OpenSees Example 3. Cantilever Column with units

Introduction

The principal features of this example is the introduction of units and the separation of the model-building and the analysis portions of the input file. For demonstration purposes, this example visits the 2D cantilever column, again.

Input

Model Building

The following tasks are performed when building the model

• define units
• define model
• define recorders for output
• define & apply gravity

Elastic Element Files Ex3.Canti2D.build.ElasticElement.tcl Notes Effective axial and flexural stiffnesses are defined at the element level elasticBeamColumn elements

Distributed Plasticity Element, Uniaxial Section Files Ex3.Canti2D.build.InelasticSection.tcl Notes Axial and flexural stiffnesses/strength are defined independently at the section level uniaxial inelastic section (moment-curvature) nonlinear beam-column elements

Distributed Plasticity Element, Fiber Section Files Ex3.Canti2D.build.InelasticFiberSection.tcl Notes The section is broken down into fibers where uniaxial materials are defined independently. The program calculates flexural and axial stiffnesses/strength by integrating strains across the section. fiber section nonlinear beam-column elements

Lateral-Load Analysis

The following tasks are performed in the analysis

• define lateral-load parameters
• analyze

Static Pushover Files Ex3.Canti2D.analyze.Static.Push.tcl Notes One-directional displacement-controlled static loading

Dynamic EQ Ground Motion Files Ex3.Canti2D.analyze.Dynamic.EQ.Uniform.tcl BM68elc.acc (ground-motion file) Notes Earthquake (from file) acceleration input Same acceleration input at all nodes restrained in specified direction

Run

The following combinations of model-building and analysis can be performed with this example:

• To run Elastic Mode, Static Pushover Analysis:

puts " -------------Elastic Model -------------"
puts " -------------Static Pushover Analysis -------------"
source Ex3.Canti2D.build.ElasticElement.tcl
source Ex3.Canti2D.analyze.Static.Push.tcl

• To run Elastic Mode, Uniform Earthquake Excitation:

puts " -------------Elastic Model -------------"
puts " -------------Uniform Earthquake Excitation -------------"
source Ex3.Canti2D.build.ElasticElement.tcl
source Ex3.Canti2D.analyze.Dynamic.EQ.Uniform.tcl

• To run Uniaxial Inelastic Section, Nonlinear Model, Static Pushover Analysis

puts " -------------Uniaxial Inelastic Section, Nonlinear Model -------------"
puts " -------------Static Pushover Analysis -------------"
source Ex3.Canti2D.build.InelasticSection.tcl
source Ex3.Canti2D.analyze.Static.Push.tcl

• To run Uniaxial Inelastic Section, Nonlinear Model, Uniform Earthquake Excitation

puts " -------------Uniaxial Inelastic Section, Nonlinear Model -------------"
puts " -------------Uniform Earthquake Excitation -------------"
source Ex3.Canti2D.build.InelasticSection.tcl
source Ex3.Canti2D.analyze.Dynamic.EQ.Uniform.tcl

• To run Uniaxial Inelastic Material, Fiber Section, Nonlinear Mode, Static Pushover Analysis

puts " -------------Uniaxial Inelastic Material, Fiber Section, Nonlinear Model -------------"
puts " -------------Static Pushover Analysis -------------"
source Ex3.Canti2D.build.InelasticFiberSection.tcl
source Ex3.Canti2D.analyze.Static.Push.tcl

• To run Uniaxial Inelastic Material, Fiber Section, Nonlinear Mode, Uniform Earthquake Excitation

puts " -------------Uniaxial Inelastic Material, Fiber Section, Nonlinear Model -------------"
puts " -------------Uniform Earthquake Excitation -------------"
source Ex3.Canti2D.build.InelasticFiberSection.tcl
source Ex3.Canti2D.analyze.Dynamic.EQ.Uniform.tcl

Notes

• This example is the first to follow most of the recommended techniques in building an input file:

• Model and analysis parameters are defined as variables
• The basic units, used to define Force, Length and Time need to be independent.
• Units need to be used consistently throughout the input file, otherwise some arguments will not scale properly
• The model-building files and the analysis files are separated. The same analysis file can be used on different model-building files (elastic or inelastic elements).
• This example does not, however, take advantage of previously-defined Tcl procedures and scripts, as will Example 4.

• In OpenSees/Tcl, units are simply defined as variables that become scaling factors. This technique allows the user to input variables with different types of units, not just the ones chosen for output. For example, section widths can be defined in inches, while element length can be defined in feet.

For example, with the following commands used in setting some of the units:

set in 1.; # define basic units -- output units
set kip 1.; # define basic units -- output units
set sec 1.; # define basic units -- output units
# -------
set ft [expr 12.*$in]; # define engineering units
set ksi [expr $kip/pow($in,2)];

When the user says:

set HCol [expr 3*$in];
set LCol [expr 30*$ft];

Tcl multiplies 30 by 12 to give the column length in inches. By scaling the input, all input processed by OpenSees is in the basic units, as is the output.

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