reu report - process of seismic simulation of a 2-bay, 2-story reinforced concrete building

8/8/2019 REU Report - Process of Seismic Simulation of a 2-Bay, 2-Story Reinforced Concrete Building

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Process of Seismic Simulation of a 2-bay, 2-story Reinforced Concrete Building

Michelle Stadel1, Yashar Moslehy2, A. Laskar3, and Y.L. Mo4

Abstract

Computer simulation through such programs as OpenSees is an effective method

for studying earthquake engineering. Three key aspects of OpenSees code are modeling,

recorders and analysis. A two-story, two-bay reinforced concrete building will be tested

with multi-directional loads and the displacement simulated with computers. The

structure can be modeled in OpenSees and programmed to output the loads and the

corresponding displacements.

1.0 Introduction

Earthquakes impact reinforced concrete structures in various ways. Structural

engineers need to be able to model these effects in order to design better RC structures

that can withstand earthquakes and preserve lives. Computer simulations are the most

cost-effective way to predict and study buildings subjected to earthquake loading.

One such program is OpenSees, which is a finite element framework developed

by the University of California Berkeley in conjunction with the Pacific Earthquake

Engineering Research Center (PEER 2001). Previous research has shown that OpenSees

can effectively model structures and the impact of earthquake loading (Howser 2007).

1Department of Civil Engineering, South Dakota School of Mines & Technology, Rapid City, SD 57701

Email: [email protected] of Civil and Environmental Engineering, University of Houston, TX, 77204-4003

Email: [email protected] of Civil and Environmental Engineering, University of Houston, Houston, 77204-4003

Email: [email protected] of Civil and Environmental Engineering, University of Houston, Houston, 77204-4003Email: [email protected], Ph # 713-743-4274, Fax # 713-743-4260


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The National Center for Research on Earthquake Engineering (NCREE) in

Taiwan has prepared a near full-scale, two-story, two-bay RC building to test with multi-

directional loading. Researchers at the University of Houston are preparing a program in

OpenSees to model this structure in order to correlate future analytical tools and new

design methods (Hwang, et. al 2006). This paper will look at the process to develop such

a program in OpenSees and the analysis of the results generated.

2.0 Simulation of Concrete Structure

OpenSees stands for Open System for Earthquake Engineering Simulation. The

program is an open framework that allows users to develop code for modeling buildings

and soils in earthquake scenarios. OpenSees uses Tcl/Tk script to develop programs. Tcl

or Tool Command Language is a string-based scripting language that means an

expression can always be seen as a numeric value, a string or another value. Tk is the

graphical extension (Schwerd 2006).

Developing code first requires understanding the main objects needed to create an

OpenSees program. The three objects are modeling, analysis and output generation

(Mazzoni 2006). To better understand these concepts, a two-dimensional structure was

modeled and analyzed.

A two-bay, two-dimensional frame, as shown in Figure 1, was used in order to

correlate the concepts necessary for developing an OpenSees program with the NCREE

model. OpenSees does not have a two-bay frame; therefore, it was necessary to create

one.


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2.1 Modeling the structure

The first step in modeling any structure is to choose a coordinate system. Nodes,

points located on the structure can be easily labeled with a coordinate system originating

from node 1. Modeling requires establishing the position of nodes in order to link the

model together. The simplest node arrangement is to place one at each beam and column

intersection. For this problem, each beam was made up of four nodes and each column

had three nodes, one at each end and one in the center.

Each beam and column will be made up of different materials arranged in a

different fashion; therefore, it is necessary to define the cross-sections for both the beams

and the columns. To create a cross-section in OpenSees, the section command, which

represents force-deformation relationships at beam-column points, is used. Furthermore,

the cross-sections were defined as fibers, a command which creates smaller regions for

which the materials stress-strain response is integrated to give resultant behavior

(Mazzoni 2006). The fiber command is perfect for reinforced concrete to establish the

locations of materials such as cover concrete, core concrete and rebar in the cross-section.

