Fundamentals of pushover analysis

Initial idea

Linear analysis methods, such as modal spectral analysis or the equivalent forces method, enable structures to be designed to withstand seismic actions. However, these procedures do not adequately represent the actual behaviour of a structure during high-intensity earthquakes.

When severe earthquakes occur, structural elements can experience cracking, plastic deformation and loss of stiffness – these are phenomena that are not captured by conventional elastic analyses.

The pushover analysis incorporates these effects through a non-linear approach, making it possible to assess the structure's capacity and seismic performance under extreme loads in a more realistic manner.

References and standard terminology

Pushover analysis is referred to in various standards using the following terminology:

• NSR-10 (Colombia): Method for static non-linear analysis of progressive yielding; "push-over" or progressive yielding procedure.
• NC-2017 (Cuba): Non-linear static "pushover" analysis
• Eurocode 8: Non-linear static analysis (incremental forces); Analysis by incremental forces (pushover)
• CFE-08 (Mexico): Non-linear analysis under a monotonically increasing load, also colloquially known as the "push-over" method
• NSRM-2021 (Managua): “…increasing lateral loads that progressively push the structure until it reaches its ultimate displacement.”
• R-001 2011 (Dominican Republic): Static pushover method
• RPA-2024 (Morocco): Méthode dite "Pushover" (Poussée Progressive) ["Pushover" method (Progressive Push)]

How does pushover analysis work?

Pushover analysis is a non-linear static analysis with displacement control. This entails the following:

• A pattern of lateral loads is applied incrementally to the structure to assess its behaviour beyond the elastic range. The process continues until a target displacement is reached at a control node (usually 5 per cent of the structure's height) or until collapse occurs.
• The method accounts for material non-linearities by defining plastic hinges, thereby enabling the simulation of cracking, plasticisation and the progressive degradation of structural stiffness.
• Pushover analysis is carried out using displacement control, by imposing successive increments of displacement at a control node and calculating the loads required to achieve them. This distinguishes it from non-linear stress-strain analysis, which is based on force control, where successive load increments are applied until the target load is reached.
• During the pushover analysis, the so-called capacity curve is obtained, which relates the base shear to the displacement of the control node. This curve makes it possible to identify the gradual loss of stiffness, assess the structure’s load-bearing capacity and analyse the sequence of plastic hinge formation.
• Furthermore, the procedure provides information on the collapse mechanism and the expected seismic performance, facilitating the detection of brittle deformation and the verification of performance-based design objectives.