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The following examples are listed in order of simplicity.</p>
The following examples are listed in order of simplicity.


NOTE: gravity analysis is always included as part of the model building.</p>
NOTE: gravity analysis is always included as part of the model building.


<h1 class="heading1">Introductory Example</h1>
* <big><strong> [[OpenSees Examples -- Introductory Example]]</strong></big>
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<td style = "border-left:2px solid #010101;" colspan="4" width="558"><p class="heading3"><strong class="buttons">[[OpenSees Example 1a. 2D Elastic Cantilever Column]]</strong></p>
<td style = "border-left:2px solid #010101;" colspan="4" width="558"><big>[[OpenSees Example 1a. 2D Elastic Cantilever Column]] </big>
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<td width="210"><p class="tablebodytext">&nbsp;</p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">overview of basic OpenSees input structure</li><li class="listbullet">coordinates, boundary conditions, element connectivity, nodal masses, nodal loads, etc.</li><li class="listbullet">two-node, one element</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">overview of basic OpenSees input structure</li><li class="listbullet">coordinates, boundary conditions, element connectivity, nodal masses, nodal loads, etc.</li><li class="listbullet">two-node, one element</li></ul></td>
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<td style = "border-left:2px solid #010101;" colspan="4" width="558"><p class="heading3"><strong class="buttons">[[OpenSees Example 1b. 2D Elastic Portal Frame]]</strong></p>
<td style = "border-left:2px solid #010101;" colspan="4" width="558"><big>[[OpenSees Example 1b. Elastic Portal Frame]]</big>
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<td width="210"><p class="tablelistbullet">&nbsp;</p>
<td width="210"><p class="tablelistbullet">&nbsp;</p>
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<td style = "border-bottom:2px solid #010101;" width="270"><p class="tablebodytext"><img src="3459.png" alt="Embedded Power-Point Image" height="205.7" width="237.6" vspace="0" hspace="0" align="bottom" border="0"></p>
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<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">two element types</li><li class="listbullet">distributed element loads</li></ul></td>
<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">two element types</li><li class="listbullet">distributed element loads</li></ul></td>
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<h2 class="heading2"><a id="h3620" class="" title="Simple Nonlinear-Analysis Example" href="3587.htm" target="_self">Simple Nonlinear Analysis Example</a></h2>
* <big><strong> [[OpenSees Examples -- Simple Nonlinear Analysis Example]]</strong></big>
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<td style = "border-left:2px solid #010101;" colspan="5" width="768"><h2 class="heading2"><strong class="buttons"><a id="h3602" class="jumptemplate" title="Example 2a. Elastic Cantilever Column with variables" href="3599.htm" target="_self">Example 2a. Elastic Cantilever Column</a></strong><strong class="buttons"> with variables</strong></h2>
<td style = "border-left:2px solid #010101;" colspan="5" width="768"><big> [[OpenSees Example 2a. Elastic Cantilever Column with variables]]</big>
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<td style = "border-right:2px solid #010101;" colspan="2" width="456"><p class="tablelistbullet">&nbsp;</p>
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<td width="270"><p class="tablebodytext"><img src="3895.png" alt="Embedded Power-Point Image" height="171.05" width="160.6" vspace="0" hspace="0" align="bottom" border="0"></p>
<td width="270"><p class="tablebodytext">image</p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">introduce variable: define &amp; use</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">introduce variable: define &amp; use</li></ul></td>
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<td style = "border-left:2px solid #010101;" colspan="5" width="768"><h2 class="heading2"><strong class="buttons"><a id="h3603" class="" title="Example 2b. Nonlinear Cantilever Column: Uniaxial Inelastic Section" href="3600.htm" target="_self">Example 2b. Nonlinear Cantilever Column: Uniaxial Inelastic Section</a></strong></h2>
<td style = "border-left:2px solid #010101;" colspan="5" width="768"><big>[[OpenSees Example 2b. Nonlinear Cantilever Column: Uniaxial Inelastic Section]]</big>
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<td style = "border-right:2px solid #010101;" colspan="2" width="456"><p class="tablelistbullet">&nbsp;</p>