The element command is the key to linking the nodes and the cross-sections

together. OpenSees contains ten different types of elements. In this scenario, nonlinear

beam-column elements were used to represent both beams and columns. These objects

were classified as nonlinear beam-columns because of the force formulation and the

spread of plasticity along the element. An element requires a unique element tag, two

different nodes to be linked, the number of integration points, the section tag or the

number that corresponds to the correct cross-section and the value that corresponds to the

correct coordinate transformation(Mazzoni 2006).


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The user must be sure to check units because OpenSees does not keep track of

units. Units were a problem in this example because the dimensions were metric and the

material properties were in English units. It was decided to convert all frame dimensions

from millimeters to inches.

2.1.1 Dimensions and cross-sections

Each column is 3,000 mm high with a 300 mm deep by 400 mm wide cross-

section, as shown in Figure 2a. The stirrups in the columns were No. 3 rebar spaced at

200 mm on center in addition to three rows of No. 7 rebar running the entire vertical

length of the column. All reinforcement was covered with at least 50 mm of concrete

Each beam was 4,000 mm in length and consisted of the same cross-sectional

area. The beams were 200 mm deep and 350 mm high. Reinforcement was again No. 3

rebar spaced at 250 mm on center. Two, No. 7 rebars run across the top of the beam

while the bottom row contained four bars as shown in Figure 2b.

2.1.2 Material properties

Defining the concrete properties was the next step in the model. The core concrete

of each section differed from the outside, cover concrete. The core concrete had a

measured 28-day compressive strength of 6.0 psi and a strain of 0.004 at max strength. At

the point of crushing, the concrete had a measured strength of 5.0 psi and a strain of

0.014.

The 50 millimeters of cover concrete had a 5.0 psi 28-day compressive strength.

A strain of 0.002 was measured at max strength. No crushing strength was found, but a

strain of 0.006 was measured.


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The reinforcing steel had a yield stress of 60.0 psi and a modulus of elasticity, E,

of 30,000 psi. No. 7 rebar has an area of 0.6 in2. The steel also had a strain hardening

ratio of 0.01.

Material properties were classified by the uniaxialMaterial command. The

concrete was represented by Concrete01, a zero tensile strength concrete. The reinforcing

steel was represented by Steel01, which is a uniaxial bilinear steel material object

(Mazzoni 2006). Also properties based on compression are entered as negative numbers.

2.1.3 Loading

Since earthquake loading acts in the horizontal direction, a lateral load of 100 kips

was applied to the top right corner (node 15) of Figure 1. In simulating a real-life model,

gravity loads should also be applied to the structure at this time, but for simplification of

the scenario, gravity loads were ignored.

2.2 Recorder generation

The purpose of this example is to find when the structure fails with this loading.

So the next step is to generate recorders that will output the displacement. The node

recorder and the element recorder are perhaps the most essential commands for

generating data in a pushover analysis. The recorder command generates a file which can

be opened in a database program and analyzed. Using the recorder plot command, it is

also possible to watch the data that is being stored in the file be graphed as it is obtained.

This can be useful in determining if the program is generating reasonable responses.


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2.3 Analysis

The analysis object is the last piece of the code generated. Analysis consists of six

components: constraint handler, degrees of freedom numberer, analysis model, integrator,

the solution algorithm and the system of equations.

First, the system of equations can be defined. This specifies how to store and

solve the system of equations for the analysis. Banded general was used to create an un-

symmetric banded system of equations object which will be factored and solved during

the analysis using the Lapack band general solver (Mazzoni 2006).

Second, the constraint handler, which tells OpenSees how to handle the boundary

conditions and imposed displacements, can be defined. The transformation method was

employed which reduces the size of the system for multi-point constraints.

Third, a numberer, either plain or a Reverse Cuthill-McKee (RCM) algorithm, is

chosen. For this example, the RCM numberer was used because this is the best algorithm

for large problems and will output a warning when the structure is disconnected.

