Properly Capturing Euler Buckling Load in OpenSEEs

[ysir]

Dear All,

I am now analyzing a 2D single steel I-Section or W-section using fiber section with pinned at bottom and roller at top( free in vertical direction but fix in horizontal direction).
A vertical compressional load is applied at top.
I wish to obtained the elastic buckling force but seems OpenSEEs does't automatically capture the Euler buckling load.

Is there any way or method to properly capture the euler's load?

PS. I am using nonlinearbeamColumn for element, Steel02 for material.

[fmk]

if you are trying to capture the buckling load by creating a column and placing a load on top of it, don't forget that you need to include some imperfection in the shape of the column .. otherwise it will not buckle.

[yigitozcelik]

you may refer to "Model for Cyclic Inelastic Buckling of Steel Braces" by Patxi Uriz; Filip C. Filippou; and Stephen A. Mahin

I hope it helps

[ysir]

Thanks and really appreciate those comments.
I just want to ensure that my method is corrected. I use an initial out-of-Straightness with a sinusoidal shape by changing the nodal coordinates. Is it the right way to impose initial out of straightness effect??

Another question is that how would I make a pinned beam-column connection?

Thanks very much,

[yigitozcelik]

For simple connection, you need to use zerolength elements and equalDOF command between different nodes at same coordinates
there is a example about it
opensees.berkeley.edu/community/viewtopic.php?t=16686

[ysir]

Dear yigitozcelik,

I have built the model as the example shows with master and slave node. My model is a 2-bay 1 story frame. The support are pinned, fixed, and pinned for left column, central column and right column respectively.
i.e.
____________ <---H
| | |
|LC |CC |RC
| | |
pin fix pin

The pinned column-beam connection is at where left column (LC) and the adjoint beam which is at top left connection. On the other hand, the left column can be considered as a leaning column.
However, the results shows that there is no axial force (or very small relatively to RC). Would you know what is the problem for this??

Thanks

[yigitozcelik]

Dear ysir,

I can't see where the problem is
if you send your script, hopefully i help you

[ysir]

Dear yigitozcelik,

Here is my Script file.
Noted that I have subdivided each member into 8 sub-elements
# OpenSees Frame 2
# Two-bay one-story Frame
# ___________________
# | | |
# | | |
# | | |
# 3m 7m
# pin fix pin
#
# Units: kN, m, s
# --------------------------
# Start of model generation
# --------------------------
# Create ModelBuider (with two-dimensions and 2 DOF/nods)
wipe

model BasicBuilder -ndm 2 -ndf 3
source UCsectionhm.tcl

# Create nodes & add to Domain - Command: node nodeID xCrd yCrd
set sb1 [expr 3000/8]
set sb2 [expr 7000/8]
set sh [expr 3000/8]

#LH Col
node 1 0.0 0.0
node 2 0.0 [expr $sh*1]
node 3 0.0 [expr $sh*2]
node 4 0.0 [expr $sh*3]
node 5 0.0 [expr $sh*4]
node 6 0.0 [expr $sh*5]
node 7 0.0 [expr $sh*6]
node 8 0.0 [expr $sh*7]
node 9 0.0 [expr $sh*8] # master node
# LH Beam
node 10 [expr $sb1*1] [expr $sh*8]
node 11 [expr $sb1*2] [expr $sh*8]
node 12 [expr $sb1*3] [expr $sh*8]
node 13 [expr $sb1*4] [expr $sh*8]
node 14 [expr $sb1*5] [expr $sh*8]
node 15 [expr $sb1*6] [expr $sh*8]
node 16 [expr $sb1*7] [expr $sh*8]
# Central Col
node 17 [expr $sb1*8] 0.0
node 18 [expr $sb1*8] [expr $sh*1]
node 19 [expr $sb1*8] [expr $sh*2]
node 20 [expr $sb1*8] [expr $sh*3]
node 21 [expr $sb1*8] [expr $sh*4]
node 22 [expr $sb1*8] [expr $sh*5]
node 23 [expr $sb1*8] [expr $sh*6]
node 24 [expr $sb1*8] [expr $sh*7]
node 25 [expr $sb1*8] [expr $sh*8]
# RH Beam
node 26 [expr $sb1*8+$sb2*1] [expr $sh*8]
node 27 [expr $sb1*8+$sb2*2] [expr $sh*8]
node 28 [expr $sb1*8+$sb2*3] [expr $sh*8]
node 29 [expr $sb1*8+$sb2*4] [expr $sh*8]
node 30 [expr $sb1*8+$sb2*5] [expr $sh*8]
node 31 [expr $sb1*8+$sb2*6] [expr $sh*8]
node 32 [expr $sb1*8+$sb2*7] [expr $sh*8]
# RH Col
node 33 [expr $sb1*8+$sb2*8] 0.0
node 34 [expr $sb1*8+$sb2*8] [expr $sh*1]
node 35 [expr $sb1*8+$sb2*8] [expr $sh*2]
node 36 [expr $sb1*8+$sb2*8] [expr $sh*3]
node 37 [expr $sb1*8+$sb2*8] [expr $sh*4]
node 38 [expr $sb1*8+$sb2*8] [expr $sh*5]
node 39 [expr $sb1*8+$sb2*8] [expr $sh*6]
node 40 [expr $sb1*8+$sb2*8] [expr $sh*7]
node 41 [expr $sb1*8+$sb2*8] [expr $sh*8]
node 42 0.0 [expr $sh*8] #slave node

