OpenSees Example 9. Build & Analyze a Section Example

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Introduction

For the case of the uniaxial section, moment-curvature and axial force-deformation curves are defined independently, and numerically.

For the case of the fiber sections (steel and RC), uniaxial materials are defined numerically (stress-strain relationship) and are combined into a fiber section where moment-curvature and axial force-deformation characteristics and their interaction are calculated computationally.



Input

Model Building

  • 2D vs. 3D
While this distinction does not affect the section definition itself, it affects the degree-of-freedom associated with moment and curvature in the subsequent analysis.
There are two differences between the two models:
1. The space defined with the model command (# Define the model builder, ndm=#dimension, ndf=#dofs)
2D
model BasicBuilder -ndm 2 -ndf 3;
3D
model BasicBuilder -ndm 3 -ndf 6;
2. In the 3D model, torsional stiffness needs to be aggregated to the section


Uniaxial Section

ExampleSection Uniaxial.GIF

Files
Notes
  • Flexure and axial behavior are uncoupled in this type of section

Fiber Section: AISC Standard W Section

ExampleSection W.GIF

Files
Notes
  • Coupled biaxial flexure and axial behavior

Fiber Section: Reinforced Concrete Section -- Rectangular Symmetric Section, Unconfined Concrete

ExampleSection RCSymmUnconf.GIF

Files
Notes
  • Coupled biaxial flexure and axial behavior

Fiber Section: Reinforced Concrete Section -- Rectangular Symmetric Section, Confined Concrete Core

ExampleSection RCSymmConf.GIF

Files
Notes
  • Coupled biaxial flexure and axial behavior

Fiber Section: Reinforced Concrete Section -- Rectangular Section

ExampleSection RCrect.GIF

Files
Notes
  • Coupled biaxial flexure and axial behavior
  • generic rectangular section

Fiber Section: Reinforced Concrete Section -- Circular Section, Confined Core

ExampleSection RCcirc.GIF

Files
Notes
  • Coupled biaxial flexure and axial behavior
  • generic circular section

Fiber Section: Reinforced Concrete Hollow Section -- Symmetric Section, Confined Concrete

HollowRC.PNG

Files
Notes
  • Coupled biaxial flexure and axial behavior

Moment-Curvature Analysis

  • This example introduces the moment-curvature procedures for sections in 2D or 3D space, as built in the previous section. (the only difference between them is the degree-of-freedom corresponding to curvature).
  • The moment-curvature analysis of a section is by creating a zero-length rotational-spring element. This section is subjected to a user-defined constant axial load and to a linearly-increasing moment to a user-defined maximum curvature.


2D Moment-Curvature Analysis

Files
Notes

3D Moment-Curvature Analysis

Files
Notes



Run

The model and analysis combinations for this example are numerous. The following are an small subset, for demonstration purposes:

  • To run Uniaxial-Section Model, 2D
puts " --------------------------------- 2D Model ---------------"
puts " a. Uniaxial Section"
source Ex9a.build.UniaxialSection2D.tcl
source Ex9.analyze.MomentCurvature2D.tcl
  • To run RC Section: Rectangular, Confined, Symmetric Model, 3D
puts " --------------------------------- 3D Model ---------------"
puts " d. RC Section: Rectangular, Confined, Symmetric"
source Ex9d.build.RCSection.RectConfinedSymm3D.tcl
source Ex9.analyze.MomentCurvature3D.tcl

Notes


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