Seismic Assessment of Steel MRFs by Cyclic Pushover Analysis

The Open Construction and Building Technology Journal 31 Jan 2019 RESEARCH ARTICLE DOI: 10.2174/18748368019130012



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%.

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