# Set the boundary conditions - command: fix nodeID xResrnt? yResrnt?
fix 1 1 1 0
fix 17 1 1 1
fix 33 1 1 0
fix 9 0 0 0

equalDOF 9 42 1 2
# Define Geometric Transformation $TransTag
#geomTransf Linear 1
#geomTransf PDelta 1
geomTransf Corotational 1

# Define materials for truss elements
#-------------------------------
# General Property (Yield stress and Residual stress)
set rs 0.0
set fy 300
# Define Section for LH col (100UC14.
set d1 97
set bf1 99
set tf1 7
set tw1 5
UCsectionhm 1 $fy $d1 $bf1 $tf1 $tw1 $rs
# Define Section for Central Col (500WC440)
set d2 480
set bf2 500
set tf2 40
set tw2 40
UCsectionhm 2 $fy $d2 $bf2 $tf2 $tw2 $rs
# Define Section for RH Col (Modified Section 1)
set d3 325
set bf3 1250
set tf3 40
set tw3 40
UCsectionhm 3 $fy $d3 $bf3 $tf3 $tw3 $rs
# Define Section for Beam (Modified Section 2)
set d4 750
set bf4 500
set tf4 40
set tw4 40
UCsectionhm 4 $fy $d4 $bf4 $tf4 $tw4 $rs
# Define elements
#---------------------
#Create nonlinear elements - command: element NBC <ID node1 node2 Intpoint sectag $TransTag>
# LH col
element nonlinearBeamColumn 1 1 2 5 1 1
element nonlinearBeamColumn 2 2 3 5 1 1
element nonlinearBeamColumn 3 3 4 5 1 1
element nonlinearBeamColumn 4 4 5 5 1 1
element nonlinearBeamColumn 5 5 6 5 1 1
element nonlinearBeamColumn 6 6 7 5 1 1
element nonlinearBeamColumn 7 7 8 5 1 1
element nonlinearBeamColumn 8 8 9 5 1 1
# Central Col
element nonlinearBeamColumn 9 17 18 5 2 1
element nonlinearBeamColumn 10 18 19 5 2 1
element nonlinearBeamColumn 11 19 20 5 2 1
element nonlinearBeamColumn 12 20 21 5 2 1
element nonlinearBeamColumn 13 21 22 5 2 1
element nonlinearBeamColumn 14 22 23 5 2 1
element nonlinearBeamColumn 15 23 24 5 2 1
element nonlinearBeamColumn 16 24 25 5 2 1
# RH Col
element nonlinearBeamColumn 17 33 34 5 3 1
element nonlinearBeamColumn 18 34 35 5 3 1
element nonlinearBeamColumn 19 35 36 5 3 1
element nonlinearBeamColumn 20 36 37 5 3 1
element nonlinearBeamColumn 21 37 38 5 3 1
element nonlinearBeamColumn 22 38 39 5 3 1
element nonlinearBeamColumn 23 39 40 5 3 1
element nonlinearBeamColumn 24 40 41 5 3 1
#LH Beam
element nonlinearBeamColumn 25 42 10 5 4 1
element nonlinearBeamColumn 26 10 11 5 4 1
element nonlinearBeamColumn 27 11 12 5 4 1
element nonlinearBeamColumn 28 12 13 5 4 1
element nonlinearBeamColumn 29 13 14 5 4 1
element nonlinearBeamColumn 30 14 15 5 4 1
element nonlinearBeamColumn 31 15 16 5 4 1
element nonlinearBeamColumn 32 16 25 5 4 1
# RH Beam
element nonlinearBeamColumn 33 25 26 5 4 1
element nonlinearBeamColumn 34 26 27 5 4 1
element nonlinearBeamColumn 35 27 28 5 4 1
element nonlinearBeamColumn 36 28 29 5 4 1
element nonlinearBeamColumn 37 29 30 5 4 1
element nonlinearBeamColumn 38 30 31 5 4 1
element nonlinearBeamColumn 39 31 32 5 4 1
element nonlinearBeamColumn 40 32 41 5 4 1

