Technical Papers
Sep 17, 2021

Simplified Modal Pushover Analysis to Estimate First- and Higher-Mode Force Demands for Design of Strongback-Braced Frames

Publication: Journal of Structural Engineering
Volume 147, Issue 12

Abstract

Strongback-braced frames employ an essentially elastic truss, or strongback, that defines an elastic load path to redistribute seismic demands and mitigate the formation of story mechanisms. However, unlike the forces from traditional capacity design—which assumes that inelastic response limits the earthquake-induced forces—design forces in the strongback arise from a nonlinear first mode and near-elastic higher-mode response, because the strongback is designed to remain elastic in every mode. A design method using modal pushover analysis, which combines the response from pushover analyses in multiple modes, can estimate the magnitude and distribution of the force demands in the first and higher modes, including inelastic response. The existing modal pushover analysis procedure is simplified and applied to the design of the strongback in strongback-braced frames. Accounting for only the first mode of response resulted in estimates below the 16th percentile of force demands extracted from nonlinear dynamic analysis. However, a modal pushover approach using multiple modes resulted in improved estimates able to represent both the distribution and magnitude of the peak force demands from nonlinear dynamic analysis of eight- and four-story strongback-braced frames with buckling-restrained braces, while maintaining the conceptual simplicity of nonlinear static analysis procedures.

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Data Availability Statement

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon request.

Acknowledgments

This study was the result of many years of support and guidance from Professor Stephen Mahin. This work would not have been possible without his insight and advice. Numerous individuals, companies, and organizations donated their time, expertise, and services and were essential to the completion of this work, including Rafael Sabelli (Walter P. Moore and Associates, Inc.), James Malley (Degenkolb Engineers), Leo Panian (Tipping Structural Engineers), and Walterio Lopez (Rutherford + Chekene), among many others. The analytical work reported herein was supported by a research grant titled “Design of Strongback Braced Frames,” funded by the American Institute of Steel Construction (AISC). Any opinions, findings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of AISC or other participants in the research program.

