# Simplified Pushover Analysis for Rapid Assessment of Shear-Type Frames
###### Abstract  
A simplified pushover method for rapidly assessing the seismic capacity of shear-type frames is presented. The frame global force-displacement capacity is described as a trilinear curve passing through three limit states (LS): Damage LS (DLS), Life safety LS (LLS), and Collapse LS (CLS). The global LSs are obtained consequently to the attainment of story-level, element-level, and section-level LSs. All LS capacities are described through closed-form equations. The validity of the proposed method is verified by applying it on several reinforced concrete (RC) frames with a varying number of stories. The results obtained with such an analytical procedure show a good match with those obtained from pushover based on finite element method (FEM) analysis models, in terms of both global force-displacement capacity curves and story displacements at various LSs. The proposed method has the potential to be conveniently applied in large-scale vulnerability/risk assessment studies, where the quality and quantity of the available data call for the use of simplified yet accurate models. More refined models would in fact require significantly heavier computational efforts, not justified by the quality of the results that are usually obtained. The simplicity of the proposed method in such a context is demonstrated through the development of the fragility curves of a five-story shear-type reinforced concrete frame, starting from a predefined set of mechanical and geometrical features characterizing a building typology. a _Applied_  
for example, in the Italian construction code [4]. Alternatively, pushover analysis aims to describe the dynamic nonlinear response of a structure through the application of an equivalent static system of forces or displacements. The method is relatively simple to use, and the results obtained are easy to interpret, since the response can be depicted in the form of a curve showing the variation of the total base-shear as a function of the displacement of a certain control point. The profile of the forces distribution along the height can be either fixed or adaptive. The fixed profile is effective in estimating the response of low-to-mid-height structures where the contribution of higher modes is negligible, and the plastic deformations are well distributed throughout the height [5; 6; 7; 8; 9; 10; 11; 12]. The adaptive profile is applied in assessment of taller irregular structures where the deformation and inertial forces are not dominated by first mode [13; 14; 15; 16]. Pushover analysis was originally formulated for single degree-of-freedom systems [17; 18; 19] but is now extensively used for the assessment of regular and irregular multistory buildings and bridge structures [20; 21; 22]. In the literature, there are currently different formulations suggested for pushover analysis, with a detailed indication of the pros and cons of each formulation presented in [23]. Pushover analysis is now recognized as a reliable assessment procedure, with the capability of guiding towards the identification of critical components in a structure [24]. It is therefore recommended as an effective assessment tool by a number of codes around the world [4; 23; 25; 26]. Despite the recognized advantages of the standard pushover analysis, its application in performing large-scale analyses (for example, territorial risk/vulnerability assessments) is limited because of its extensive computational load, due to the numerous calculation steps needed to follow the entire structural response well into the nonlinear range. For this reason, the development of a non-iterative simplified pushover procedure is essential to provide an acceptable compromise between accuracy and computational effort. An analytical simplified procedure for pushover analysis has already been proposed for the case of existing masonry structures [27] and of masonry building clusters [28; 29].