Fourth, a normal displacement increment test was chosen for the convergence

test. This command requires a convergence tolerance and the maximum number of

iterations to be performed before failure to converge is returned, to be defined. Fifty

iterations and a convergence tolerance of 1.0e-12 were used in this analysis.

Fifth, the user must specify the solution algorithm that will be used to solve the

non-linear equation. For this example, the Newton-Raphson method was used to advance

to the next time step.

Finally, the integrator is chosen. In this case, displacement control was used to

help narrow down the results. This command uses a specified displacement increment to


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find the load at that displacement for the specified load. In this case, an increment of 0.1

was applied to node 15.

Before running the program, the user must define the type of analysis and the

number of iterations for the analysis to run. In this case, a static analysis was chosen and

fifty iterations were used. The complete program code for this example can be found in

appendix A.

3.0 Simulation of the Subject Building

3.1 Modeling the structure

Many basic elements of modeling remained the same for this structure. Major

differences include nodes only at beam-column intersections, shear walls, section

aggregators, loading, and the type of material properties in the shear walls.

Shear walls are introduced in this model. These are modeled using the standard

brick element as will be discussed later. For the shear walls, a different type of material

was introduced, nDMaterial. This command constructs an object which represents stress-

strain relationships at integration points of force-deformation elements (Mazzoni 2006).

The Elastic Isotropic Material was used because it can model a plane stress element

which is what the shear walls are. The shear walls are modeled as plane stress elements

because one of the principal stresses is zero.

Beams and columns were again modeled as nonlinear beam-columns. In addition,

to compensate for torsion that might occur with the presence of the shear walls, section

aggregators were incorporated.


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3.1.1 Dimensions and cross-sections

In order to describe this structure, it is important to define some terms and

positioning. Column line A refers to the columns supporting the shear wall or the left side

of Figure 3. Column line B is the center columns and column line C is the remaining two

columns on the right side of Figure 3. Column lines A and B are 5,500 mm apart and the

distance from columns B to C is 3,500 mm. So the length of the entire structure or the

distance from A to C is 9,000 mm.

The columns are 4,300 mm high. The distance from the ground to the first floor

slab is 2,200 mm and the distance between floors is 1,900 mm. The columns have a 400

mm square cross-section, as shown in Figure 4a. There are four rows of No. 6 rebar, four

bars in each of the top and bottom rows and two bars in each of the remaining middle

rows. Stirrups are No. 3 rebar, spaced 300 mm apart.

Beam cross sections are 400 mm high and 300 mm across. The beams are

reinforced by four rows of rebar each containing two bars of No. 6 rebar as shown in

Figure 4b. Stirrups made of No. 3 rebar are spaced 100 mm apart.

3.1.2 Material properties

Defining the material properties for the beams and columns was the next step. The

core concrete and the concrete covering the rebar had slightly different properties. The

core concrete had a measured 28-day compressive strength of 34.8 Pascals and a strain of

0.003 at max strength. At the point of crushing, the concrete had a measured strength of

27.5 Pa and a strain of 0.002. The concrete was again modeled by the uniaxial material

concrete01.


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The 50 millimeters of cover concrete had a 27.5 Pa 28-day compressive strength.

A strain of 0.003 was measured at max strength. A crushing strength of 2.75 Pa was

found along with a strain of 0.006 at crushing. The concrete was also modeled by the

uniaxial material concrete01.

The reinforcing steel had a yield stress of 659 Pa and a modulus of elasticity, E, of

200,000 Pa. No. 7 rebar has an area of 387.1 mm2

(0.6 in2). The steel also had a strain

hardening ratio of 0.017. The steel was again modeled by the uniaxial material steel01.

3.1.3 Shear Walls

The shear walls were reinforced concrete plane stress elements and were modeled

with the standard brick element. The standard brick element creates an eight-node brick

object. Each shear wall was represented by two bricks each one-half the thickness of the

shear wall.

