OpenSees Example 9. Build & Analyze a Section Example

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

Files Ex9a.build.UniaxialSection2D.tcl Ex9a.build.UniaxialSection3D.tcl LibUnits.tcl

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

Fiber Section: AISC Standard W Section

Files Ex9b.build.WSection2D.tcl Ex9b.build.WSection3D.tcl LibUnits.tcl

Notes Coupled biaxial flexure and axial behavior

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

Files Ex9c.build.RectUnconfinedSymm2D.tcl Ex9c.RectUnconfinedSymm3D.WSection3D.tcl LibUnits.tcl

Notes Coupled biaxial flexure and axial behavior

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

Files Ex9d.build.RectUnconfinedSymm2D.tcl Ex9d.build.RectUnconfinedSymm3D.tcl LibUnits.tcl

Notes Coupled biaxial flexure and axial behavior

Fiber Section: Reinforced Concrete Section -- Rectangular Section

Files Ex9e.build.Rect2D.tcl Ex9e.build.Rect3D.tcl LibUnits.tcl

Notes Coupled biaxial flexure and axial behavior generic rectangular section

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

Files Ex9f.build.Circ2D.tcl Ex9f.build.Circ3D.tcl LibUnits.tcl

Notes Coupled biaxial flexure and axial behavior generic circular section

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 Ex9.analyze.MomentCurvature2D.tcl MomentCurvature2D.tcl

Notes

3D Moment-Curvature Analysis

Files Ex9.analyze.MomentCurvature3D.tcl MomentCurvature3D.tcl

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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