chapter-5 basic steps to perform pushover_66-96
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SEISMIC EVALUATION OF BUILDING WITH POST TENSIONED FLOORS BY PUSHOVER ANALYSIS Page66
BASIC STEPS TO PERFORM PUSHOVER
ANALYSIS IN SAP 2000
5.1 OVERVIEW
SAP 2000 is the finite element method based commercial software.
The analysis in SAP 2000 involves the following four steps:
1. Modeling
2. Static analysis
3. Designing
4. Pushover analysis
1. Modeling
Modeling is the primary task of any analytical study and the
result obtained to a large extent depends on the simplification taken
during this step. Modeling involves creation of geometry of overall
structure by including elements of various components representing
respective structural behavior including boundary conditions. In the
considered problem, material properties of various elements and loads
on various elements and its combinations are defined. The various
steps involved in the modeling are as follows:
1. Units are set for the convenience.
2. Define the properties of various materials used in the
models.
3. Define the section properties of various structural elements
of the model.
4. Draw the model in the graphical environment.
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5. Define different loads and their combination. Including
cases of pushover analysis.
6. Assign section properties to the model and boundary
condition.
7. Assign the various loads on the structure.
8. Draw tendon elements in PT beam elements.
9. Assign prestressed loads and post tensioning parameters to
tendon elements.
10. Assign nonlinear hinges on beams and columns.
2. Static Analysis
Once the model is built, the static analysis is performed after
defining the various loads and their combinations.
3. Design
In RC frame sections, properties of nonlinear hinges are mainly
based on the outcome of the designed section. So, prior to pushover
analysis it is necessary to do design. Using appropriate code
recommendations, model is first designed for the response to the static
analysis.
4. Pushover Analysis
Many nonlinear static analyses are possible. But it is usual to
consider only three primary cases that are Push1- gravitational push,
Push2- push staring from the end of gravitational push and it is in X-
direction, and the last one is Push3- this also starts from end of the
gravitational push but in Y-direction.
The following general sequences of steps are involved in performing
a static nonlinear analysis:
1.Create a model just like any other analysis.
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2.Define frame hinge properties and assign them to the frame
elements.
3.Define any Load Cases and static and dynamic Analysis Cases
that may be needed for steel or concrete design of the frame
elements, particularly if default hinges are used.
4.Run the Analysis Cases needed for design.
5.If any concrete hinge properties are based on default values to
be computed by the program, you must perform concrete
design so that reinforcing steel is determined.
6.If any steel hinge properties are based on default values to
be computed by the program for Auto-Select frame section
properties, you must perform steel design and accept the
sections chosen by the program.
7.Define the Load Cases that are needed for use in the
pushover analysis, including:
Gravity loads and other loads that may be acting on the
structure before the lateral seismic loads are applied.
You may have already defined these Load Cases above
for design.
Lateral loads that will be used to push the structure. If
you are going to use Acceleration Loads or modal loads,
you don’t need any new Load Cases, although modal
loads are required to define a Modal Analysis Case.
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8.Define the nonlinear static Analysis Cases to be used for
pushover analysis, including:
A sequence of one or more cases that start from zero and
apply gravity and other fixed loads using load control.
These cases can include staged construction and geometric
nonlinearity.
One or more pushover cases that start from this sequence
and apply lateral pushover loads. These loads should be
applied under displacement control.
The monitored displacement is usually at the roof level of
the structure and will be used to plot the pushover curve.
9. Run the push over Analysis Cases.
10. Review the pushover results: Plot the pushover curve,
the Deflected shape showing the hinge states, force and
moment plots, and print or display any other results you
need.
11. Revise the model as necessary and repeat.
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5.2 BASIC STEPS
5.2.1 Create a model
1. Create the Basic Grid System
In this step, creating the basic grid system. The structural objects
are set relative to the grid system.
Begin creating the grid system by clicking the File menu > New
Model command or the New Model button , the form shown in
Fig.5.1 will be displayed.
Fig.5.1 The New Model Initialization form
Select the Grid Only button on the form shown in Fig.5.1,
form shown in Fig.5.2 will be displayed and in this form, define Grid
Dimensions, Story Dimensions and Units.