3.1.4 Loading

Four lateral loads were applied to this frame. Nodes 3 and 4, which are the nodes

at the first floor slab on the right side of Figure 3, loaded with 6,000 N. Nodes 5 and 6,

the nodes on the second floor slab directly above the previous two, were loaded with

twice the amount, 12,000 N.

3.2 Recorder generation

Node recorders were created to monitor the displacements at the nodes where the

loads were being applied. Results for this model were based on the displacement of one

of the top nodes, node 6.


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3.3 Analysis

The same analysis procedure, previously described for the 2D frame, was used

except for the factors associated with the convergence test and the displacement intervals.

The convergence tolerance was set at 1.0e-2. In addition, the test was supposed to

conduct 5,000 iterations before returning a failure to converge message. The

displacement was controlled by node 6 at intervals of 0.001 mm. The complete code used

for this frame can be found in Appendix B.

4.0 Simulated Results

Each program was set to output the displacement increment and the

corresponding load step. Graphing the displacement versus the load produces a stress-

strain curve also called a backbone curve.

4.1 Simple 2D structure

Analysis of the output file generates a stress-strain curve, otherwise known as a

backbone curve. The stress-strain curve for the 2D structure, as shown in Figure 5, has an

ultimate strength of approximately 64 kips. The output file shows that rupture occurred

around 63.4 kips. A modulus of elasticity of 40 ksi can be calculated based on the

straight-line portion of the curve.

4.2 NCREE model

The stress-strain curve generated from the code for the NCREE structure can be

found in Figure 6. Results show an ultimate strength of 650 kN. The material ruptures at

284 kN. From calculating the slope of the straight-line portion of the graph, a modulus of

elasticity of 498 GPa can be found.


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5.0 Conclusions

OpenSees is a valuable tool for studying the effects of earthquakes on reinforced

concrete structures. Programs can be generated to output the displacement and the

loading. From the output files, stress-strain curves can be developed.

Time constraints limited the scope of this research to studying the process

necessary to develop a simulation of the structure. Further development of this code

might include adding gravity loads and cyclic loading to completely study the results of

earthquake loading on the shear walls. Currently, the code to study the cyclic loading is

being developed by Dr. Y.L. Mos researchers.

6.0 Acknowledgements

The research study described herein was sponsored by the National Science

Foundation under the Award No. EEC-0649163. The opinions expressed in this study are

those of the authors and do not necessarily reflect the views of the sponsor.

7.0 References

Howser, Rachel, A. Laskar, Y.L. Mo. (2007) Seismic Interaction of Flexural Ductilityand Shear Capacity in Reinforced Concrete Columns.

Hwang, S.J., M. Saiid Saiidi, Sara Wadia-Fascetti, JoAnn Browning, Jerry P. Lynch,

Kamal Tawfig, K.C. Tsai, G. Song, Y.L. Mo. (2006) Experiments andSimulation of Reinforced Concrete Buildings Subjected to Reversed Cyclic

Loading and Shake Table Excitation.

Mazzoni, Silvia, Frank McKenna, Michael H. Scott, Gregory L. Fenves, et. al. (2006).

Open System for Earthquake Engineering Simulation User Command-LanguageManual, Pacific Earthquake Engineering Research Center, UC Berkeley,

http://opensees.berkeley.edu/OpenSees/manuals/usermanual/index.html.

Pacific Earthquake Engineering Research Center (PEER). (2001) Open System forEarthquake Engineering Simulation.

http://peer.berkeley.edu/news/2001spring/opensees.html

Schwerd, Daniel. (2006) Scriptics.com the Script Archive.http://dev.scriptics.com/software/tcltk/.

Tseng, Chien-Chuang. (2006) Experiment of Reinforced Concrete Building Frame

Presentation.