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<td width="270"><p class="tablebodytext"><img src="3896.png" alt="Embedded Power-Point Image" height="171.05" width="175.45" vspace="0" hspace="0" align="bottom" border="0"></p>
<td width="270"><p class="tablebodytext">image</p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">first example of nonlinear model, set nonlinearity at section level</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">first example of nonlinear model, set nonlinearity at section level</li></ul></td>
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<td style = "border-left:2px solid #010101;" colspan="5" width="768"><h2 class="heading2"><strong class="buttons"><a id="h3604" class="" title="Example 2c. Nonlinear Cantilever Column: Inelastic Uniaxial Materials in Fiber Section" href="3601.htm" target="_self">Example 2c. Nonlinear Cantilever Column: Inelastic Uniaxial Materials in Fiber Section</a></strong></h2>
<td style = "border-left:2px solid #010101;" colspan="5" width="768"><big>[[OpenSees Example 2c. Nonlinear Cantilever Column: Inelastic Uniaxial Materials in Fiber Section]]</big>
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<td style = "border-right:2px solid #010101;" colspan="2" width="456"><p class="tablelistbullet">&nbsp;</p>
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<td style = "border-bottom:2px solid #010101;" width="270"><p class="tablebodytext"><img src="3897.png" alt="Embedded Power-Point Image" height="171.05" width="218.9" vspace="0" hspace="0" align="bottom" border="0"></p>
<td style = "border-bottom:2px solid #010101;" width="270"><p class="tablebodytext">image</p>
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<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">set nonlinearity at material level</li><li class="listbullet">material stress-strain response is assembled into fiber section</li><li class="listbullet">reinforced-concrete fiber section</li></ul></td>
<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">set nonlinearity at material level</li><li class="listbullet">material stress-strain response is assembled into fiber section</li><li class="listbullet">reinforced-concrete fiber section</li></ul></td>
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<td colspan="3" width="468"><h2 class="heading2">&nbsp;</h2>
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<h2 class="heading2"><a id="h3621" class="" title="2D Structural Modelling &amp; Analysis Examples" href="3588.htm" target="_self">2D Structural Modelling &amp; Analysis Examples</a></h2>
* <big><strong> [[OpenSees Examples -- 2D Structural Modelling &amp; Analysis Examples]]</strong></big>
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<td style = "border-left:2px solid #010101;" colspan="4" width="558"><p class="heading3"><strong class="buttons"><a id="h3503" class="" title="Example 3. 2D RC Cantilever" href="3472.htm" target="_self">Example 3. Cantilever Column</a></strong><strong class="buttons"> with units</strong></p>
<td style = "border-left:2px solid #010101;" colspan="4" width="558"><big>[[OpenSees Example 3. 2D RC Cantilever]]</big>
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<td width="210"><p class="tablebodytext">&nbsp;</p>
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<td width="270"><p class="tablebodytext"><img src="3460.png" alt="Embedded Power-Point Image" height="213.95" width="103.4" vspace="0" hspace="0" align="bottom" border="0"></p>
<td width="270"><p class="tablebodytext">image</p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">units, defined and used (they will be used in all subsequent examples)</li><li class="listbullet">separate model-building and analysis files</li><li class="listbullet">introduce PDelta effects (or not)</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">units, defined and used (they will be used in all subsequent examples)</li><li class="listbullet">separate model-building and analysis files</li><li class="listbullet">introduce PDelta effects (or not)</li></ul></td>
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<td style = "border-left:2px solid #010101;" colspan="4" width="558"><p class="heading3"><strong class="buttons"><a id="h3504" class="" title="Example 4. 2D RC Portal Frame" href="3312.htm" target="_self">Example 4.  Portal Frame</a></strong></p>
<td style = "border-left:2px solid #010101;" colspan="4" width="558"><big>[[OpenSees Example 4.  Portal Frame]]</big>
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<td width="270"><p class="tablebodytext"><img src="3461.png" alt="Embedded Power-Point Image" height="202.4" width="234.3" vspace="0" hspace="0" align="bottom" border="0"></p>