References

AISC (American Institute of Steel Construction). 2016. Seismic provisions for structural steel buildings. AISC 341-16. Chicago: AISC.
ASCE. 2016. Minimum design loads for buildings and other structures. ASCE 7-16. Reston, VA: ASCE.
ASCE. 2017. Seismic evaluation and retrofit of existing buildings. ASCE 41-17. Reston, VA: ASCE.
Bosco, M., E. Marino, and P. Rossi. 2018. “A design procedure for pin-supported rocking buckling-restrained braced frames.” Earthquake Eng. Struct. Dyn. 47 (14): 2840–2863. https://doi.org/10.1002/eqe.3112.
Bracci, J. M., S. K. Kunnath, and A. M. Reinhorn. 1997. “Simplified seismic performance and retrofit evaluation of reinforced concrete structures.” J. Struct. Eng. 123 (1): 3–10. https://doi.org/10.1061/(ASCE)0733-9445(1997)123:1(3).
Buniya, M. B., S. Macedo, J. Vergaray, and A. Barbosa. 2020. “Collapse fragility function development using conditional scenario spectra: application to a multi-story reinforced concrete shear wall.” In Proc., World Conf. on Earthquake Engineering. Tokyo: Japan Association for Earthquake Disaster Prevention.
Chen, L., R. Tremblay, and L. Tirca. 2019. “Practical seismic design procedure for steel braced frames.” J. Constr. Steel Res. 153 (Feb): 395–415. https://doi.org/10.1016/j.jcsr.2018.10.010.
Chen, X., T. Takeuchi, and R. Matsui. 2018. “Seismic performance and evaluation of controlled spine frames applied in high-rise buildings.” Earthquake Spectra 34 (3): 1431–1458. https://doi.org/10.1193/080817EQS157M.
Chopra, A. K. 2011. Dynamics of structures—Theory and applications to earthquake engineering. 4th ed. Upper Saddle River, NJ: Prentice Hall.
Chopra, A. K., and R. K. Goel. 2002. “A modal pushover analysis procedure for estimating seismic demands for buildings.” Earthquake Eng. Struct. Dyn. 31 (3): 561–582. https://doi.org/10.1002/eqe.144.
Chopra, A. K., and R. K. Goel. 2004. “Evaluation of a modified MPA procedure assuming higher modes as elastic to estimate seismic demands.” Earthquake Spectra 20 (3): 757–778.
Djojo, G. S., G. C. Clifton, and R. S. Henry. 2014. “Rocking steel shear walls with energy dissipation devices.” In Proc., New Zealand Society for Earthquake Engineering Conf. Wellington, New Zealand: New Zealand Society on Earthquake Engineering.
Eberhard, M., and M. Sozen. 1993. “Behavior-based method to determine design shear in earthquake-resistant walls.” J. Struct. Eng. 119 (2): 619–640. https://doi.org/10.1061/(ASCE)0733-9445(1993)119:2(619).
Eibl, J., and E. Keintzel. 1988. “Seismic shear forces in RC cantilever shear walls.” In Proc., 9th World Conf. on Earthquake Engineering. Tokyo: Japan Association for Earthquake Disaster Prevention.
Fajfar, P., and M. Fischinger. 1988. “N2—A method for non-linear seismic analysis of regular structures.” In Proc., 9th World Conf. on Earthquake Engineering. Tokyo: Japan Association for Earthquake Disaster Prevention.
FEMA. 2000. Prestandard and commentary for the seismic rehabilitation of buildings. FEMA 356. Washington, DC: FEMA.
FEMA. 2005. Improvement of nonlinear static seismic analysis procedures. FEMA 440. Redwood City, CA: Applied Technology Council.
FEMA. 2009. Quantification of building seismic performance factors. FEMA P695. Redwood City, CA: Applied Technology Council.
Goel, R. K., and A. K. Chopra. 2005a. “Evaluation of modal and FEMA pushover analyses: SAC buildings.” Earthquake Spectra 20 (1): 225–254. https://doi.org/10.1193/1.1646390.
Goel, R. K., and A. K. Chopra. 2005b. “Extension of modal pushover analysis to compute member forces.” Earthquake Spectra 21 (1): 125–139. https://doi.org/10.1193/1.1851545.
Lai, J., and S. Mahin. 2013. Experimental and analytical studies on the seismic behavior of conventional and hybrid braced frames. Berkeley, CA: Univ. of California, Berkeley.
Lai, J., and S. Mahin. 2014. “Strong-back system: A way to reduce damage concentration in steel braced frames.” J. Struct. Eng. 141 (9): 04014223. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001198.
Liu, J., and A. Astaneh-Asl. 2000. “Cyclic testing of simple connections including effects of slab.” J. Struct. Eng. 126 (1): 32–39. https://doi.org/10.1061/(ASCE)0733-9445(2000)126:1(32).
Ma, X., H. Krawinkler, and G. Deierlein. 2011. Seismic design and behavior of self-centering braced frame with controlled rocking and energy dissipating fuses. Stanford, CA: Stanford Univ.
Mar, D. 2010. “Design examples using mode shaping spines for frame and wall buildings.” In Proc., 9th US National and 10th Canadian Conf. on Earthquake Engineering. Oakland, CA: Earthquake Engineering Research Institute.
Martin, A., G. Deierlein, and X. Ma. 2019. “Capacity design procedure for rocking braced frames using modified modal superposition method.” J. Struct. Eng. 145 (6): 04019041. https://doi.org/10.1061/(ASCE)ST.1943-541X.0002329.
McKenna, F., M. Scott, and G. Fenves. 2010. “Nonlinear finite-element analysis software architecture using object composition.” J. Comput. Civ. Eng. 24 (1): 95–107. https://doi.org/10.1061/(ASCE)CP.1943-5487.0000002.
Merritt, S., C. Uang, and G. Benzoni. 2003. Subassemblage testing of star seismic buckling-restrained braces. La Jolla, CA: Univ. of California.
Merzouq, S., and R. Tremblay. 2006. “Seismic design of dual concentrically braced steel frames for stable seismic performance for multi-story buildings.” In Proc., 8th US National Conf. on Earthquake Engineering. Oakland, CA: Earthquake Engineering Research Institute.
Osteraas, J., J. Hunt, and G. Luth. 2017. “Performance based seismic design of the gigafactory in tesla time.” In SEAOC convention. Sacramento, CA: Structural Engineers Association of California.