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8.0 List of Tables and Figures

Figure 1 2D Frame 12

Figure 2 2D Frame cross-sections . 12

Figure 3 NCREE frame . 13

Figure 4 NCREE frame cross-sections . 13

Figure 5 2D Frame stress-strain curve .. 14

Figure 6 NCREE frame stress-strain curve ... 14

Figure 1 A drawing of the 2D frame problem.

(a) (b)

Figure 2 Cross-sectional views of (a) the columns and (b) the beams of the 2D frame. The column

cross-section represents the line AA on Figure 1 while the beam cross-section comes from line BB.


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Figure 3 A drawing of the two-bay, two-story reinforced concrete building constructed at the

National Center for Research on Earthquake Engineering (Tseng).

(a) (b)

Figure 4 Cross-sectional views of (a) the columns and (b) the beams of the two-bay, two-story

reinforced concrete structure (Tseng).


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Appendix A

# 2D frame example problem

# Units: kips, inches

model basic -ndm 2 -ndf 3

# Define nodes -------------------------

set width 315.0

set height 118.1

# Define some parameters

set x1 [expr $width/2]

set y1 [expr $height/2]

# node tag X Y

node 1 0 0

node 2 $x1 0

node 3 $width 0

node 4 0 $y1

node 5 $x1 $y1

node 6 $width $y1

node 7 0 $height

node 8 [expr $width/8] $height

node 9 [expr $x1/2] $height

node 10 [expr 3*$x1/4] $height

node 11 $x1 $height

node 12 [expr 5*$width/8] $height

node 13 [expr 3*$width/2] $heightnode 14 [expr 7*$width/8] $height

node 15 $width $height

# Fix constraints

fix 1 1 1 1

fix 2 1 1 1

fix 3 1 1 1

# Define MATERIALS

# -------------------------

# CONCRETE tag f'c epsc0 fcu epsU

# Core Concrete (confined)

uniaxialMaterial Concrete01 1 -6.0 -0.004 -5.0 -0.014

# Cover concrete (unconfined)

uniaxialMaterial Concrete01 2 -5.0 -0.002 0.0 -0.006

# STEEL

# Reinforcing Steel

set fy 60.0; # Yield stress

set E 30000.0; # Young's modulus

# tag fy E0 b


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uniaxialMaterial Steel01 3 $fy $E 0.01

# Define Column cross-section

# ------------------------------------

# Column parameters

set cWidth 15.7; # column width

set cDepth 11.8; # column height

set cover 2.0; # cover

set As7 0.6; # area of no. 7 bars

# Variables derived from parameters

set cy1 [expr $cDepth/2.0]

set cz1 [expr $cWidth/2.0]

# Create a Uniaxial Fiber object

section Fiber 1 {

# Create the concrete core fibers

# patch rect $matTag $numSubdivIJ $numSubdivJK $yI $zI $yJ $zJ$yK $zK $yL $zL

patch rect 1 10 1 [expr $cover-$cy1] [expr $cover-$cz1] [expr

$cy1-$cover] [expr $cz1-$cover];

# Create the concrete cover fibers (top, bottom, left, right)

patch rect 2 10 1 [expr -$cy1] [expr $cz1-$cover] $cy1 $cz1;

patch rect 2 10 1 [expr -$cy1] [expr -$cz1] $cy1 [expr $cover-

$cz1];

patch rect 2 2 1 [expr -$cy1] [expr $cover-$cz1] [expr $cover-

$cy1] [expr $cz1-$cover];

patch rect 2 2 1 [expr $cy1-$cover] [expr $cover-$cz1] $cy1

[expr $cz1-$cover];

# Create the reinforcing fibers (3 layers)

# layer straight $matTag $numBars $areaBar $yStart $zStart $yEnd

$zEnd

layer straight 3 3 $As7 [expr $cy1-$cover] [expr $cover-$cz1]

[expr $cover-$cy1] [expr $cover-$cz1]

layer straight 3 2 $As7 $cy1 0 [expr -$cy1] 0

layer straight 3 3 $As7 $cy1 [expr $cy1-$cover] [expr -$cy1]

