The Open Construction & Building Technology Journal

ISSN: 1874-8368 ― Volume 13, 2019

Seismic Assessment of Steel MRFs by Cyclic Pushover Analysis

F. Barbagallo*, M. Bosco, A. Ghersi, E.M. Marino, P.P. Rossi
Department of Civil Engineering and Architecture, University of Catania, via Santa Sofia, Catania, 64, Italy



Structural members subjected to strong earthquakes undergo stiffness and strength degradation. To predict accurately the seismic behaviour of structures, nonlinear static methods of analysis have been developed in scientific literature. Generally, nonlinear static methods perform the pushover analysis by applying a monotonic lateral load. However, every earthquake input is characterized by several repeated loads with reverse in signs and the strength and deformation capacities of structures are generally related to the cumulative damage. This aspect is neglected by the conventional monotonic approaches, which tend to overestimate the strength and stiffness of structural members.


This paper aims to investigate the possibility that the Cyclic Pushover Analysis (CPA) may be used as a tool to assess the seismic behaviour of structures. During the CPA, the structure is subjected to a distribution of horizontal forces that is reversed in sign when predefined peak displacements of the reference node are attained. This process repeats in cycles previously determined in a loading protocol.


To investigate the effectiveness of the CPA in predicting the structural response, a steel moment resisting frame is designed as a case study building. A numerical model of this frame is developed in OpenSees. To examine the influence of the loading protocols on the seismic response, the CPA is run following the ATC-24 and the SAC protocols. Additionally, the seismic demand of the case study frame is determined by a Monotonic Pushover Analysis (MPA) and by Incremental nonlinear Dynamic Analysis (IDA).

Results and Conclusions:

The following results are obtained:

• Despite the differences between the SAC and the ATC-24 loading protocols, the CPA applied according to those two protocols led to almost the same structural response of the case study frame.

• The CPA showed the capability of catching the stiffness and strength degradation, which is otherwise neglected by the MPA. In fact, given a base shear or peak ground acceleration, the CPA leads to the estimation of larger displacement demands compared to the MPA.

• During long (or medium) duration earthquakes, the CPA was necessary to estimate accurately the response of the structure. In fact, at a PGA equal to 1 g, the CPA estimated the top displacement demand with an error lower than 10%, while the MPA underestimated it by 18%.

• The importance of considering the cyclic deterioration is shown at local level by the damage indexes of the frame. In the case of long earthquakes, given a top displacement of 600 mm (corresponding to a PGA equal to 1 g), the CPA estimated the damage indexes with an error equal to 12%.

Article Information

Identifiers and Pagination:

Year: 2019
Volume: 13
First Page: 12
Last Page: 26
Publisher Id: TOBCTJ-13-12
DOI: 10.2174/18748368019130012

Article History:

Received Date: 27/10/2018
Revision Received Date: 17/12/2018
Acceptance Date: 10/1/2019
Electronic publication date: 31/1/2019
Collection year: 2019

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© 2019 Barbagallo et al.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil Engineering and Architecture, University of Catania, via Santa Sofia, Catania, 64, Italy; Tel: +390957382254; E-mail:


"We greatly appreciate the efficient, professional and rapid processing of our paper by your team. The editors are so kind and professional to send us the reviewers' feedback in time. Those comments were all valuable and very helpful for us in revising and improving our paper."

Hailong Zhao
School of Civil Engineering,
Tianjin University, Tianjin,

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