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PRACTICAL THREE DIMENSIONAL
NONLINEAR STATIC PUSHOVER ANALYSIS
By Ashraf Habibullah, S.E.1, and Stephen Pyle, S.E.2 (Published
in Structure Magazine, Winter, 1998)
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 FEMA-273 documents.
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
Deformation
Figure 1: Force-Deformation For Pushover Hinge
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 as shown in Figure 2. The
graphical interface of SAP2000 makes this a quick and easy task.
Figure
2: Basic SAP2000 Model (Without
Pushover Data)
1.
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
useful for preliminary analyses, but user-defined properties are
recommended for final analyses. This example
uses default properties.
2.
3. Locate
the pushover hinges on the model by selecting one or more frame members and
assigning them one or more hinge properties and hinge locations as shown in
Figure 4.
3.
4. 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. The dialog box
shown in Figure 5 shows 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.
Figure 3: Frame
Hinge Property
Figure 4: Assign
Pushover Hinges
Figure 5: Pushover Load
Case Data
1.
5. Run
the basic static analysis and, if desired, dynamic analysis. Then run the static nonlinear pushover analysis.
2.
6. Display
the pushover curve as shown in Figure 6. 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). This table is shown in Figure 7.
7. Display
the capacity spectrum curve as shown in Figure 8. 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 (also known as ADRS format, see page 8-12 in
ATC-40).
3.
8. Review
the pushover displaced shape and sequence of hinge formation on a
step-by-step basis as shown in the left-hand side of Figure 9. 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 of screen).
4.
Figure 6: Pushover
Curve
Figure
7: Tabular Data For Pushover Curve
Figure 8: Capacity
Spectrum Curve
1.
9. Review
member forces on a step-by-step basis as shown in the right-hand side of
Figure 9. 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, as shown in Figure 9. These windows can be
synchronized to the same step, and can thus greatly enhance the
understanding of the pushover results.
2.
10. 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 (step 7, Figure 8). 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 (step
2, Figures 1 and 3) and rerunning the analysis.
References
ATC, 1996 Seismic Evaluation
and Retrofit of Concrete Buildings, Volume 1, ATC40 Report, Applied
Technology Council, Redwood City, California.
FEMA, 1997
NEHRP Guidelines for the Seismic Rehabilitation of Buildings, Developed by
the Building Seismic Safety Council for the Federal Emergency Management
Agency (Report No. FEMA
273), Washington, D.C.
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