[expr $cz1-$cover]

}

# Define beam cross-section

# ------------------------------------

# Beam parameters

set bWidth 7.9; # beam width

set bDepth 13.8; # beam height

# Variables derived from parameters

set by1 [expr $bDepth/2.0]

set bz1 [expr $bWidth/2.0]



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section Fiber 2 {


# patch rect $matTag $numSubdivIJ $numSubdivJK $yI $zI $yJ $zJ

$yK $zK $yL $zL

patch rect 1 10 1 [expr $cover-$by1] [expr $cover-$bz1] [expr

$by1-$cover] [expr $bz1-$cover];


patch rect 2 10 1 [expr -$by1] [expr $bz1-$cover] $by1 $bz1;

patch rect 2 10 1 [expr -$by1] [expr -$bz1] $by1 [expr $cover-

$bz1];

patch rect 2 2 1 [expr -$by1] [expr $cover-$bz1] [expr

$cover-$by1] [expr $bz1-$cover];

patch rect 2 2 1 [expr $by1-$cover] [expr $cover-$bz1] $by1

[expr $bz1-$cover];

# Create the reinforcing fibers (top, bottom)

# layer straight $matTag $numBars $areaBar $yStart $zStart $yEnd

$zEnd

layer straight 3 2 $As7 [expr $by1-$cover] [expr -$bz1] [expr$cover-$by1] [expr -$bz1]

layer straight 3 4 $As7 [expr $by1-$cover] $bz1 [expr $cover-

$by1] $bz1

}

# Define Columns -----------------------------------

geomTransf Linear 1

# element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts

$secTag $transfTag

element nonlinearBeamColumn 1 1 4 2 1 1






# Define Beams ------------------------------------

geomTransf Linear 2

# element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts$secTag $transfTag









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# Define LATERAL LOADS -------------------------------------

pattern Plain 1 Linear {

# nodeID Fx Fy Mz

load 15 100.0 0.0 0.0

}

# Create RECORDERS -----------------------------------------

recorder Node -file Node15.out -time -node 15 -dof 1 disp

# ANALYSIS -----------------------------------------

system BandGeneral

constraints Transformation

numberer RCM

test NormDispIncr 1.0e-12 50 0

algorithm Newton

integrator DisplacementControl 15 1 0.1

analysis Staticinitialize

analyze 50

print node 1 15

Appendix B

# 2-story, 2-bay frame with shear walls

# NCREE Frame

# Units: N, mm, sec, MPa


# Define variables -------------------------

# Constants

set PI [expr 2*asin(1.0)]

set g 9810

set U 1.e10;

set u [expr 1/$U]

# Material Tags

set IDcore 1;set IDcover 2;

set IDsteel 3;

set IDTors 4;

set IDwSteel 5;

set IDwCon 6;

set IDei 7;

# Define frame variables -------------------------

set deltaBC 3500; # distance from column lines B & C


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set deltaAB 5500; # distance between column lines A & B

set deltaAC 9000; # distance between column lines A & C

set delta12 3000; # distance from node 1 to node 2

set CH1 2200; # height to center of 2nd floor slab

set CH2 4100; # height to center of 3rd floor slab

# Create nodes -------------------------

node 1 0 0 0

node 2 0 $delta12 0

node 3 0 0 $CH1

node 4 0 $delta12 $CH1

node 5 0 0 $CH2

node 6 0 $delta12 $CH2

node 7 $deltaBC 0 0

node 8 $deltaBC $delta12 0

node 9 $deltaBC 0 $CH1

node 10 $deltaBC $delta12 $CH1

node 11 $deltaBC 0 $CH2node 12 $deltaBC $delta12 $CH2

node 13 $deltaAC 0 0

node 14 $deltaAC $delta12 0

node 15 $deltaAC 0 $CH1

node 16 $deltaAC $delta12 $CH1

node 17 $deltaAC 0 $CH2

node 18 $deltaAC $delta12 $CH2

# Fix supports

fix 1 1 1 1 1 1 1; # fully fixed

fix 2 1 1 1 1 1 1;

fix 13 1 1 1 1 1 1;

fix 14 1 1 1 1 1 1;

fix 7 1 1 1 1 1 1;

fix 8 1 1 1 1 1 1;