<td width="270"><p class="tablebodytext">image</p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">use previously-defined procedures to simplify input</li><li class="listbullet">introduce more analysis types</li><li class="listbullet">introduce procedure to read database input motion files (data with text in first lines)</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">use previously-defined procedures to simplify input</li><li class="listbullet">introduce more analysis types</li><li class="listbullet">introduce procedure to read database input motion files (data with text in first lines)</li></ul></td>
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<td style = "border-left:2px solid #010101;" colspan="5" width="768"><p class="heading3"><strong class="buttons"><a id="h3505" class="" title="Example 5. 2D Frame ? 3-story, 3-bay (RC &amp; W-section)" href="3326.htm" target="_self">Example 5. 2D Frame, 3-story 3-bay</a></strong><strong class="buttons">, Reinforced-Concrete Section &amp; Steel W-Section</strong></p>
<td style = "border-left:2px solid #010101;" colspan="5" width="768"><big>[[OpenSees Example 5. 2D Frame ? 3-story, 3-bay (RC &amp; W-section)]]</big>
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<td style = "border-right:2px solid #010101;" colspan="2" width="456"><p class="bodytext">&nbsp;</p>
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<td style = "border-left:2px solid #010101;" colspan="2" width="324"><p class="tablebodytext"><img src="3462.png" alt="Embedded Power-Point Image" height="234.3" width="380.6" vspace="0" hspace="0" align="bottom" border="0"></p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">2D frame of fixed geometry: 3-story, 3-bay</li><li class="listbullet">nodes and elements are defined manually, one by one</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">2D frame of fixed geometry: 3-story, 3-bay</li><li class="listbullet">nodes and elements are defined manually, one by one</li></ul></td>
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<td style = "border-left:2px solid #010101;" colspan="5" width="768"><p class="heading3"><strong class="buttons"><a id="h3506" class="" title="Example 6. Generic 2D Frame, N-story, N-bay (RC &amp; W-section)" href="3329.htm" target="_self">Example 6.  generic 2D Frame, N-story N-bay</a></strong><strong class="buttons">, Reinforced-Concrete Section &amp; Steel W-Section</strong></p>
<td style = "border-left:2px solid #010101;" colspan="5" width="768"><big>[[OpenSees Example 6. Generic 2D Frame: N-story, N-bay (RC &amp; W-section)]]</big>
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<td style = "border-right:2px solid #010101;" colspan="2" width="456"><p class="bodytext">&nbsp;</p>
<td style = "border-right:2px solid #010101;" colspan="2" width="456"><p class="bodytext">&nbsp;</p>
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<td style = "border-left:2px solid #010101;border-bottom:2px solid #010101;" colspan="2" width="324"><p class="tablebodytext"><img src="3502.png" alt="Embedded Power-Point Image" height="260.15" width="435.05" vspace="0" hspace="0" align="bottom" border="0"></p>
<td style = "border-left:2px solid #010101;border-bottom:2px solid #010101;" colspan="2" width="324"><p class="tablebodytext">image</p>
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<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">2D frame geometry of variable geometry ( # stories and # bays are variables)</li><li class="listbullet">node and element definition is automated</li><li class="listbullet">use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 2D</li></ul></td>
<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">2D frame geometry of variable geometry ( # stories and # bays are variables)</li><li class="listbullet">node and element definition is automated</li><li class="listbullet">use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 2D</li></ul></td>
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<td colspan="4" width="558"><h2 class="heading2">&nbsp;</h2>
<td colspan="6" width="558">
<h2 class="heading2"><a id="h3622" class="" title="3D Structural Modelling &amp; Analysis Examples" href="3589.htm" target="_self">3D Structural Modelling &amp; Analysis Examples</a></h2>
* <big><strong> [[OpenSees Examples -- 3D Structural Modelling &amp; Analysis Examples]]</strong></big>
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<td style = "border-left:2px solid #010101;border-right:2px solid #010101;" colspan="7" width="1224"><p class="heading3"><strong class="buttons"><a id="h3507" class="" title="Example 7. 3D Moment-Resisting Frame  (RC &amp; W-section)" href="3330.htm" target="_self">Example 7.  3D Frame, 3-story 3-bayX 3-bayZ</a></strong><strong class="buttons">, Reinforced-Concrete Section &amp; Steel W-Section</strong></p>
