A design procedure for dual eccentrically braced systems: Numerical investigation M. Bosco, P.P. Rossi ⁎ Department of Civil and Environmental Engineering, v.le Doria 6, 95125 Catania, Italy abstract article info Article history: Received 29 July 2011 Accepted 23 August 2012 Available online 8 November 2012 Keywords: Dual braced frame Link overstrength factor Damage distribution capacity Eccentrically braced frame Moment-resisting frame Earthquake-resistant design The paper investigates the seismic response of dual braced structures constituted by eccentrically braced frames and moment resisting frames. The response of dual braced structures designed according to the pro- cedure described in the companion paper is first examined with the aim of suggesting behaviour factors vary- ing with the mechanical length of the links. A larger set of structures is then designed according to the proposed values of the behaviour factor to validate the expression adopted. The seismic response of these structures is obtained by incremental dynamic analyses with reference to deterministic and random values of strength of steel. To highlight the qualities of the response of these structures the results of the dynamic analyses are compared to those obtained from structures designed according to procedures suggested by codes. A comparison is also carried out with conventional eccentrically braced frames in which the degree of interaction between the eccentrically braced frames and the other parts of the structure is purposely held very low. © 2012 Elsevier Ltd. All rights reserved. 1. Introduction In the past, many researchers demonstrated that the seismic re- sponse of steel systems can benefit from the interaction between mo- ment resisting frames (MRFs) and braced frames. Some papers have underlined that this interaction can reduce the interstorey displace- ments demanded by low intensity earthquakes to moment resisting frames [1] or the residual displacements developed by concentrically braced frames [2]. Some other papers [3–6] have highlighted that the presence of MRFs and braced frames in a single system can lessen the differences in the inelastic interstorey displacements along the height of the building and reduce the sensitivity of the seismic response to realistic variations in the mechanical properties of members. Despite the great importance attributed to the interaction between MRFs and braced frames, design methods proposed by building codes for dual framed systems still remain simplistic and often not very effec- tive. In the earliest formal appearance of the dual framed system in codes, the MRF was conceived as a reserve system and designed to pro- vide failsafe in the event of degradation of the braced frame [7]. The codes which conceived as such the dual framed system required that the braced frames resisted the whole seismic load and that the MRFs were capable of resisting not less than 25 % of the design base shear. This view of the dual framed system has changed in the course of time and more recent codes testify the transition of the MRF from an indepen- dent reserve system to part of the primary lateral system. In accordance with this new view, braced frames and MRFs of dual systems are now designed to resist seismic forces which derive from the distribution of the seismic load between frames according to their lateral stiffness (e.g. [8,9]). In an attempt to place a lower limit on the strength and stiffness of the MRFs, some building codes (e.g. [10,11]) also require that the MRFs are designed to resist at least 25% of the design base shear. As highlighted by some researchers [3,4] these design provisions do not ensure a substantial improvement in the seismic behaviour of braced structures because often the lateral strength and particularly the stiffness of the MRFs are much lower than those of the braced frames. Aware of this deficiency, in the late eighties Whittaker et al. [3] proposed designing MRFs for a higher lateral stiffness and strength. The design method remained centred on provisions which referred to global structural properties. Therefore, it was not able to adjust the lat- eral stiffness and strength of the single storey so as to achieve assigned distributions of the interstorey displacements. Also, the design method did not consider the deformative capacity of the single storey and thus was not able to ensure fairly uniform distributions of damage in the el- ements designated to the inelastic response. These drawbacks appear to be overcome by the design procedure pro- posed in the companion paper [12] for dual eccentrically braced struc- tures, i.e. for structures constituted by MRFs and eccentrically braced frames (EBFs). The procedure stems from previous studies on the inelastic behaviour of EBFs and is founded on the overstrength factor of links and on the damage distribution capacity factor of the single storey [13]. Owing to the dependency on local parameters, the proposed procedure can ensure design objectives which are more stringent than those usually considered in modern seismic codes. In particular, the seismic response Journal of Constructional Steel Research 80 (2013) 453–464 ⁎ Corresponding author. Tel.: +39 095 7382279; fax: +39 095 7382249. E-mail address: prossi@dica.unict.it (P.P. Rossi). 0143-974X/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jcsr.2012.08.003 Contents lists available at SciVerse ScienceDirect Journal of Constructional Steel Research