Pushover analysis

A new advanced analysis type is available on Advance Design 2021 – the Pushover analysis.

The pushover is a method to predict the non-linear behavior of a structure under seismic loads. It can help demonstrate how progressive failure in buildings really occurs, and also identify the mode of final failure. The advantage of the pushover analysis is that the material nonlinearity and plastic hinging are considered but without the complications of the dynamic behavior.
The principle of the pushover method is applying lateral loads to the structure in an incremental manner and monitoring the occurrence of non-linear behavior (at fixed points called plastic hinges) in order to finally obtain a base shear versus control node displacement diagram.

Introduction to the Pushover method

The pushover analysis consists of several steps of calculations that need to be conducted in the following order.

Determination of the seismic lateral load pattern

In order to perform the pushover analysis, we need to increment the lateral loads following a specified fixed pattern. There are many possible load patterns described in the literature and seismic standards. For example, loads can be applied on the gravity center of each story linearly increasing in height, where load values are based on the seismic base shear force.

Defining plastic hinges in the model at locations where plasticity is expected to occur

During the pushover analysis the loads are incremented on the structure while plastic deformations are being constantly monitored. As plastic deformations are most likely to occur at specific locations, we define the non-linear behavior locally, on elements, via the plastic hinges, whilst maintaining the elastic behavior on all other elements. Generally, the behavior of plastic hinges is provided by seismic codes, in the form of tables or formulas that make it possible to construct the characteristic curves for plastic hinges. In the case of concrete elements, characteristic curves strongly depend on the provided reinforcement. For this reason, an initial classic linear seismic analysis should be conducted prior to the pushover analysis in order to provide an initial value for sections reinforcements.

Pushover calculations

The pushover analysis is a list of sequential actions. First, linear finite element analysis is run. One of the results used further on is the reinforcements of elements, used in defining the characteristic curve of plastic hinges. Next, the lateral load pattern is obtained and it applies to the structure. Then, in an iterative process, these loads are gradually increased. At every increment the internal forces at the location of potential plastic hinges, the base shear and the control point displacement are monitored. When the internal forces at a potential plastic hinge reach a yielding level, the plastic hinge is activated according to its characteristic curve previously defined. The stiffness matrix is adjusted accordingly, and the finite element calculation is continued. The incrementing lateral load is continued, and the matrix update process is repeated for all activated plastic hinges. Calculations are continued until either: the target displacement is reached; the structure becomes a mechanism; analysis does not converge anymore, or a maximum number of steps is reached.

At every step of incrementation the displacement of a control point on the structure is recorded with its corresponding base shear value. This data is then plotted on a curve, called the pushover curve. It is initially linear at relative low values of base shear (the structure is still elastic), then becomes non-linear for higher values of base shear due to plastic deformations occurring in the structure.

Pushover analysis on Advance Design
Main features of the Pushover analysis in Advance Design 2021:

Extended definition of Plastic Hinges
– Plastic hinges (linear elastic-perfect plastic) can be easily defined on linear elements;
– Available on the axial (Tx) and flexural (Ry and Rz) degrees of freedom;
– Can be defined automatically and fully customizable with respect to FEMA 356 and EC8-3;
– Automatic definition can be done for steel I – cross sections (IPE, HEA, W, …) and concrete Square, Rectangular and T-shaped cross sections;
– For concrete element plastic hinges can be computed using the real reinforcement (for Eurocode) or the theoretical reinforcement (North America codes);
– Can be user defined – allows for applying plastic hinges on any type of cross section, for both steel and concrete linear elements.
2. Automatic generation of pushover loads with extensive parameterization capabilities
– Pushover point & surface loads are defined at each floor;
– Possibility for selecting the load distribution on the height of the structure within several types: Concentrated, Uniform distributed, Triangular distributed, Parabolic distributed, User defined (fully customizable);
– Possibility for computing the maximum total lateral load by using the Percentage of the total gravity loads, by Seismic base shear force on X, and by Seismic base shear force on Y;
– Up to 8 load cases can be defined: 2 distributions (as required by FEMA356 and EC8-3) and 4 directions (+/-X, +/-Y).
3. Wide range of available Results
– FEM results and reports;
– The pushover force-displacement curve;
– Reports tables with status of hinges and the overstrength ratio (αu/α1);
– Graphical results showing the status of hinges at each load step.