<td style = "border-left:2px solid #010101;border-right:2px solid #010101;" colspan="7" width="1224"><big>[[OpenSees Example 7. 3D Moment-Resisting Frame  (RC &amp; W-section)]]</big>
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<td style = "border-left:2px solid #010101;" colspan="2" width="324"><p class="tablebodytext"><img src="3779.png" alt="Embedded Power-Point Image" height="372.9" width="298.65" vspace="0" hspace="0" align="bottom" border="0"></p>
<td style = "border-left:2px solid #010101;" colspan="2" width="324"><p class="tablebodytext">image</p>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">3D frame of fixed geometry</li><li class="listbullet">nodes and elements are manually manually, one by one</li><li class="listbullet">introduce rigid floor diaphragm</li><li class="listbullet">use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 3D</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">3D frame of fixed geometry</li><li class="listbullet">nodes and elements are manually manually, one by one</li><li class="listbullet">introduce rigid floor diaphragm</li><li class="listbullet">use previously-defined procedures to view model node numbers and elements, deformed shape, and displacement history, in 3D</li></ul></td>
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<td style = "border-left:2px solid #010101;border-right:2px solid #010101;" colspan="7" width="1224"><p class="heading3"><strong class="buttons"><a id="h3508" class="" title="Example 8. generic 3D Frame ? Nstory, NbayX,NBayZ (RC &amp; W-section)" href="3332.htm" target="_self">Example 8.  generic 3D Frame, NStory NBayX NBayZ</a></strong><strong class="buttons">, Reinforced-Concrete Section &amp; Steel W-Section</strong></p>
<td style = "border-left:2px solid #010101;border-right:2px solid #010101;" colspan="7" width="1224"><big>[[OpenSees Example 8. generic 3D Frame ? Nstory, NbayX,NBayZ (RC &amp; W-section)]] </big>
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<td style = "border-left:2px solid #010101;border-bottom:2px solid #010101;" colspan="2" width="324"><p class="tablelistbullet"><img src="3904.png" alt="Embedded Power-Point Image" height="429" width="391.6" vspace="0" hspace="0" align="bottom" border="0"></p>
<td style = "border-left:2px solid #010101;border-bottom:2px solid #010101;" colspan="2" width="324"><p class="tablelistbullet">image</p>
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<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">3D frame geometry of variable geometry ( # stories and # bays in X and Z are variables)</li><li class="listbullet">node and element definition is automated</li><li class="listbullet">introduce user-input interface, the user is given the option as to what to view in model</li></ul></td>
<td style = "border-bottom:2px solid #010101;" colspan="2" width="234"><ul class="listbullet"><li class="listbullet">3D frame geometry of variable geometry ( # stories and # bays in X and Z are variables)</li><li class="listbullet">node and element definition is automated</li><li class="listbullet">introduce user-input interface, the user is given the option as to what to view in model</li></ul></td>
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<td colspan="4" width="558"><h2 class="heading2"><strong class="buttons"><a id="h3859" class="" title="Section Modelling And Analysis" href="3590.htm" target="_self">Section Modelling And Analysis</a></strong></h2>
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* <big><strong> [[OpenSees Examples -- Section Modelling And Analysis]]</strong></big>
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<td style = "border-left:2px solid #010101;border-top:2px solid #010101;" colspan="4" width="558"><p class="tablelistbullet"><strong class="buttons"><a id="h3585" class="" title="Example 9. Build a Fiber Section" href="3534.htm" target="_self">Example 9. Build  &amp; Analyze a Section</a></strong></p>
<td style = "border-left:2px solid #010101;border-top:2px solid #010101;" colspan="4" width="558"><big>[[OpenSees Example 9. Build a Fiber Section]]</big>
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<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">defined section using uniaxial behavior (define moment-curvature curve) or</li><li class="listbullet">define section using uniaxial materials (define stress curve) in fiber section</li></ul></td>
<td colspan="2" width="234"><ul class="listbullet"><li class="listbullet">defined section using uniaxial behavior (define moment-curvature curve) or</li><li class="listbullet">define section using uniaxial materials (define stress curve) in fiber section</li></ul></td>
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Latest revision as of 20:36, 9 November 2009


