Engineering Structures 26 (2004) 2021–2035 www.elsevier.com/locate/engstruct Seismic response of steel frames under repeated earthquake ground motions M. Fragiacomo  , C. Amadio, L. Macorini Department of Civil Engineering, University of Trieste, Piazzale Europa 1, 34127 Trieste, Italy Received 26 June 2003; received in revised form 6 August 2004; accepted 6 August 2004 Abstract Seismic sequences characterized by the repetition of medium–strong earthquake ground motions occurring at short time one after the other were observed in many parts of the world. The paper investigates the effects produced by these events on steel structures. Single-degree-of-freedom (SDOF) systems with elastic–plastic laws, moment resistant frames with rigid and semi-rigid joints, and a concentrically braced steel frame have been analysed under seismic sequences. Both the SDOF systems and steel frames are characterized by a significant damage accumulation with respect to only one event. According to the approach where, for damage control limit state verifications, the seismic analysis of a non-linear system is performed through an elastic analysis by using the q-factor, a reduction in the q-factor is hence proposed. This reduction in the behaviour factor should be considered in earthquake-prone regions, where the repetition of seismic events may have a high probability of occurrence. # 2004 Elsevier Ltd. All rights reserved. Keywords: Behaviour factor; Concentrically braced frames; Damage control limit state; Moment resisting frames; Repeated earthquake ground motions; Seismic analysis; Single-degree-of-freedom systems; Steel frames 1. Introduction Many multi-level design approaches have recently been proposed as a basic philosophy for designing buildings in earthquake-prone regions. According to Eurocode 8 [1], for example, both ultimate and service- ability limit states (or damage limitation requirements) have to be satisfied by any structural system. Service- ability limit states are reached when damage compro- mises functionality of the structure. This type of control requires that the structure remains elastic with limited interstorey drift under medium intensity earthquakes (periods of return about 35–95 years according to Euro- code 8). Ultimate limit states are reached when any type of structural collapse, dangerous for the human life, may occur. In this case, the control requires a significant dissipative capacity of the structure in order to adequately resist destructive earthquakes (periods of return 475 years or 2500 years according to Eurocode 8 and US regulations, respectively). Other authors, such as Bertero [2], Mazzolani and Piluso [3], and Anastasiadis et al. [4], proposed three levels of verification: serviceability, damage control, and ultimate limit states. Four levels of structural per- formance were considered in SEAOC Vision 2000 [5,6]: fully operational, operational, life safety and near collapse for frequent, occasional, rare and very rare earthquakes, respectively. According to these criteria, a correct seismic design criterion should provide for a control on stiffness, strength, and ductility for each level of performance. By adopting a three-level design approach, generally suitable to achieve a fair compromise between accuracy of design and complexity of calculation, the following verifications may be required: . Serviceability limit state—control of structural stiff- ness under frequent earthquakes with low intensity, by performing a linear analysis;  Corresponding author. Tel.: +39-040-5583845; fax: +39-040- 54413. E-mail address: fragiacomo@dic.univ.trieste.it (M. Fragiacomo). 0141-0296/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2004.08.005