dynam., 25(7), 711–725.
Stoakes, C. D. (2012). “Beam-column connection flexural behavior and seismic collapse performance of concentrically braced frames.” Ph.D. dissertation, Dep. of Civil Engineering, Univ. of Illinois at Urbana-Champaign, IL.
Stoakes, C. D., and Fahnestock, L. A. (2011). “Cyclic flexural testing of concentrically braced frame beam-column connections.” J. Struct. Eng., 739–747.
Suita, K., Yamada, S., Tada, M., Kasai, K., Matsuoka, Y., and Shimada, Y. (2008). “Collapse experiment on 4-story steel moment frame: Part 2 detail of collapse behaviour.” Proc., 14th World Conf. on Earthquake Engineering, (14WCEE), China Earthquake Administration, Ministry of Housing and Urban-Rural Development, Beijing, China.
Tremblay, R. (2002). “Inelastic seismic response of steel bracing members.” J. Construct. Steel Res., 58(5–8), 665–701.
Tremblay, R., Bruneau, M., Nakashima, M., Prion, H. G. L., Filiatrault, A., and DeVall, R. (1996). “Seismic design of steel buildings: Lessons from the 1995 Hyogo-ken Nanbu earthquake.” Can. J. Civ. Eng., 23(3), 727–756.
Uriz, P. (2005). “Towards earthquake resistant design of concentrically braced steel structures.” Ph.D. dissertation, Dept. of Civil and Environmental Engineering, Univ. of California, Berkeley, CA.
USGS. (2011). “Java ground motion parameter calculator.” Version 5.1.0., U.S. Geological Survey, 〈http://earthquake.usgs.gov/hazards/designmaps/javacalc.php〉 (June 10th, 2012).
Vamvatsikos, D. (2011). Some thoughts on methods to compare the seismic performance of alternative structural designs, 1st Ed., M. Dolšek, ed., Springer, NY.
Vamvatsikos, D., and Cornell, C. A. (2002). “Incremental dynamic analysis.” Earthquake Eng. Struct. Dynam., 31(3), 491–514.
Wakabayashi, M., Nakamura, T., and Yoshida, N. (1977). “Experimental studies on the elastic-plastic behavior of braced frames under repeated horizontal loading. Part 1 experiments of braces with an H-shaped cross section in a frame.” Bull. Disast. Prev. Res. Inst., 27(3), 121–154.
Yang, F., and Mahin, S. (2005). “Limiting net section fracture in slotted tube braces.” Steel TIPS Report 2005, Structural Steel Educational Council.
Zareian, F., and Krawinkler, H. (2009). “Simplified performance based earthquake engineering.”, Stanford Univ., Stanford, CA.
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Published In
Journal of Structural Engineering
Volume 140 • Issue 8 • August 2014
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Dec 30, 2012
Accepted: Nov 25, 2013
Published online: May 28, 2014
Published in print: Aug 1, 2014
Discussion open until: Oct 28, 2014
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