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 performancebased design has brought thenonlinear static pushover analysisprocedure to the forefront. Pushoveranalysis is a static, nonlinearprocedure in which the magnitude ofthe structural loading is incrementallyincreased in accordance with a certainpredefined pattern. With the increasein the magnitude of the loading, weaklinks and failure modes of thestructure are found. The loading ismonotonic with the effects of thecyclic behavior and load reversalsbeing estimated by using a modifiedmonotonic force-deformation criteriaand with damping approximations.Static pushover analysis is an attemptby the structural engineeringprofession to evaluate the realstrength of the structure and itpromises to be a useful and effectivetool for performance based design.

The ATC-40 and FEMA-273documents have developed modelingprocedures, acceptance criteria andanalysis procedures for pushoveranalysis. These documents define

force-deformation criteria for hingesused in pushover analysis. As shownin Figure 1, five points labeled A, B,C, D, and E are used to define theforce deflection behavior of the hingeand three points labeled IO, LS andCP are used to define the acceptancecriteria for the hinge. (IO, LS and CPstand for Immediate Occupancy, LifeSafety and Collapse Preventionrespectively.) The values assigned toeach of these points vary dependingon the type of member as well asmany other parameters defined in theATC-40 and FEMA-273 documents.

This article presents the steps used inperforming a pushover analysis of asimple three-dimensional building.SAP2000, a state-of-the-art, general-purpose, three-dimensional structuralanalysis program, is used as a tool forperforming the pushover. TheSAP2000 static pushover analysiscapabilities, which are fullyintegrated into the program, allowquick and easy implementation of thepushover procedures prescribed in theATC-40 and FEMA-273 documents

for both two and three-dimensionalbuildings.

The following steps are included inthe pushover analysis. Steps 1through 4 discuss creating thecomputer model, step 5 runs theanalysis, and steps 6 through 10review the pushover analysis results.

1. Create the basic computer model(without the pushover data) inthe usual manner as shown inFigure 2. The graphical interfaceof SAP2000 makes this a quickand easy task.

Figure 2: Basic SAP2000 Model (Without Pushover Data)

Deformation

For

ce

A

BC

D E

IO LS CP

Figure 1: Force-Deformation ForPushover Hinge

2. Define properties and acceptancecriteria for the pushover hinges asshown in Figure 3. The programincludes several built-in default hingeproperties that are based on averagevalues from ATC-40 for concretemembers and average values fromFEMA-273 for steel members. Thesebuilt in properties can be useful forpreliminary analyses, but user-defined properties are recommendedfor final analyses. This example usesdefault properties.

3. Locate the pushover hinges on themodel by selecting one or more framemembers and assigning them one ormore hinge properties and hingelocations as shown in Figure 4.

4. Define the pushover load cases. InSAP2000 more than one pushoverload case can be run in the sameanalysis. Also a pushover load casecan start from the final conditions ofanother pushover load case that waspreviously run in the same analysis.Typically the first pushover load caseis used to apply gravity load and thensubsequent lateral pushover loadcases are specified to start from thefinal conditions of the gravitypushover. Pushover load cases canbe force controlled, that is, pushed toa certain defined force level, or theycan be displacement controlled, thatis, pushed to a specifieddisplacement. Typically a gravityload pushover is force controlled andlateral pushovers are displacementcontrolled. SAP2000 allows thedistribution of lateral force used inthe pushover to be based on auniform acceleration in a specifieddirection, a specified mode shape, ora user-defined static load case. Thedialog box shown in Figure 5 showshow the displacement controlledlateral pushover case that is based ona user-defined static lateral loadpattern (named Push) is defined forthis example.

Figure 3: Frame Hinge Property

Figure 4: Assign Pushover Hinges

Figure 5: Pushover Load Case Data

5. Run the basic static analysis and,if desired, dynamic analysis.Then run the static nonlinearpushover analysis.

6. Display the pushover curve asshown in Figure 6. The Filemenu shown in this displaywindow allows you to view andif desired, print to either a printeror an ASCII file, a table whichgives the coordinates of each stepof the pushover curve andsummarizes the number of hingesin each state as defined in Figure1 (for example, between IO andLS, or between D and E). Thistable is shown in Figure 7.

7. Display the capacity spectrumcurve as shown in Figure 8. Notethat you can interactively modifythe magnitude of the earthquakeand the damping information onthis form and immediately seethe new capacity spectrum plot.The performance point for agiven set of values is defined bythe intersection of the capacitycurve (green) and the singledemand spectrum curve (yellow).Also, the file menu in thisdisplay allows you to print thecoordinates of the capacity curveand the demand curve as well asother information used to convertthe pushover curve toAcceleration-DisplacementResponse Spectrum format (alsoknown as ADRS format, seepage 8-12 in ATC-40).

8. Review the pushover displacedshape and sequence of hingeformation on a step-by-step basisas shown in the left-hand side ofFigure 9. The arrows in thebottom right-hand corner of thescreen allow you to movethrough the pushover step-by-step. Hinges appear when theyyield and are color coded basedon their state (see legend atbottom of screen).

Figure 6: Pushover Curve

Figure 7: Tabular Data For Pushover Curve

Figure 8: Capacity Spectrum Curve

9. Review member forces on a step-by-step basis as shown in theright-hand side of Figure 9.Often it is useful to view themodel in two side-by-sidewindows with the step-by-stepdisplaced shape in one windowand the step-by-step memberforces in the other, as shown inFigure 9. These windows can besynchronized to the same step,and can thus greatly enhance theunderstanding of the pushoverresults.

10. Output for the pushover analysiscan be printed in a tabular formfor the entire model or forselected elements of the model.The types of output available inthis form include joint

displacements at each step of thepushover, frame member forcesat each step of the pushover, andhinge force, displacement andstate at each step of the pushover.

For buildings that are beingrehabilitated it is easy to investigatethe effect of different strengtheningschemes. The effect of addeddamping can be immediately seen onthe capacity spectrum form (step 7,Figure 8). You can easily stiffen orstrengthen the building by changingmember properties and rerunning theanalysis. Finally you can easilychange the assumed detailing of thebuilding by modifying the hingeacceptance criteria (step 2, Figures 1and 3) and rerunning the analysis.

References

ATC, 1996Seismic Evaluation and Retrofit ofConcrete Buildings, Volume 1, ATC-40 Report, Applied TechnologyCouncil, Redwood City, California.

FEMA, 1997NEHRP Guidelines for the SeismicRehabilitation of Buildings,Developed by the Building SeismicSafety Council for the FederalEmergency Management Agency(Report No. FEMA 273),Washington, D.C.

1. President, Computers and Structures, Inc., Berkeley, CA.2. Senior Structural Engineer, Computers and Structures, Inc., Berkeley, CA.

Figure 9: Step-By-Step Deformations and Member Forces For Pushover