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Open System for Earthquake Engineering Simulation (OpenSees) OpenSees Examples Primer Silvia Mazzoni, Frank McKenna, Michael H. Scott, Gregory L. Fenves, Boris Jeremic Printed on 14 June, 2006

Contents Introduction EXAMPLE 1 - Truss Example iii 5 7 EXAMPLE 2 - Moment-Curvature Analysis of a Reinforced Concrete Section 12 EXAMPLE 3 - Portal Frame Examples 19 Example 3.1 .................................................................................................................................20 Example 3.2 .................................................................................................................................26 Example 3.3 .................................................................................................................................29 EXAMPLE 4 - Multibay Two Story Frame EXAMPLE 5 - Three-Dimensional Rigid Frame EXAMPLE 6 - Simply Supported Beam EXAMPLE 7 - Dynamic Shell Analysis EXAMPLE 8 - Cantilever Beam 35 43 52 57 61 Reinforced Concrete Plane Frame Examples 65 Example3.1.tcl....................................................................................................................65 Example3.2.tcl....................................................................................................................68 Example3.3.tcl....................................................................................................................71 PortalFrame.tcl...................................................................................................................73 Example4.1.tcl....................................................................................................................78 RCFrame1.tcl.....................................................................................................................83 RCFrame2.tcl.....................................................................................................................86 RCFrame3.tcl.....................................................................................................................90 RCFrame4.tcl.....................................................................................................................92 RCFrame5.tcl.....................................................................................................................95

Contents iv Steel Plane Frame Examples 100 SteelFrame1.tcl ......................................................................................................................... 100 SteelFrame2.tcl ......................................................................................................................... 103 SteelFrame3.tcl ......................................................................................................................... 105 Rigid Floor Diaphragm Example 109 RigidFrame3D.tcl....................................................................................................................... 109 Zero Length Element Examples 114 ZeroLength1.tcl ......................................................................................................................... 114 ZeroLength2.tcl ......................................................................................................................... 115 ZeroLength3.tcl ......................................................................................................................... 116 ZeroLength4.tcl ......................................................................................................................... 117 ZeroLength5.tcl ......................................................................................................................... 118 Section Analysis Example 120 Example2.1.tcl........................................................................................................................... 120 Quad Examples 122 Brick Examples 123 solid01.tcl .................................................................................................................................. 123 Reliability Examples 125 Script Utilities Library 126 genPlaneFrame.tcl .................................................................................................................... 126 matTest.tcl................................................................................................................................. 128 MomentCurvature.tcl................................................................................................................. 130 RCcircSection.tcl....................................................................................................................... 131 RCcircSectionFEDEAS.tcl ........................................................................................................ 133 RCFrameDisplay.tcl .................................................................................................................. 135 RCsection.tcl ............................................................................................................................. 135 RCsectionFEDEAS.tcl............................................................................................................... 138 ReadSMDFile.tcl ....................................................................................................................... 142 RotSpring2D.............................................................................................................................. 144 StFramePZLdisplay.tcl .............................................................................................................. 145 Wsection.tcl............................................................................................................................... 145 RigidFrame3Ddisplay.tcl ........................................................................................................... 146 Index 149