# Define materials -------------------------

# Define property variables

set fc [expr -27.5];

set Ec [expr 4700.*sqrt(-$fc)];

set fc1C [expr 1.26394*$fc];

set eps1C [expr 2.*$fc1C/$Ec];

set fc2C $fc;

set eps2C [expr 2.*$fc2C/$Ec];

set fc1U $fc;

set eps1U -0.003;set fc2U [expr 0.1*$fc];

set eps2U -0.006;

set v 0.15; # Poisson's Ratio

set Fy 411.9; # yield stress

set Es 200000; # modulus of elasticity

set epsY [expr $Fy/$Es]

set Fy1 559.;

set epsY1 0.03;


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# Beam element

# -----------------------------------------------

# Beam paramaters

set bWidth 300.0; # beam width

set bDepth 400.0; # beam height

# Variables derived from the parameters

set by1 [expr $bDepth/2.0];

set bz1 [expr $bWidth/2.0];


section Fiber 4 {


# mat num num

patch rect $IDcore 2 2 [expr $cover-$by1] [expr $cover-$bz1] [expr

$by1-$cover] [expr $bz1-$cover];


patch rect $IDcover 2 2 [expr -$by1] [expr $bz1-$cover] $by1 $bz1;

patch rect $IDcover 2 2 [expr -$by1] [expr -$bz1] $by1 [expr $cover-

$bz1];

patch rect $IDcover 2 2 [expr -$by1] [expr $cover-$bz1] [expr $cover-

$by1] [expr $bz1-$cover];

patch rect $IDcover 2 2 [expr $by1-$cover] [expr $cover-$bz1] $by1

[expr $bz1-$cover];

# Create the reinforcing fibers (4 layers)

layer straight $IDsteel 2 $As6 [expr $by1-$cover] [expr $bz1-$cover]

[expr $by1-$cover] [expr $cover-$bz1];

layer straight $IDsteel 2 $As6 [expr -($bWidth-2*$cover)/6] [expr

$bz1-$cover] [expr -($bWidth-2*$cover)/6] [expr $cover-$bz1];

layer straight $IDsteel 2 $As6 [expr ($bWidth-2*$cover)/6] [expr

$bz1-$cover] [expr ($bWidth-2*$cover)/6] [expr $cover-$bz1];

layer straight $IDsteel 2 $As6 [expr $cover-$by1] [expr $bz1-$cover]

[expr $cover-$by1] [expr $cover-$bz1];

}

# Create section aggregators (puts torsion in sections)

# -----------------------------------------------------

set G $U; # shear modulus -- describes an object's tendency to shear

set J 1.;

set GJ [expr $G*$J]

uniaxialMaterial Elastic $IDTors $GJ

set IDcolSec 1

set IDbeamSec 3

# tag uniTag uniCode secTag

section Aggregator $IDcolSec $IDTors T -section 2

section Aggregator $IDbeamSec $IDTors T -section 4


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# Create columns

# -------------------------

geomTransf Linear 1 0 1 0

# element nonlinearBeamColumn $eleTag $iNode $jNode $numIntgrPts

$secTag $transfTag

element nonlinearBeamColumn 1 1 3 3 $IDcolSec 1












# Create beams

# -------------------------

geomTransf Linear 2 0 0 -1

element nonlinearBeamColumn 13 3 4 3 $IDbeamSec 2













# ---------------------------------------------------------------------# Create ModelBuilder for 3D elements in Y-Z Plane