Let’s take a closer look at the next steps of the process. We start from the stage when a model is already prepared for linear statics calculations (including defined geometry, levels, loads, etc.).

Definition of plastic hinges
In order to perform the pushover analysis, the user first needs to define the plastic hinges at locations where they are expected to occur (ends of beams), or at locations where their arise needs to be monitored (ends of columns). The plastic hinges can be defined on individual linear elements from the properties panel.

The user is able to select the degrees of freedom for which this hinge is applicable, separate for each extremity. The ID name of a plastic hinge is generated automatically, and it consists of prefix PLH-L (plastic hinge on linear element), ID of the element, the extremity (1 or 2) and the type of the element (B – for beams, C for columns). The definition of parameters of the plastic hinge can be done by using a dialog opened by a button on the Definition property.

In a case when the user decides that parameters should be calculated automatically, then he can select the code (EC 8-3 or FEMA 356) and plastic hinge type. The available types (steel or concrete beams and columns) depend on the selected code and degree of freedom. Note that some of the parameters are computed only during the next stage, during the pushover analysis. In a case when the user decides to define the properties of the plastic hinge manually, the Definition should be set to User defined. Then, each property can be unlocked and edited individually.
When plastic hinges are applied to elements, they can be presented graphically (on the descriptive model) by using a grey symbol.

Definition of Pushover loads
The next stage is the creation of pushover load cases and generation of pushover loads.
For this, a new Pushover load case family type can be defined from the Create load case family. On its property list we can set the basic data for load generation such as: the distribution type, the point of application and the directions of the loads.

Looking on the distribution types – there are several distribution types of the pushover forces on the height of the structure available:

Using the right click menu on the Pushover load case family we can then automatically generate the pushover load cases and loads. On the property list of each generated pushover load case we can set details related to the maximum total lateral load.
The maximum total lateral load is the cumulated sum of the lateral loads applied on the last step of the pushover analysis. This load can be defined either as the imposed value or as a percentage of the load applied on the structure, prior to the pushover. For each load case, a different definition of the maximum lateral load can be selected.

The Master node is used for tracking the displacement of the structure and generating the pushover load-displacement curve. This node can be either defined (as an ID of a mesh node), or the Max displacement option can be used. In this case, the maximum displacement, on the direction of the pushover load case, at each step of the analysis will be used for plotting the pushover curve.
Similar to the classical NL analysis, additional calculation conditions can be set for the PushOver Analysis as well. The analysis could either run until the total lateral load is applied (last step) or it could be stopped earlier due to the instability of the non-linear calculations – usually when a mechanism state is reached. In this case the results will be available for the calculated steps.

Calculations
The pushover analysis is a list of sequential actions, activated by a dedicated Pushover checkbox control in Calculation sequence dialog.

During the process several steps are performed automatically, including:

· a standard linear static and seismic calculation;
· the design of steel linear elements / design of concrete linear elements (including the real reinforcement);and finally, the main non-linear static calculation for the pushover load cases with incrementing lateral loads and an appropriate activation of plastic hinges.

Results
After successful completion of pushover calculations, a set of different types of results is available.
FEM results
As with normal static calculations, FEM results such as displacements and internal forces are available. The results can be checked as for the non-linear calculations for each of the subsequent calculation steps.

The pushover force-displacement curve
Using a new Pushover results curve command, available on the Results ribbon, a pushover capacity curve can be generated. It displays a relationship diagram of the displacement of the node with respect to the total applied lateral load.

Reports tables
For the results from the pushover analysis a set of new dedicated report tables is available, including:

Flexural plastic hinges status by load step

Axial plastic hinges status by load step

The overstrength ratio (αu/α1)

Graphical results showing the status of hinges at each load step
A new Pushover Results entry is available on the FEM results selection that allows selecting the Hinge status result for linear elements. When activated, it shows the status of defined plastic hinges for selected step of the selected pushover case. The status is displayed by using colors.