C H A P T E R 1 Introduction 5 The objective of this primer is to provide new users of OpenSees (Open System for Earthquake Engineering Simulation) familiar structural engineering examples as a convenient method for learning how to use the software. OpenSees is an object-oriented framework for building models of structural and geotechnical systems, performing nonlinear analysis with the model, and processing the response results. The goal for OpenSees is to support a wide range of simulation applications in earthquake engineering. The details, however, on how OpenSees accomplishes this goal are not particularly important for new users, who are primarily interested in how to solve problems. This primer examines a few typical examples. Most users will conduct a simulation with a scripting language that has been extended to incorporate the features of OpenSees. As new features are developed, such as material models, elements, solution methods, etc., the scripting language can be extended to include them. The scripting language is named Tcl/Tk, and it has many features for dealing with variables, expressions, loops, data structures, input/output, that are useful for doing a simulation. Some of the basic features of Tcl will be illustrated in the examples. Although users do not need to understand the object-oriented principles in the OpenSees framework, some terminology helps in the description of the examples. We talk about commands creating objects, which may be a specific material, element, analysis procedure, etc. To conduct a simulation, the user creates objects for three main purposes: Modeling: The user first creates a ModelBuilder object which defines the type of model, and commands available for building the model. With a ModelBuilder defined, the user then creates the Element, Node, LoadPattern and Constraint objects that define the model. In this primer, the use of a basic ModelBuilder will be demonstrated. Analysis: After defined the model, the next step is to create the Analysis object for analyzing the model. This may be a simple static linear analysis or a transient non-linear analysis. In OpenSees, an Analysis object is composed of several component objects, which define how the analysis is performed. The component objects consist of the following: {SolutionAlgorithm}, {Integrator}, { ConstraintHandler}, { DOF\_Numberer}, { SystemOfEqn}, { Solver}, and { AnalysisModel}. This approach provides a great deal of flexibility in how an analysis is conducted. Output Specification: Once the model and analysis have been defined, the user has the option of specifying what is to be monitored during the analysis. This, for example, could be the displacement history at a node or internal state of an element in a transient analysis or the entire state of the model at each step in the solution procedure. Several Recorder objects are created to store what the user wants to examine.

Chapter 1 错误！未定义样式。 6 In the examples, Tcl scripts are used to create a model, analysis, and output specification. The examples are (1) simple truss structure, (2) reinforced concrete portal frame, (3) two-story multi- bay reinforced concrete frame, and (4) a three-dimensional frame. The examples are not meant to be completely realistic, but they are representative of typical structures. The analyses performed on these models consist of simple static analysis, pushover analysis and transient analysis. An example of moment-curvature analysis is also performed on a reinforced concrete section.

C H A P T E R 2 EXAMPLE 1 - Truss Example 7 The first example is a simple truss structure. The purpose of this example is to show that model generation in OpenSees can resemble typical finite element analysis programs with the definition of nodes, materials, elements, loads and constraints. The example also demonstrates how an analysis object is 'built' from component objects. This example is of a linear-elastic three bar truss, as shown in the figure (page 7), subject to static loads. Files Required Example1.1.tcl Model The model consists of four nodes, three truss elements, a single load pattern with a nodal load acting at node 4, and constraints at the three support nodes. Since the truss elements have the same elastic material, a single Elastic material object is created. Figure 1: Example 1.1 Truss Analysis

Chapter 2 错误！未定义样式。 8 The model is linear, so we use a solution Algorithm of type Linear. Even though the solution is linear, we have to select a procedure for applying the load, which is called an Integrator. For this problem, a LoadControl integrator advances the solution. The equations are formed using a banded system, so the System is BandSPD (banded, symmetric positive definite). This is a good choice for most moderate size models. The equations have to be numbered, so typically an RCM numberer object is used (for Reverse Cuthill-McKee). The constraints are most easily represented with a Plain constraint handler. Once all the components of an analysis are defined, the Analysis object itself is created. For this problem a Static Analysis object is used. Output Specification When the analysis is complete the state of node 4 and all three elements will be printed to the screen. Nothing is recorded for later use. OpenSees Script The Tcl script for the example is shown below. A comment is indicated by a \# symbol. In the comments below, the syntax for important commands are given. # OpenSees Example 1.1 # OpenSees Primer # # Units: kips, in, sec # ------------------------------ # Start of model generation # ------------------------------ # Create ModelBuilder (with two-dimensions and 2 DOF/node) model BasicBuilder -ndm 2 -ndf 2 # Create nodes & add to Domain - command: node nodeId xCrd yCrd node 1 0.0 0.0 node 2 144.0 0.0 node 3 168.0 0.0 node 4 72.0 96.0 # Set the boundary conditions - command: fix nodeID xResrnt? yRestrnt? fix 1 1 1 fix 2 1 1 fix 3 1 1 # Define materials for truss elements # ----------------------------------- # Create Elastic material prototype - command: uniaxialMaterial Elastic matID E

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