Examples Manual

Introduction

The examples in this manual are listed in order of simplicity.

NOTE: gravity analysis is always included as part of the model building

Models

The following types of models are represented in these examples:

Elastic Elements

OpenSees Elastic Beam Column Element

The elastic, uncoupled, axial and flexural stiffnesses are defined at the element level

user specifies: E,I,A

Inelastic Elements

OpenSees Force-Based Beam-Column Element

Two types of sections

Uniaxial Section

The inelastic, uncoupled, axial and flexural stiffnesses are defined at the section level

The OpenSees Uniaxial Section Command is used

User specifies:

Axial stiffness A

Section Moment-Curvature characteristics via the OpenSees UniaxialMaterial Command

Fiber Section

The section is broken down into fibers where uniaxial materials are defined independently.

The program calculates the coupled flexural and axial stiffnesses/strength by integrating strains across the section

The OpenSees Fiber Section Command is used

User specifies

Stress-Strain characteristics via the OpenSees UniaxialMaterial Command for all number of materials

Section geometry via series of Patches and Layers in the fiber section

Two Section Geometries are presented

*RC Rectangular Section

*Standard AISC W section

Lateral Loads

The following types of lateral loads are represented in these examples:

Static Pushover

Control node is located at the highest floor

Lateral-load distribution is proportional the the mass distribution along the height of the building

Static analysis

Two types

Monotonic Pushover

One-directional displacement-controlled static lateral loading

Reversed Cyclic Pushover

One-directional displacement-controlled static lateral loading

Displacement cycles are imposed in positive and negative direction

Time-Dependent Dynamic Loads

Transient analysis

Four types

Uniform Sine-Wave

Sine-wave acceleration input

Same acceleration input at all nodes restrained in specified direction

Multiple-Support Sine-Wave

Sine-wave displacement input

Different displacements are specified at particular nodes in specified directions

Uniform Earthquake

Earthquake (from file) acceleration input

Same acceleration input at all nodes restrained in specified direction

Multiple-Support Earthquake

Earthquake (from file) displacement input

Different displacements are specified at particular nodes in specified direction

Bidirectional Earthquake

Different inputs are specified for two directions

Same acceleration input at all nodes restrained in specified direction

Simulation Process

Each example script does the following:

Build the model

1. model dimensions and degrees-of-freedom
2. nodal coordinates
3. nodal constraints -- boundary conditions
4. nodal masses
5. elements and element connectivity
6. recorders for output

Define & apply gravity load

1. nodal or element load
2. static-analysis parameters (tolerances & load increments)
3. analyze
4. hold gravity loads constant
5. reset time to zero

Define and apply lateral load

1. load pattern (nodal loads for static analysis, support ground motion for earthquake)
2. lateral-analysis parameters (tolerances & displacement/time increments)
   • Static Lateral-Load Analysis
     • define the displacement increments and displacement path
   • Dynamic Lateral-Load Analysis
     • define the input motion and all associated parameters, such as scaling and input type
     • define analysis duration and time increment
     • define damping
3. analyze

Introductory Examples

The objective of Example 1a and Example 1b is to give an overview of input-file format in OpenSees using simple scripts.
These scripts do not take advantage of the Tcl scripting capabilities shown in the later examples. However, they do provide starting a place where the input file is similar to that of more familiar Finite-Element Analysis software. Subsequent examples should be used as the basis for user input files.

OpenSees Example 1a. 2D Elastic Cantilever Column

Objectives overview of basic OpenSees input structure coordinates, boundary conditions, element connectivity, nodal masses, nodal loads, etc. two-node, one element

Models elastic elements

Analyses static pushover dynamic earthquake-input

OpenSees Example 1b. Elastic Portal Frame

Objectives two element types distributed element loads

Models elastic elements

Analyses static pushover dynamic earthquake-input

Simple Examples of Nonlinear-Models

OpenSees Example 2a. Elastic Cantilever Column with variables

Objectives introduce variable: define & use

Models elastic element

Analyses static pushover dynamic earthquake-input

OpenSees Example 2b. Nonlinear Cantilever Column: Uniaxial Inelastic Section

Objectives first example of nonlinear model, set nonlinearity at section level

Models nonlinearBeamColumn element uniaxial section

Analyses static pushover dynamic earthquake-input

OpenSees Example 2c. Nonlinear Cantilever Column: Inelastic Uniaxial Materials in Fiber Section

Objectives set nonlinearity at material level material stress-strain response is assembled into fiber section reinforced-concrete fiber section

Models nonlinearBeamColumn element uniaxial material fiber section (Reinforced-concrete fiber section)

Analyses static pushover dynamic earthquake-input

2D Structural Modeling & Analysis Examples

These examples take advantage of the Tcl scripting language starting from simple variable substitutions in the initial examples, to the more advanced techniques of array management and logical expressions (if-then statements).

