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 isincrementally 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 anattempt 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. Asshown 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 aswell 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, generalpurpose, three-dimensional structural analysis program, is used as a tool for performing the pushover. The SAP2000 static pushover analysis capabilities, which are fullyintegrated into the program, allow quick and easy implementation of the pushover procedures prescribed in the ATC-40 and FEMA-273 documents
C IO LS CP D E
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 runsthe 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)
Define properties and acceptance criteria for the pushover hinges as shown inFigure 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 userdefined properties are recommended for final analyses. This example uses default properties. Locate the pushover hinges on the model byselecting one or more frame members and assigning them one or more hinge properties and hinge locations as shown in Figure 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 pushoverload 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...