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Fig.5.2 Building Plan Grid System and Story Data Definition form
2. Define material properties
Begin defining various material properties used in the model by
clicking the Define menu > Material Properties command, the form
shown in Fig.5.3 will be displayed.
Fig.5.3 Define Materials form
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Fig.5.4 Material Property Data form
Select the Add New Material Or Modify/Show Material
button on the form shown in Fig.5.3, form shown in Fig.5.4 will be
displayed and in this form, Define Material Property data.
3. Define section properties
Begin defining various section properties used in the model by
clicking the Define menu > Frame Sections command, the form
shown in Fig.5.5 will be displayed.
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Fig.5.5 Define Frame Properties form
Select the Add New Property button on the form shown in
Fig.5.5, form shown in Fig.5.6 will be displayed and in this form, Add
Frame Section Property.
Fig.5.6 Frame Section Properties form
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Select the Concrete from Frame Section Property Type and
Select Rectangular button on the form shown in Fig.5.6, form shown
in Fig.5.7 will be displayed and in this form, Define Section Property
data.
Fig. 5.7 Rectangular Property form
4. Add structural objects
Objects, such as columns, beams, and floors, can be drawn
manually as follows:
Draw Frame Elements:
Make sure that in case of drawing columns elevation view is
active and in case of drawing beams plan view is active. Click the Draw
Frame/Tendon Elements or Click button , or use the Draw
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menu > Draw Frame/Tendon Elements > Create Columns in
Region. The Properties of Object pop-up box for frame elements
shown in Fig.5.8 will be displayed and using this command Draw
Frame/Tendon Elements.
Fig.5.8 Properties Of Frame/Tendon Elements
Select type of section as Column in case of drawing columns in
model and select type of section as Beam in case of drawing beam
elements in model.
Draw the Floor:
Make sure that the Plan View is active. Click the Draw Poly
Areas button , or select the Draw menu > Draw Poly Area
Objects > Draw Areas command. The Properties of Object pop-up
box for areas shown in Fig.5.9 will be displayed and using this
command Draw Area Objects.
Fig.5.9 Properties Of Object Box For Areas
Similarly, using Draw menu you can construct other objects like secondary beams, point objects etc.
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Draw Tendons
First we need to define Tendon properties, click Define menu >
Materials > Add New Material, so the Form as shown in Fig. 5.10
will be displayed. Select Tendon from Material Type and in this form
define Tendon Material property.
Fig. 5.10 Tendon property data form
Click the Draw Frame/Tendon Elements or Click button , or use
the Draw menu > Frame/Cable/Tendons command to access the
Properties of Object form. The Properties of Object pop-up box for
frame elements shown in Fig.5.11 will be displayed,
1. Click the Line Object Type drop-down list and select the Tendon
option.
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Click on the joint at one end of the beam and then click on the
joint at the other end of the beam to draw the tendon. The
Tendon Data for Line Object 2 form will display when you
release the mouse button.
Fig. 5.11 Properties of Object box for Tendons
Fig. 5.12 Tendon data for Line Object form
With the Tendon Data for Line Object form as displayed in Fig.
5.12, click the Parabolic Calculator button to access the Define
Parabolic Tendon Layout for Line Object 2 form as shown in Fig.
5.13. In that form,
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Select 1 from the Quick Start drop-down list in the lower
left corner of the form.
Click the Quick Start button to update the Tendon Layout
Data spreadsheet. In the spreadsheet area,
o Enter the values of elevation of cable from center of
beam to generate the parabolic profile in the beam.
o The values of elevation are defined at a distance of
L/20 for each span.
Click the Refresh button to update the spreadsheet area
and the graphical display area.
Click the Done button to close the Define Parabolic
Tendon Layout for Line Object form and redisplay the
Tendon Data for Line Object form.
Fig. 5.13 Define Parabolic Tendon Layout for line object form
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With the Tendon Data for Line Object form redisplayed,
click the Add button in the Tendon Loads area of the form to
access the Tendon Load form. This form is displayed in Fig.
