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Capacity Design of Rocking Braced Frames

Graduate Researcher(s): 
Amory Martin (Ph.D. 2020,
Xiang Ma (Ph.D. 2010)
Faculty Advisor/PI: 
Greg Deierlein
Matthew Eatherton, Jerome Hajjar, Sarah Billington, Helmut Krawinkler, David Mar, Greg Luth, Lydell Wiebe
Project Sponsor: 
National Science Foundation (NSF), Grant No. DGE-114747

In the event of strong earthquakes, rocking braced frames offer improved seismic performance by quasi-eliminating residual drifts with post-tensioning (PT) cables and allocating all structural damage to energy dissipating (ED) devices. These ED elements consist of either fluid viscous dampers, steel shear plates, friction sliders or buckling restrained braces. The steel braced frame remains elastic while all of the inelasticity is concentrated at the rocking hinge in the ED elements. These innovative structural systems are advantageous since they lead to a pre-allocation of structural damage and hence reduction in overall downtime of the building.

Preliminary research focused on proof of concept and quantifying seismic performance through large experimental programs at the University of Illinois at Urbana-Champaign and E-Defense in Japan [3, 4, 5]. Steel plate butterfly shear fuses were tested in the Blume Center at Stanford University to investigate their performance as energy dissipating replaceable fuses [6, 7]. Key limit states and recommendations for desiging the PT and ED were determined based on experimental testing and computational studies [3]. Finally, a capacity design methodology was developed for the rocking spine using modified response spectrum analyses [1, 2]. Current research is focused on applying the capacity design methodology to alternative rocking configurations, coupled, stacked rocking as well as the strongback systems. 



[1] Martin, A., Deierlein, G. G., Ma, X. (2019). Capacity Design Procedure for Rocking Braced Frames Using Modified Modal Superposition Method. Journal of Structural Engineering, 145(6), 04019041.
[2] Martin, A. (2020). Capacity Design and Topology Optimization of Rocking Spine Systems for Nonlinear Earthquake Response. Ph.D. Dissertations, Stanford University.
[3] Eatherton, M., Ma, X., Krawinkler, H., Mar, D., Billington, S., Hajjar, J., and Deierlein, G. (2014). "Design Concepts for Controlled Rocking of Self-Centering Steel-Braced Frames." J. Struct. Eng., 10.1061/(ASCE)ST.1943-541X.0001047, 04014082.
[4] Eatherton, M., Ma, X., Krawinkler, H., Deierlein, G., and Hajjar, J. (2014). "Quasi-Static Cyclic Behavior of Controlled Rocking Steel Frames." J. Struct. Eng., 10.1061/(ASCE)ST.1943-541X.0001005, 04014083.
[5] Deierlein, G., Krawinkler, H., Ma, X. , Eatherton, M., Hajjar, J., Takeuchi, T., Kasai, K. and Midorikawa, M. (2011), Earthquake resilient steel braced frames with controlled rocking and energy dissipating fuses. Steel Construction, 4: 171–175. doi:10.1002/stco.201110023
[6] Ma, X and Krawinkler, H and Deierlein, GG. (2013). Seismic Design and Behavior of Self-Centering Braced Frame with Controlled Rocking and Energy Dissipating Fuses. John A. Blume Earthquake Engineering Center Technical Report 174. Stanford Digital Repository. Available at:
[7] Ma, X, Borchers, E, Peña, A, Krawinkler, H, Billington, SL and Deierlein, GG. (2010). Design and behavior of steel shear plates with openings as energy-dissipating fuses. John A. Blume Earthquake Engineering Center Technical Report 173. Stanford Digital Repository. Available at: