Chapter-5 Basic Steps to Perform Pushover_66-96

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.

Basic Steps To Perform Pushover Analysis In SAP 2000


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.



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.



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.



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.



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



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.



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



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



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.



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.



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,



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



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



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



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)



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.



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



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



(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



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



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



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.



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



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.



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.



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



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.



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



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



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

Documents

Chapter-5 Basic Steps to Perform Pushover_66-96