5.14 as Tendon Load Assignment Data form. In that form,
Select the PRESTRESS load case from the Load Case Name
drop-down list.
Enter value of Tendon End Force edit box.
Ensure that all of the Friction and Anchorage Losses and
Other Loss Parameters are zero. Type the values of the
Curvature Coefficient, Wobble Coefficient, Anchorage Set
Slip as specified in the technical note of ADAPT Corporation.
Elastic Shortening Stress, Creep Stress, Shrinkage Stress
and Steel Relaxation Stress are not used as tendons are
modelled as elements in the analysis model.
Click the OK buttons on the Tendon Load form and the
Tendon Data for Line Object form to close those forms.
Fig. 5.14 Tendon Load Assignment data form
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5. Define hinge properties
To Define hinge properties, select frame member and then
click the Assign menu > Frame > Hinges command the form as
shown in Fig.5.15 will be displayed and using this form, you can define
Frame Hinge Properties. There are also some defined default hinges are
available.
Fig.5.15 Define Frame Hinge Properties form
Type of hinges:
Yielding and post-yielding behaviour can be modelled using
discrete user-defined hinges. Currently hinges can only be
introduced into frame elements; they can be assigned to a frame
element at any location along that element. Uncoupled moment,
torsion, axial force and shear hinges are available. There is also a
coupled P-M2-M3 hinge which yields based on the interaction of
axial force and bending moments at the hinge location. More than
one type of hinge can exist at the same location, for example,
you might assign both a M3 (moment) and a V2 (shear) hinge to
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the same end of a frame element. Default hinge properties are
provided based on FEMA-356 [19] criteria.
Default Hinge Properties:
A hinge property may use all default properties, or one may
partially defines and use only some default properties. Default
hinge properties are based upon a simplified set of assumptions
that may not be appropriate for all structures. You may want to
use default properties as a starting point, and explicitly override
properties as needed during the development of your model.
Default properties require that the program have detailed
knowledge of the Frame Section property used by the element
that contains the hinge. This means:
• The material must have a design type of concrete or steel
• For concrete Sections:
The shape must be rectangular or circular
The reinforcing steel must be explicitly defined, or else
have already been designed by the program before
nonlinear analysis is performed.
• For steel Sections, the shape must be well defined:
General and Nonprismatic Sections cannot be used
Auto select Sections can only be used if they have already
been designed so that a specific section has been chosen
before nonlinear analysis is performed.
For situations where design is required, you can still define
and assign hinges to Frame elements, but you should not run any
nonlinear analyses until after the design has been run.
Default properties are available for hinges in the following
degrees of freedom:
Axial (P)
Major shear (V2)
Major moment (M3)
Coupled P-M2-M3 (PMM)
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Plastic Deformation Curve:
For each degree of freedom, one can define a force-
displacement (moment-rotation) curve that gives the yield value
and the plastic deformation following yield. This is done in terms
of a curve with values at five points, A-B-C-D-E, as shown in
Fig.5.16. You may specify a symmetric curve, or one that differs
in the positive and negative direction.
Fig.5.16 The A-B-C-D-E curve for Force vs. Displacement
The shape of this curve as shown in Fig.5.16 is intended
for pushover analysis. You can use any shape you want. The
following points should be noted:
Point A is always the origin.
Point B represents yielding. No deformation occurs in the
hinge up to point B, regardless of the deformation value
specified for point B. The displacement (rotation) at point B
will be subtracted from the deformations at points C, D, and
E. Only the plastic deformation beyond point B will be
exhibited by the hinge.
Point C represents the ultimate capacity for pushover
analysis. However, you may specify a positive slope from C
to D for other purposes.
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Point D represents a residual strength for pushover
analysis. However, you may specify a positive slope from C
to D or D to E for other purposes.
Point E represents total failure. Beyond point E the hinge
will drop load down to point F (not shown) directly below
point E on the horizontal axis. If you do not want your
hinge to fail this way, be sure to specify a large value for
the deformation at point E.
One may specify additional deformation measures at points IO
(immediate occupancy), LS (life safety), and CP (collapse
prevention). These are informational measures that are reported
in the analysis results and used for performance-based design.