OpenSees Example 3. Cantilever Column with units

Objectives units, defined and used (they will be used in all subsequent examples) separate model-building and analysis files introduce PDelta effects (or not)

Models elastic elements inelastic uniaxial section fiber section (Reinforced-concrete fiber section) Linear, PDelta or Corotational Transformation

Analyses static pushover dynamic earthquake-input

OpenSees Example 4. Portal Frame

Objectives use previously-defined procedures to simplify input introduce more analysis types introduce procedure to read database input motion files (data with text in first lines)

Models elastic elements inelastic uniaxial section inelastic fiber section (Reinforced-concrete fiber section)

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

OpenSees Example 5. 2D Frame, 3-story 3-bay, Reinforced-Concrete Section & Steel W-Section

Objectives 2D frame of fixed geometry: 3-story, 3-bay nodes and elements are defined manually, one by one

Models Reinforced-Concrete Section Steel W-Section elastic uniaxial section inelastic uniaxial section inelastic fiber section

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

OpenSees Example 6. generic 2D Frame, N-story N-bay, Reinforced-Concrete Section & Steel W-Section

Objectives 2D frame geometry of variable geometry ( # stories and # bays are variables) node and element definition is automated use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 2D

Models Reinforced-Concrete Section Steel W-Section elastic uniaxial section inelastic uniaxial section inelastic fiber section

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

OpenSees Example 5. 2D Frame, 3-story 3-bay, Reinforced-Concrete Section & Steel W-Section

Objectives 2D frame of fixed geometry: 3-story, 3-bay nodes and elements are defined manually, one by one

Models Reinforced-Concrete Section Steel W-Section elastic uniaxial section inelastic uniaxial section inelastic fiber section

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

OpenSees Example 6. generic 2D Frame, N-story N-bay, Reinforced-Concrete Section & Steel W-Section

Objectives 2D frame geometry of variable geometry ( # stories and # bays are variables) node and element definition is automated use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 2D

Models Reinforced-Concrete Section Steel W-Section elastic uniaxial section inelastic uniaxial section inelastic fiber section

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

3D Structural Modeling & Analysis Examples

A few items are new in 3D:

• Additional coordinates need to be considered in defining nodes
• Additional degrees of freedom need to be considered in defining the following:
  • nodal constraints (boundary conditions)
  • nodal masses
  • nodal loads
• The transformation from local element/section coordinates to global system coordinates needs to be specified
• Element loads are specified in local coordinates
• Additional arguments are required for many elements (bending about local-y axis) properties
• Element/Section torsional stiffness needs to be considered
• Rigid floor diaphragms need be included for building models

OpenSees Example 7. 3D Frame, 3-story 3-bayX 3-bayZ, Reinforced-Concrete Section & Steel W-Section

Objectives 3D frame of fixed geometry nodes and elements are manually manually, one by one introduce rigid floor diaphragm use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 3D

Models Reinforced-Concrete Section Steel W-Section Elastic or Fiber Section option is a variable within one input file rigid diaphragm

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

OpenSees Example 8. generic 3D Frame, NStory NBayX NBayZ, Reinforced-Concrete Section & Steel W-Section

Objectives 3D frame geometry of variable geometry ( # stories and # bays in X and Z are variables) node and element definition is automated introduce user-input interface, the user is given the option as to what to view in model

Models Reinforced-Concrete Section Steel W-Section Elastic or Fiber Section option is a variable within one input file optional rigid diaphragm

Analyses static reversed cyclic analysis dynamic sine-wave input analysis (uniform excitation) dynamic earthquake-input analysis (uniform excitation) dynamic sine-wave input analysis (multiple-support excitation) dynamic earthquake-input analysis (multiple-support excitation) dynamic bidirectional earthquake-input analysis (uniform excitation)

Section Modeling And Analysis Examples

OpenSees Example 9. Build & Analyze a Section Example

Objectives defined section using uniaxial behavior (define moment-curvature curve) or define section using uniaxial materials (define stress-strain curve) in fiber section

Models Uniaxial Nonlinear section Fiber Steel W-section Fiber RC symmetric rectangular unconfined-concrete section Fiber RC symmetric rectangular unconfined & confined-concrete section Fiber RC generalized rectangular section Fiber RC generalized circular section

Analyses 2D static unidirectional moment-curvature analysis 3D static unidirectional moment-curvature analysis

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