#--------------------------
# Start of recorder generation
#--------------------------
#--------Recording file-----------------
recorder Node -file dispn9.out -time -node 9 -dof 1 disp
recorder Node -file dispn41.out -time -node 41 -dof 1 disp
recorder Element -file LHC1.out -time -ele 1 globalForce
recorder Element -file LHC8.out -time -ele 8 globalForce
recorder Element -file CC9.out -time -ele 9 globalForce
recorder Element -file CC16.out -time -ele 16 globalForce
recorder Element -file RHC17.out -time -ele 17 globalForce
recorder Element -file RHC24.out -time -ele 24 globalForce

# Define loads
#-----------------------
# Create a Plain load pattern with a linear TimeSeries
pattern Plain 1 "Linear" {

#Create the load - command: load nodeID xForce(N) yForce(N)
load 41 -1000.0 0.0 0.0
}

#-------------------------------------
# End of model generation
#-------------------------------------
# Start of analysis generation
#-------------------------------------
#----------system-----------------------
system BandGeneral
#system BandSPD
#system UmfPack

#--------DOF numberer-------------------
numberer RCM

#--------Constraints--------------------
#constraints Plain
constraints Transformation

#--------Convergence test---------------
test NormDispIncr 1.0e-6 30 0

#--------Integrator---------------------
integrator LoadControl 1
#integrator DisplacementControl
#--------Algorithm----------------------
#algorithm ModifiedNewton
#algorithm Linear
algorithm Newton

#--------Analysis scheme----------------
# Perform the analysis
analysis Static
analyze 500

puts "End of Analysis"
#--------------------------
# End of analysis
#--------------------------

Thanks very much for your time!

[yigitozcelik]

I am sorry but i couldn't figure it out
by the way, application of lateral load at both exterior nodes (node 9 and node 41) would be more accurate approach

[ysir]

Dear yigitozcelik,

I think I kind of figure out what wrong with my code.
I would like to know what are the parameters represented in the results file.

For element recorder, it can records both local element force and global force.
i.e. recorder Element -file LHC1.out -time -ele 1 localForce(globalforce)
For both results, what are each columns represents?

Thanks,

[yigitozcelik]

globalForce 2D, 3dof: FX FY MZ
localForce 2D, 3dof: Fx Fy Mz
X,Y and Z for global coordinates
x,y and z for local coordinate system of members
for your columns, if you use localForce recorder that Fx will be axial load
since you include -time expression than 2nd column will be axial load

[ysir]

Thanks very much, yigitozcelik

I think I just mixed up these two columns (I was using globalForce and thought that the first column was axial force)

Thanks very much for your time.

[rajaeian]

dear all,
how can I impose initial out of straightness effect to a column?
regards.

[yigitozcelik]

Try dividing your column into two segments and moving the midnode sideways for initial imperfection. For details, you can refer to Uriz et al.

Uriz P., Filippou F., and Mahin S., “Model for cyclic inelastic buckling of steel braces”, ASCE Journal of Structural Engineering, 134(4), 619-628, 2008.