They do not have any effect on the behaviour of the structure.
Prior to reaching point B, all deformation is linear and occurs
in the Frame element itself, not the hinge. Plastic deformation
beyond point B occurs in the hinge in addition to any elastic
deformation that may occur in the element. When the hinge
unloads elastically, it does so without any plastic deformation,
i.e., parallel to slope A-B. Program itself calculate the yield values
from the frame section properties.
When you display the deflected shape in the graphical user
interface for a nonlinear static case, the hinges are plotted as
coloured dots indicating their most extreme state or status:
B to IO
IO to LS
LS to CP
CP to C
C to D
D to E
E
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The colours used for the different states are indicated on
the plot. Hinges that have not experienced any plastic
deformation (A to B) are not shown.
6. Assign hinge properties
To Assign hinge properties, after selecting the frame
elements, click the Assign menu > Frame > Hinges, the form shown
in Fig.5.17 will be displayed and using this form, Assign Frame Hinge
Properties.
Fig.5.17 Assign Frame Hinges (Pushover) form
In this form, select Auto and enter the relative distance of
hinges in the frame elements. Auto option is selected from the Hinge
Property drop-down list, the Auto Hinge Assignment Data form will
display when the Add button is clicked. Use that form to specify the
Auto Hinge Type based on tables in FEMA 356 or Caltrans Flexible
specifications. The Combined Axial and Flexural (PMM) type of hinges
are defined at 0.05L and 0.95L for all the column elements and Flexural
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(M3) hinges are defined at 0.05L, 0.5L and 0.95L for all beam elements
where L is the length of the beam element.
8. Define the static load cases
To add a static load case, click the Define menu > Load Cases
command or click the Define Load Cases button , to access the
Define Static Load Case Names form as shown in Fig.5.18. Complete
the following actions using that form:
1. Type the name of the load case in the Load edit box. The
program does not allow use of duplicate names.
2. Select a load type from the Type drop-down list.
3. Type a self-weight multiplier in the Self-Weight Multiplier edit
box.
4. If the load type specified is Quake or Wind, select an option
from the Auto Lateral Load drop-down list.
5. Click the Add New Load button.
Fig. 5.18 Define Load Case Names Form
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9. Assign Structural Loads
The load cases defined are required in order to be able to assign
loads to points/joints, lines/frames, and areas/shells. The user must
first select the object before a load can be assigned to the object. After
the object has been selected, click the Assign menu command to
access the applicable submenu and assignment options. Table 5.1
identifies the submenus and options.
Table 5.1 Load commands on assign menu
10. Define Mass Source
To define the mass source for Modal Analysis of the frame
structure, click the Define menu > Mass Source command to access
the Define Mass Source form as shown in Fig.5.19.
Fig.5.19 Define Mass Source form
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12.Define Analysis cases
To define the analysis cases, click the Define menu >
Analysis cases command to access the Define analysis cases form
as shown in Fig.5.20. A separate load case called prestress is
defined in the analysis models pertaining to the transfer of axial
precompression and load balancing due to post tensioned cables.
Fig.5.20 Define Analysis cases
5.2.2 Run static analysis
To run the analysis, click the Analyze menu > Run Analysis
command or the Run Analysis button .
After running analysis command, you can see the analysis results
and deformed shapes for different load cases in the Display menu.
5.2.3 Design the structure
The SAP 2000 design postprocessors include the following:
Steel Frame Design
Concrete Frame Design
Composite Beam Design
Steel Joist Design
Shear Wall Design
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To perform the design, first run the analysis, then click on the
Options menu > Preferences to select the Design Code and then
click the Design menu and select the appropriate design from the
drop-down menu. The type of design available depends on the type of
members used in the model. That is, the user cannot complete a shear
wall design if no shear walls have been included in the model.
