The most recent technical building codes have introduced nonlinear static analysis, commonly known as pushover analysis, as a further tool for evaluating the behavior of structures subjected to earthquakes [Opcm 3274 p.4.5.4.1, Ntc08 p.7.3.4.1, Ntc18 p.7.3.4.2, EN1998-1 p.4.3.3.4.2]. In particular, the points cited state that nonlinear static analysis can be applied for the following purposes and cases:

  • evaluate the overstrength ratios αu/α1 which intervenes in the calculation of the structure factor q,
  • verify the actual distribution of inelastic demand in buildings designed with the structure factor q,
  • replacing linear analysis methods for new buildings,
  • as a method of assessing the capacity of existing buildings.

This analysis method is based on two assumptions:

  • that the response of the structure can be related to that of a "reduced equivalent" system with a single degree of freedom; 
  • that the dynamic response to seismic actions of the reduced system can be traced back to that of an "equivalent" elastic system.

The first assumption implies that the deformation of the structure is ultimately controlled by a single deformation mode and maintains the same shape for the entire duration of the earthquake; the second implies an appropriate definition of the parameters of the equivalent elastic system (mass, stiffness and viscosity) so that a simple relationship can be established between the maximum displacement excursions in the two systems. 

Both hypotheses are valid only as rough approximations, however, a large series of investigations have shown that, using this approach, significant information can be obtained about the actual behavior of structures, at least in the relatively frequent cases in which the response is dominated by a single deformation mode. Pushover analysis does indeed provide information, at least qualitatively, on important aspects of the response that in analyses based on linear-elastic modeling are only taken into account in a blanket manner through the heuristic introduction of the so-called structure factor q, in particular:

  • it allows to take into account the ductility and resistance reserves that the structure retains even beyond the elastic limit; 
  • allows to take into account the degradation of resistance in elements subject to high deformations; 
  • reports the presence of potentially fragile elements and their influence on the overall safety of the structure;
  • It indicates the elements and areas of the structure potentially subject to higher deformations. 

General information about pushover analysis

Nonlinear static analysis (also called pushover analysis) is performed on the elevation structure and assumes that the reinforcement in the elements is fully defined, both in the longitudinal bars and in the stirrups, and the materials are appropriately characterized in terms of their mechanical properties. Depending on the case, the reinforcement can derive from the design procedures activated downstream of a linear analysis, as in the case of newly designed buildings, or be set manually element by element, as in the case of existing buildings, when the construction drawings from the time of construction are available, or even through a simulated analysis of the design conditions.

Pushover analysis is performed by varying the seismic direction and acceleration distribution over the building's height. The user can specifically set the number of seismic scans to perform and select the acceleration distributions to apply in the analysis (linear only, constant only, linear and constant).


The analysis is conducted by applying quasi-permanent static loads to the structure (i.e., loads associated with seismic action using the partial coefficient ψ2) and a variable distribution of seismic accelerations acting in a predetermined direction. An incremental loading process is then established on the seismic action, which continues until collapse is reached. The resistant elements are considered to have elastic-plastic behavior, with limited ductility, and the limit rotations at yield and collapse are evaluated for them, according to the indications contained in reference texts such as Ntc18 and related Application Instructions.

During the analysis, the following limit states are recognized:

  • operational limit state (SLO), indicated by the first achievement of the yield rotation in some element (optional condition) or of the interstory limit slip, as defined in the Verification options sheet (see the paragraph of the same name later in this chapter), in correspondence with one of the frame meshes marked for this verification in the Beams sheet;
  • damage limit state (DLS), signaled by the first achievement of yield rotation in some element (optional condition) or of the interstory limit slip, as defined in the Check options sheet (see the homonymous paragraph later in this chapter), in correspondence with one of the frame meshes marked for this check in the Beams sheet;
  • life safety limit state (LSS), signalled by the first achievement of a predefined rate of collapse rotation in some element or by the first occurrence of a brittle collapse (optional condition for exceeding the shear resistance in the elements or nodes); 
  • collapse limit state (SLC), indicated by a load drop equal to 15% of the maximum value reached.

Pushover analysis can also be combined with linear analysis to more reliably evaluate a fundamental parameter for this type of analysis, the structural or behavior factor q, making it possible to calculate the overstrength ratio αu/α1 (between the accelerations at the ultimate limit and at the elastic limit) which intervenes as an internal factor in the expression of the structural factor. The standards also allow the use of pushover analysis as an independent method, alternative to linear analysis, for the evaluation of the seismic safety of buildings, whether newly designed or existing.

The seismic safety assessment, in particular, is performed by calculating the ground accelerations (PGA on rock) that the structure can sustain (PGA capacity) in the limit states mentioned (SLO, SLD, SLV, SLC) and comparing them with the corresponding design accelerations imposed by the regulations (PGA demand).