Case Study of Non-Linear Static Analysis using
The recent advent of
performance based design has brought the nonlinear static pushover analysis
procedure to the forefront. Pushover analysis is a static, nonlinear procedure
in which the magnitude of the structural loading is incrementally increased in
accordance with a certain predefined pattern. With the increase in the
magnitude of the loading, weak links and failure modes of the structure are
found. The loading is monotonic with the effects of the cyclic behavior and
load reversals being estimated by using a modified monotonic force-deformation
criteria and with damping approximations. Static pushover analysis is an
attempt by the structural engineering profession to evaluate the real strength
of the structure and it promises to be a useful and effective tool for
performance based design.
The ATC-40 and FEMA-273 documents have developed modeling procedures,
acceptance criteria and analysis procedures for pushover analysis. These
documents define force-deformation criteria for hinges used in pushover
analysis. As shown in Figure 1, five points labeled A, B, C, D, and E are used
to define the force deflection behavior of the hinge and three points labeled
IO, LS and CP are used to define the acceptance criteria for the hinge. (IO,
LS and CP stand for Immediate Occupancy, Life Safety and Collapse Prevention
respectively.) The values assigned to each of these points vary depending on
the type of member as well as many other parameters defined in the ATC-40 and
This article presents the steps used in performing a pushover analysis of a
simple three-dimensional building. SAP2000, a state-of-the-art,
general-purpose, three-dimensional structural analysis program, is used as a
tool for performing the pushover. The SAP2000 static pushover analysis
capabilities, which are fully integrated into the program, allow quick and
easy implementation of the pushover procedures prescribed in the ATC-40 and
FEMA-273 documents for both two and three-dimensional buildings.
The following steps are included in the pushover analysis. Steps 1 through 4
discuss creating the computer model, step 5 runs the analysis, and steps 6
through 10 review the pushover analysis results.
1. Create the basic computer model (without the pushover data) in the
usual manner using the graphical interface of SAP2000 makes this a quick and
2. Define properties and acceptance criteria for the pushover hinges as
shown in Figure.
3. The program includes several built-in default hinge properties that
are based on average values from ATC-40 for concrete members and average
values from FEMA-273 for steel members. These built in properties can be
preliminary analyses, but user-defined properties are recommended for final
analyses. This example uses default properties.
4. Locate the pushover hinges on the model by selecting one or more
frame members and assigning them one or more hinge properties and hinge
5. Define the pushover load cases. In SAP2000 more than one pushover
load case can be run in the same analysis. Also a pushover load case can start
from the final conditions of another pushover load case that was previously
run in the same analysis.
Typically the first pushover load case is used to apply gravity load and then
subsequent lateral pushover load cases are specified to start from the final
conditions of the gravity pushover. Pushover load cases can be force
controlled, that is, pushed to a certain defined force level, or they can be
displacement controlled, that is, pushed to a specified displacement.
Typically a gravity load
pushover is force controlled and lateral pushovers are displacement
controlled. SAP2000 allows the distribution of lateral force used in the
pushover to be based on a uniform acceleration in a specified direction, a
specified mode shape, or a user-defined static load case. Here how the
displacement controlled lateral pushover case that is based on a user-defined
static lateral load pattern named PUSH is defined for this example.
6. Run the basic static analysis and, if desired, dynamic analysis. Then
run the static nonlinear pushover analysis.
7. Display the pushover curve . The File menu shown in this display
window allows you to view and if desired, print to either a printer or an
ASCII file, a table which gives the coordinates of each step of the pushover
curve and summarizes the number of hinges in each state as defined in Figure 1
(for example, between IO and LS, or between D and E).
8. Display the capacity spectrum curve. Note that you can interactively
modify the magnitude of the earthquake and the damping information on this
form and immediately see the new capacity spectrum plot. The performance point
for a given set of values is defined by the intersection of the capacity curve
(green) and the single demand spectrum curve (yellow). Also, the file menu in
this display allows you to print the coordinates of the capacity curve and the
demand curve as well as other information used to convert the pushover curve
to Acceleration-Displacement Response Spectrum format.
9. Review the pushover displaced shape and sequence of hinge formation
on a step-by-step basis . The arrows in the bottom right-hand corner of the
screen allow you to move through the pushover step-by- step. Hinges appear
when they yield and are color coded based on their state (see legend at bottom
10. Review member forces on a step-by-step basis . Often it is useful
to view the model in two side-by-side windows with the step-by-step displaced
shape in one window and the step-by-step member forces in the other. These
windows can be synchronized to the same step, and can thus greatly enhance the
understanding of the pushover
11. Output for the pushover analysis can be printed in a tabular form
for the entire model or for selected elements of the model. The types of
output available in this form include joint displacements at each step of the
pushover, frame member forces at each step of the pushover, and hinge force,
displacement and state at each step of the pushover.
For buildings that are being rehabilitated it is easy to investigate the
effect of different strengthening schemes. The effect of added damping can be
immediately seen on the capacity spectrum form. You can easily stiffen or
strengthen the building by changing member properties and rerunning the
analysis. Finally you can easily change the assumed detailing of the building
by modifying the hinge acceptance criteria and rerunning the analysis.
Limitations of Non-Linear Static Push-over Analysis