5.2.4 Pushover analysis
5.2.4.1 Define Static pushover cases
PUSH1 is the case in which the gravity loads are applied up to
their total force magnitude. It may be noted here that the jacking force
applied at ends of the PT cables as per Table 1 is already in effect
simultaneously. PUSH2 is defined as the push in the lateral X-direction,
and it starts from the end of PUSH1. The X-displacement of the roof
level node is monitored up to the magnitude of 0.4 percent of the
building height, when push is given as per the earthquake force profile
in the X-direction. To get the relevant data at the performance point,
the displacement magnitude of the roof level node is restricted to the
value of roof displacement obtained at the performance point.
To add a static pushover case, click the Define menu >
Analysis Cases command, the Define Analysis Cases form as shown in
Fig. 5.21 will be displayed.
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Fig.5.21 Define Analysis Cases form
Select the Add new Case button on the form shown in
Fig.5.21, form shown in Fig.5.22 will be displayed. In this analysis
case data form, select Analysis case type as Static, Analysis type as
Nonlinear to define data for Static Nonlinear analysis case.
Fig.5.22 Static Nonlinear Case Data form
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5.2.4.1.1 Static pushover analysis parameters
Geometric Nonlinearity:
When the load acting on a structure and the resulting deflections
are small enough, the load-deflection relationship for the structure is
linear. This permits the program to form the equilibrium equations
using the original (undeformed) geometry of the structure.
If the load on the structure and/or the resulting deflections is
large, then the load-deflection behaviour may become nonlinear.
Several causes of geometric nonlinear behaviour are as follows:
1. P-delta (large-stress) effect:
When large stresses (or forces and moments) are present
within a structure, equilibrium equations written for the original
and the deformed geometries may differ significantly, even if the
deformations are very small.
2. Large-displacement effect:
When a structure under goes large deformation (in
particular, large strains and rotations), the usual engineering
stress and strain measures no longer apply, and the equilibrium
equations must be written for the deformed geometry. This is
true even if the stresses are small.
Member (Hinge) Unloading Method:
This option is primarily intended for pushover analysis using
frame hinge properties that exhibit sharp drops in their load carrying
capacity.
When a hinge unloads, the program must find a way to remove
the load that the hinge was carrying and possibly redistribute it to the
rest of the structure. Hinge unloading occurs whenever the stress-strain
(force-deformation or moment-rotation) curve shows a drop in
capacity.
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Such unloading along a negative slope may be unstable in a static
analysis, and a unique solution is not always mathematically
guaranteed. In dynamic analysis inertia provides stability and a unique
solution.
For static analysis, special methods are needed to solve this
unstable problem. Different methods may work better with different
problems. Different methods may produce different results with the
same problem. SAP 2000 software provides three different methods to
solve this problem of hinge unloading as follows:
1. Unload Entire Structure
When a hinge reaches a negative-sloped portion of the
stress-strain curve, the program continues to try to increase the
applied load. If this results in increased strain (decreased stress)
the analysis proceeds. If the strain tries to reverse, the program
instead reverses the load on the whole structure until the hinge is
fully unloaded to the next segment on the stress-strain curve. At
this point the program reverts to increasing the load on the
structure. Other parts of the structure may now pick up the load
that was removed from the unloading hinge.
2. Apply Local Redistribution
This method is similar to the first method, except that
instead of unloading the entire structure, only the element
containing the hinge is unloaded. When a hinge is on a negative-
sloped portion of the stress-strain curve and the applied load
causes the strain to reverse, the program applies a temporary,
localized, self-equilibrating, internal load that unloads the
element. This causes the hinge to unload. Once the hinge is
unloaded, the temporary load is reversed, transferring the
removed load to neighboring elements. This process is intended
to imitate how local inertia forces might stabilize a rapidly
unloading element.
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This method is often the most effective of the three
methods available.
3. Restart Using Secant Stiffness
This method is quite different from the first two. Whenever
any hinge reaches a negative-sloped portion of the stress-strain
curve, all hinges that have become nonlinear are reformed using
secant stiffness properties, and the analysis is restarted.
This method is the least efficient of the three.
Load Application Control:
You may choose between a load-controlled or displacement-
controlled nonlinear static analysis. For both options, the pattern of
loads acting on the structure is determined by the specified
combination of loads. Only the scaling is different.
1. Load Control:
Select load control when you know the magnitude of load
that will be applied and you expect the structure to be able to
support that load.