# ---------------------------------------------------------------------


# Create nodes

node 20 9075 0 0

node 21 9000 0 0

node 22 8925 0 0

node 23 9075 3000 0


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node 24 9000 3000 0

node 25 8925 3000 0

node 26 9075 0 2200

node 27 9000 0 2200

node 28 8925 0 2200

node 29 9075 3000 2200

node 30 9000 3000 2200

node 31 8925 3000 2200

node 32 9075 0 4100

node 33 9000 0 4100

node 34 8925 0 4100

node 35 9075 3000 4100

node 36 9000 3000 4100

node 37 8925 3000 4100

node 40 0 2950 0

node 41 0 3000 0

node 42 0 3050 0

node 43 3500 2950 0

node 44 3500 3000 0

node 45 3500 3050 0node 46 0 2950 2200

node 47 0 3000 2200

node 48 0 3050 2200

node 49 3500 2950 2200

node 50 3500 3000 2200

node 51 3500 3050 2200

node 52 0 2950 4100

node 53 0 3000 4100

node 54 0 3050 4100

node 55 3500 2950 4100

node 56 3500 3000 4100

node 57 3500 3050 4100

# Set the boundary conditions

fix 20 1 1 1;

fix 21 1 1 1;

fix 22 1 1 1;

fix 23 1 1 1;

fix 24 1 1 1;

fix 25 1 1 1;

fix 40 1 1 1;

fix 41 1 1 1;

fix 42 1 1 1;

fix 43 1 1 1;

fix 44 1 1 1;

fix 45 1 1 1;

# -----------------------------------------------------------------

# Define materials for ReinforceConcretePlaneStress element

# -----------------------------------------------------------------

# STEEL

# uniaxialMaterial Steel01 $matTag $Fy $E0 $b

uniaxialMaterial Steel01 $IDwSteel $Fy $Es 0.1

# CONCRETE


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# uniaxialMaterial Concrete01 $matTag $fpc $epsc0 $fpcu $epsU

uniaxialMaterial Concrete01 $IDwCon $fc1C $eps1C $fc2C $eps2C

set rouw 0.0015

set pi 3.141592654;

# NDMaterial: ReinforceConcretePlaneStress

# tag rho s1 s2 c1 c2 angle1 angle2 rou1 rou2 fpc fy E0

nDMaterial ElasticIsotropic $IDei $Ec $v

# -----------------------------------------------------------------

# Define ReinforceConcretePlaneStress element

# -----------------------------------------------------------------

# element stdBrick eletag node1 node2 node3 node4 node5 node6 node7

node8 mattag

element stdBrick 30 22 25 24 21 28 31 30 27 $IDei




element stdBrick 40 41 44 43 40 47 50 49 46 $IDeielement stdBrick 41 42 45 44 41 48 51 50 47 $IDei



# tie nodes between beams, columns and walls

equalDOF 13 21 1 2 3






equalDOF 2 41 1 2 3

equalDOF 8 44 1 2 3

equalDOF 4 47 1 2 3


equalDOF 6 53 1 2 3


# Redefine model -------------------------------------------


# Define LATERAL LOADS -------------------------------------

pattern Plain 2 Linear {

# nodeID Fx Fy Fz Mx My Mz

load 3 6000 0 0 0 0 0

load 4 6000 0 0 0 0 0

load 5 12000 0 0 0 0 0

load 6 12000 0 0 0 0 0

}

# Create RECORDERS -----------------------------------------

recorder Node -file basicframeNode3.out -time -node 3 -dof 1 disp



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# recorder Node -file basicframeNode5.out -time -node 5 -dof 1 disp


# recorder plot basicframeNode6.out Node_6_Xdisp 400 340 300 300 -

columns 2 1

# ANALYSIS -----------------------------------------

system BandGeneral

constraints Transformation

numberer RCM

test NormDispIncr 1.0e-2 5000 0

algorithm Newton

integrator DisplacementControl 6 1 0.001

analysis Static

initialize

analyze 5000

print node 3 6

reu report - process of seismic simulation of a 2-bay, 2-story reinforced concrete building

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