The following examples are listed in order of simplicity.

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

 

Objectives and Characteristics

Model Types

Analysis Types
OpenSees Example 1a. 2D Elastic Cantilever Column

 

 

 

  • overview of basic OpenSees input structure
  • coordinates, boundary conditions, element connectivity, nodal masses, nodal loads, etc.
  • two-node, one element
  • elastic elements
  • static pushover analysis
  • dynamic earthquake-input analysis
OpenSees Example 1b. Elastic Portal Frame

 

 

 
  • two element types
  • distributed element loads
  • elastic elements
  • static pushover analysis
  • dynamic earthquake-input analysis

 

 

 

 

Objectives and Characteristics

Model Types

Analysis Types
OpenSees Example 2a. Elastic Cantilever Column with variables

 

 

image
  • introduce variable: define & use
  • elastic element
  • static pushover analysis
  • dynamic earthquake-input analysis
OpenSees Example 2b. Nonlinear Cantilever Column: Uniaxial Inelastic Section

 

 

image
  • first example of nonlinear model, set nonlinearity at section level
  • nonlinearBeamColumn element
  • uniaxial section
  • static pushover analysis
  • dynamic earthquake-input analysis

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

 

 

image
  • set nonlinearity at material level
  • material stress-strain response is assembled into fiber section
  • reinforced-concrete fiber section
  • nonlinearBeamColumn element
  • uniaxial material
  • fiber section (Reinforced-concrete fiber section)
  • static pushover analysis
  • dynamic earthquake-input analysis

 

 

 

 

 

Objectives and Characteristics

Model Types

Analysis Types
OpenSees Example 3. 2D RC Cantilever

 

 

 

image
  • units, defined and used (they will be used in all subsequent examples)
  • separate model-building and analysis files
  • introduce PDelta effects (or not)
  • elastic elements
  • inelastic uniaxial section
  • fiber section (Reinforced-concrete fiber section)
  • Linear, PDelta or Corotational Transformation
  • static pushover analysis
  • dynamic earthquake-input analysis (uniform excitation)
OpenSees Example 4. Portal Frame

 

 

 

image
  • 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)
  • elastic elements
  • inelastic uniaxial section
  • inelastic fiber section (Reinforced-concrete fiber section)
  • static pushover analysis
  • 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 (RC & W-section)

 

image
  • 2D frame of fixed geometry: 3-story, 3-bay
  • nodes and elements are defined manually, one by one
  • Reinforced-Concrete Section
  • Steel W-Section
  • elastic uniaxial section
  • inelastic uniaxial section
  • inelastic fiber section
  • static pushover analysis
  • 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 (RC & W-section)

 

image
  • 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
  • Reinforced-Concrete Section
  • Steel W-Section
  • elastic uniaxial section
  • inelastic uniaxial section
  • inelastic fiber section
  • static pushover analysis
  • 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)

 

 

 

Objectives and Characteristics

Model Types

Analysis Types
OpenSees Example 7. 3D Moment-Resisting Frame (RC & W-section)

image
  • 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
  • Reinforced-Concrete Section
  • Steel W-Section
  • Elastic or Fiber Section option is a variable within one input file
  • rigid diaphragm
  • static pushover analysis
  • 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 (RC & W-section)

image
  • 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
  • Reinforced-Concrete Section
  • Steel W-Section
  • Elastic or Fiber Section option is a variable within one input file optional rigid diaphragm
  • rigid diaphragm
  • static pushover analysis
  • 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 9. Build a Fiber Section

 

 

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

2D & 3D models of sections:

  • 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
  • 2D & 3D static unidirectional moment-curvature analysis

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 





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