2. Displacement Control:
Select displacement control when you know how far you
want the structure to move, but you don’t know how much load is
required. This is most useful for structures that become unstable
and may lose load carrying capacity during the course of the
analysis, like static pushover analysis.
3. Conjugate Displacement Control
If the analysis is having trouble converging, you can choose
the option for the program to use the conjugate displacement for
control. The conjugate displacement is a weighted average of all
displacements in the structure, each displacement degree of
freedom being weighted by the load acting on that degree of
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freedom. In other words, it is a measure of the work done by the
applied load.
Output Steps:
1. Minimum and Maximum Saved Steps:
The Minimum Number of Saved Steps and Maximum
Number of Saved Steps provide control over the number of points
actually saved in the analysis. If the minimum number of steps
saved is too small, you may not have enough points to
adequately represent a pushover curve. If the minimum and
maximum number of saved steps is too large, then the analysis
may consume a considerable amount of disk space, and it may
take an excessive amount of time to display results.
2. Save Positive Increments Only:
This option is primarily of interest for pushover analysis
under displacement control. In the case of extreme nonlinearity,
particularly when a frame hinge sheds load, the pushover curve
may show negative increments in the monitored displacement
while the structure is trying to redistribute the force from a failing
component.
You may choose whether or not you want to save only the
steps having positive increments. The negative increments often
make the pushover curve look confusing. However, seeing them
can provide insight into the performance of the analysis and the
structure.
Nonlinear Solution Control: 1. Maximum Total Steps:
This is the maximum number of steps allowed in the
analysis. It may include saved steps as well as intermediate
substeps whose results are not saved. The purpose of setting this
value is to give you control over how long the analysis will run.
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2. Maximum Null (Zero) Steps:
Null (zero) steps occur during the nonlinear solution
procedure when:
A frame hinge is trying to unload.
An event (yielding, unloading, etc.) triggers another event.
Iteration does not converge and a smaller step size is
attempted.
An excessive number of null steps may indicate that the
solution is stalled due to catastrophic failure or numerical
sensitivity.
You can set the Maximum Null (Zero) Steps so that the
solution will terminate early if it is having trouble converging. Set
this value equal to the Maximum Total Steps if you do not want
the analysis to terminate due to null steps.
3. Maximum Iterations Per Step
Iteration is used to make sure that equilibrium is achieved
at each step of the analysis. You can control the number of
iterations allowed in a step before the program tries using a
smaller sub step. The default value of 10 works well in many
situations.
4. Iteration Convergence Tolerance:
Iteration is used to make sure that equilibrium is achieved
at each step of the analysis. You can set the relative convergence
tolerance that is used to compare the magnitude of force error
with the magnitude of the force acting on the structure.
You may need to use significantly smaller values of
convergence tolerance to get good results for large-displacements
problems than for other types of nonlinearity. Try decreasing
values until you get consistent results.
5. Event Lumping Tolerance:
The nonlinear solution algorithm uses an event-to-event
strategy for the frame hinges. If you have a large number of
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SEISMIC EVALUATION OF BUILDING WITH POST TENSIONED FLOORS BY PUSHOVER ANALYSIS Page95
hinges in your model, this could result in a huge number of
solution steps. The event lumping tolerance is used to group
events together to reduce solution time.
5.2.4.2 Run static nonlinear analysis
To run the static nonlinear analysis, click the Analyze menu >
Set Analysis cases to run command.
After running static nonlinear analysis command, you can see the
analysis results and deformed shapes for different pushover cases in
the Display menu.
Fig.5.23 shows the deformed shape for pushover case with
hinges deformation levels.
Fig.5.23 Deformed shape for pushover case with hinges
deformation levels
Basic Steps To Perform Pushover Analysis In SAP 2000
SEISMIC EVALUATION OF BUILDING WITH POST TENSIONED FLOORS BY PUSHOVER ANALYSIS Page96
5.2.4.3 Display Static pushover curve
To see the static pushover curve, click the Display menu >
Show Static Pushover Curve command, the form as shown in
Fig.5.24 will be displayed.
Fig.5.24 Pushover curve form