Panagiotou, M., and J. Restrepo. 2011. “Displacement-based method of analysis for regular reinforced-concrete wall buildings: Application to a full-scale 7-story building slice tested at UC–San Diego” J. Struct. Eng. 137 (6): 677–690. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000333.
Panian, L., N. Bucci, and B. Janhunen. 2015. “BRBM Frames: an improved approach to seismic-resistant design using buckling-restrained braces.” In Proc., 2nd ATC & SEI Conf. on Improving the Seismic Performance of Existing Buildings and Other Structures. Reston, VA: ASCE.
PEER (Pacific Earthquake Engineering Research Center). 2017. Tall building initiative: Guidelines for performance-based seismic design of tall buildings, version 2.0. Berkeley, CA: Univ. of California, Berkeley.
Pollino, M., D. Slovenec, B. Qu, and G. Mosqueda. 2017. “Seismic rehabilitation of concentrically braced frames using stiff rocking cores.” J. Struct. Eng. 143 (9): 04017080. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001810.
Priestley, M., and A. Amaris. 2003. “Dynamic amplification of seismic moments and shear forces in cantilever walls.” In Proc., FIB Symp. Concrete Structures in Seismic Regions, Lausanne, Switzerland: International Federation for Structural Concrete.
Qu, Z., A. Wada, S. Motoyui, H. Sakata, and S. Kishiki. 2012. “Pin-supported walls for enhancing the seismic performance of building structures.” Earthquake Eng. Struct. Dyn. 41 (14): 2075–2091. https://doi.org/10.1002/eqe.2175.
Roke, D., R. Sause, J. Ricles, and N. Gonner. 2009. “Damage-free seismic-resistant self-centering steel concentrically braced frames.” In Proc., 6th Int. Conf. on Behaviour of Steel Structures in Seismic Areas (STESSA 2009). Boca Raton, FL: CRC Press.
Rossi, P. 2007. “A design procedure for tied braced frames.” Earthquake Eng. Struct. Dyn. 36 (14): 2227–2248. https://doi.org/10.1002/eqe.734.
SEAOC (Structural Engineers Association of California). 2008. Reinforced concrete structures. Redwood City, CA: SEAOC.
Simpson, B. 2018. Design development for steel strongback braced frames to mitigate concentrations of damage. Berkeley, CA: Univ. of California, Berkeley.
Simpson, B. 2020. “Higher-mode force response in multi-story strongback-braced frames.” Earthquake Eng. Struct. Dyn. 49 (14): 1406–1427. https://doi.org/10.1002/eqe.3310.
Simpson, B., and S. Mahin. 2018. “Experimental and numerical investigation of strongback braced frame system to mitigate weak story behavior.” J. Struct. Eng. 144 (2): 04017211. https://doi.org/10.1061/(ASCE)ST.1943-541X.0001960.
Standards Association of New Zealand. 2006. Concrete design standard, NZS3101:2006, Part 1 and commentary on the concrete design standard. NZS 3101. Wellington, New Zealand: Standards Association of New Zealand.
Steele, T., and L. Wiebe. 2016. “Dynamic and equivalent static procedures for capacity design of controlled rocking steel braced frames.” Earthquake Eng. Struct. Dyn. 45 (14): 2349–2369. https://doi.org/10.1002/eqe.2765.
Stoakes, C. D., and L. A. Fahnestock. 2011. “Cyclic flexural testing of concentrically braced frame beam-column connections.” J. Struct. Eng. 137 (7): 739–747. https://doi.org/10.1061/(ASCE)ST.1943-541X.0000326.
Sullivan, T., M. Priestley, and G. Calvi. 2008. “Estimating the higher-mode response of ductile structures.” J. Earthquake Eng. 12 (3): 456–472. https://doi.org/10.1080/13632460701512399.
Tremblay, R. 2003. “Achieving a stable inelastic seismic response for multi-story concentrically braced steel frames.” AISC Eng. J. 40 (1): 111–129.
Tremblay, R., L. Chen, and L. Tirca. 2014. “Enhancing the seismic performance of multi-story buildings with a modular tied braced frame system with added energy dissipating devices.” Int. J. High-Rise Build. 3 (1): 21–33.
Tremblay, R., and L. Poncet. 2007. “Improving the seismic stability of concentrically braced steel frames.” Eng. J. AISC 44 (2): 103–116.
Wiebe, L., C. Christopoulos, R. Tremlay, and M. Leclerc. 2013. “Mechanisms to limit higher mode effects in a controlled rocking steel frame. 1: Concept, modelling, and low-amplitude shake table testing.” Earthquake Eng. Struct. Dyn. 42 (7): 1053–1068. https://doi.org/10.1002/eqe.2259.
Wiebe, L., G. Sidwell, and S. Gledhill. 2015. Design guide for controlled rocking steel braced frames. Manukau City, New Zealand: Steel Construction New Zealand.
Zsarnoczay, A. 2013. Experimental and numerical investigation of buckling restrained braced frames for Eurocode conform design procedure development. Budapest, Hungary: Budapest Univ. of Technology and Economics.

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Go to Journal of Structural Engineering
Journal of Structural Engineering
Volume 147Issue 12December 2021

History

Received: Jun 5, 2020
Accepted: Jun 29, 2021
Published online: Sep 17, 2021
Published in print: Dec 1, 2021
Discussion open until: Feb 17, 2022

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Assistant Professor, School of Civil and Construction Engineering, Oregon State Univ., 340 Owen Hall, Corvallis, OR 97331 (corresponding author). ORCID: https://orcid.org/0000-0002-3661-9548. Email: [email protected]
Design Engineer, Gregory P. Luth & Associates, Inc., 3350 Scott Blvd., Bldg. 48, Santa Clara, CA 95054. ORCID: https://orcid.org/0000-0002-8357-0513. Email: [email protected]

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  • Evaluation of Methods of Design for Strongback Braced Frames, Journal of Structural Engineering, 10.1061/JSENDH.STENG-13403, 150, 11, (2024).

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