File:Pushover Analysis of 2-Story Frame with Concentrated Plastic Hinges.doc: Difference between revisions

Example posted by: Laura Eads, Stanford University

This example demonstrates how to perform a pushover (nonlinear static) analysis in OpenSees using a 2-story, 1-bay steel moment resisting frame. The nonlinear behavior is represented using the concentrated plasticity concept with rotational springs. These rotational springs follow a bilinear hysteretic response based on the Modified Ibarra Krawinkler Deterioration Model (Ibarra et al. 2005, Lignos and Krawinkler 2009, 2010). For this example, all modes of cyclic deterioration are neglected. A leaning column carrying gravity loads is linked to the frame to simulate P-Delta effects.

The files needed to analyze this structure in OpenSees are included here:

• The main file: pushover-example.tcl
• Supporting procedure files

* DisplayModel2D.tcl  – displays a 2D perspective of the model
* DisplayPlane.tcl  – displays a plane in the model
* rotSpring2DModIKModel.tcl – creates a nonlinear rotational spring that follows the Modified Ibarra Krawinkler Deterioration Model
* rotLeaningCol.tcl – creates a low-stiffness rotational spring used in a leaning column

• All files are available in a compressed format here: pushover-example.zip

The rest of this example describes the model and compares the analysis results from OpenSees to the results from SAP2000 (http://csiberkeley.com/products_SAP.html).

Model Description

The 2-story, 1-bay steel moment resisting frame is modeled with elastic beam-column elements connected by zeroLength elements which serve as rotational springs to represent the structure’s nonlinear behavior. The springs follow a bilinear hysteretic response based on the Modified Ibarra Krawinkler Deterioration Model which will be described in more detail later. A leaning column with gravity loads is linked to the frame by truss elements to simulate P-Delta effects. An idealized schematic of the model is presented in Figure 1. To simplify this model, panel zone contributions are neglected and plastic hinges form at the beam-column joints, i.e., centerline dimensions are used. Subsequent examples will explicitly model the panel zone shear distortions and include reduced beam sections (RBS).

The units of the model are kips, inches, and seconds.

Basic Geometry

The basic geometry of the frame is defined by input variables for the bay width, height of the first story, and height of a typical (i.e. not the first) story. These values are set as WBay = 360”, HStory1 = 180”, and HStoryTyp = 144”. The leaning column line is located one bay width away from the frame. In addition to the nine beam-column joint nodes, there is one additional node for each spring, which connects the spring to the elastic element. This makes a total of 24 nodes in the structure.

Leaning Columns and Frame Links

The leaning columns are modeled as elastic beam-column elements. These columns have moments of inertia and areas about two orders of magnitude larger than the frame columns in order to represent aggregate effect of all the gravity columns (Aleaning column = 1,000.0 in2 and Ileaning column = 100,000.0 in4. The columns are connected to the beam-column joint by zeroLength rotational spring elements with very small stiffness values so that the columns do not attract significant moments. These springs are created using rotLeaningCol.tcl.

Truss elements are used to link the frame and leaning columns and transfer the P-Delta effect. The trusses have areas about two orders of magnitude larger than the frame beams in order to represent aggregate effect of all the gravity beams (Atruss = 1,000.0 in2) and can be assumed to be axially rigid.

Rotational Springs and the Modified Ibarra Krawinkler Deterioration Model

The rotational springs capture the nonlinear behavior of the frame. As previously mentioned, the springs in the example employ a bilinear hysteretic response based on the Modified Ibarra Krawinkler Deterioration Model. Detailed information about this model and the modes of deterioration it simulates can be found in Ibarra et al. (2005) and Lignos and Krawinkler (2009, 2010). In this example, the zeroLength spring elements connect the elastic frame elements to the beam-column joint nodes. The springs are created using rotSpring2DModIKModel.tcl. The input parameters for the springs’ behavior are determined using empirical relationships developed by Lignos and Krawinkler (2010) which are derived from an extensive database of steel component tests. Alternatively, these input parameters can be determined using approaches similar to those described in FEMA 356 (http://www.fema.gov/library/viewRecord.do?id=1427), ATC-72 and ATC-76 (http://www.atcouncil.org/index.php?option=com_content&view=article&id=45&Itemid=54). In order to simplify the model and compare with SAP2000, cyclic deterioration was ignored. This was accomplished by setting all of the “L” deterioration parameter variables to 1000.0, all of the “c” exponent variables to 1.0, and both “D” rate of cyclic deterioration variables to 1.0.