For Peer Review EARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS Earthquake Engng Struct. Dyn. 2015; 00:1–22 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/eqe Dynamic and equivalent static procedures for capacity design of controlled rocking steel braced frames Taylor C. Steele, Lydell D. A. Wiebe ∗, † Department of Civil Engineering, McMaster University, Hamilton ON, Canada SUMMARY Controlled rocking steel braced frames (CRSBFs) have been proposed as a low-damage seismic force resisting system with reliable self-centering capabilities. Vertical post-tensioning tendons are designed to self-center the system after rocking, and energy dissipation may be provided to limit the peak displacements. The post-tensioning and energy dissipation can be designed using simple methods that rely primarily on the first-mode response. However, the frame member forces are highly influenced by the higher-mode response, resulting in more complex methods to design the frame members. This paper examines previous proposals, and also proposes two new capacity design methods for CRSBFs. The first is a dynamic procedure that requires a truncated response spectrum analysis on a model of the frame with modified boundary conditions to consider the rocking behaviour. The second is an equivalent static method that does not require any modifications to the elastic frame model, instead using theory-based lateral force distributions to consider the higher modes of the rocking structure. Neither method requires empirical calibration. The dynamic procedure is used to design CRSBFs with three, six, nine, twelve, and eighteen stories, first using a response modification factor of R = 8, and again using up to R = 20. Based on the results of 800 non-linear time history analyses, both methods are generally more accurate than the previous capacity design methods, and at least as simple to implement. Finally, the displacement results suggest that taller CRSBFs designed using R ≥ 8 could still limit interstorey drifts to approximately 2.5% at the maximum considered earthquake level in the cases considered. Copyright c  2015 John Wiley & Sons, Ltd. Received . . . KEY WORDS: self-centering systems; controlled rocking steel braced frames; higher-mode effects; capacity design; truncated response spectrum analysis, equivalent static procedure 1. INTRODUCTION Current seismic design code provisions have been successful in aiding engineers to design structures that maintain life-safety during design-level earthquakes. However, these structures are often severely damaged by earthquakes and must be repaired or replaced, at great expense to the owner. In Christchurch, New Zealand, over 70% of the buildings in the central business district were demolished rather than replaced, with reconstruction costs estimated at approximately $20B USD [1]. State-of-the-art self-centering lateral force resisting systems have been in development to mitigate damage to structural components during earthquakes beyond the design level; one such system is a controlled rocking steel braced frame (CRSBF). CRSBFs are lateral force resisting systems that are designed to uplift from the foundation after a predetermined base overturning moment is exceeded. Figure 1 displays the idealised response * Correspondence to: Lydell Wiebe, Department of Civil Engineering, McMaster University, 1280 Main St. West, Hamilton ON, L8S 4L7, Canada. † Email: wiebel@mcmaster.ca Copyright c  2015 John Wiley & Sons, Ltd. Prepared using eqeauth.cls [Version: 2010/03/05 v3.00] Page 1 of 22 http://mc.manuscriptcentral.com/eqe Earthquake Engineering and Structural Dynamics 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60