Reaction

[Fame]

Hi everyone,
I am modeling a 2 spans bridge with two columns using nonlinear element for columns and elastic elements for girder and cap beam. The bridge is pinned at the column bases with roller abutments.
The gravity analysis gives reactions at the supports that are different from my hand calculations. The reactions at the column bases are just what i should have if i have two columns with beam and reactions at the girder are just the results i should have if i have a simply supported beam. It seem that the girder and column bent are not working together. I checked my model and the elements are well connected. There isn't any error messages during the analysis.
Can anyone please help?
Thanks

[vesna]

For comparison with the hand calc it is the best to model all elements as elastic.

[Fame]

Hi vesna,
I run the analysis as you suggested, but the results are the same.
Following are some parameters and results.
column linear mass 30KN/m, 8.5m
cap beam linear mass 90KN/m, 11m
girder linear mass 271KN/m, 15m each span
Based on these values i should have a column base reaction close to 2535KN, but the analysis gave 598KN.
And at the abutment i have 4195KN instead of 2033KN.
I can post portion of my model if you would like to take a look at it.
Thanks

[vesna]

Would you post your model with all elements being elastic.

[Fame]

Here is my model:

puts "The units are in KN and meter"

puts "The origin of the axis is at midpoint between the column \
(it also corresponds to the horizontal projection of the intersection point between the girder and beam cap lines)"

puts "The axis are defined as follow: X-parallel to the bridge longitudinal direction; Z- parallel to the cap beam(positive pointing out of the screen); Y- parallel to the column (positive pointing up)."

#---------------------------------------------------------------------------------
#Build the model
model BasicBuilder -ndm 3 -ndf 6

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

#Unit conversion
set meter 1.0
set KPa 1.0
set KN 1.0
set Kip [expr 4.448*$KN]
set inch [expr 0.0254*$meter]
set ft [expr 12.0*$inch]
set Ksi [expr 6896.6*$KPa]
set small 1.0e-8
set big 1.0e6

#Constant
set pi 3.1416
set g 9.81
set fy [expr 60.0*$Ksi];
set fye [expr 68.0*$Ksi]
set Es [expr 29000.0*$Ksi]

#Concrete Properties
set w [expr 0.14396*$Kip/pow($ft,3)]; #unit weight of concrete in KN/m^3
set pois_ratio 0.2
set fc [expr 4.0*$Ksi]
set Ec [expr 4700.0*sqrt($fc/1000.0)*1000.0]
set G [expr $Ec/(2*(1+$pois_ratio))]

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

#Bridge parameters
set Hcol [expr 7.50*$meter]; #Height of column
set Dcol [expr 1.3*$meter]; #Column diameter
set Sp [expr 15.0*$meter]; #Span
set Total_Span [expr 30.0*$meter]; #Bridge total span
set Dcg [ expr 1.0*$meter]; #Deck centroid
set Lcap [expr 5.5*$meter]; #Length from the origin of the axis to the column centroid
set Dw [expr 23.0*$meter]; #Deck width

puts "Done defining bridge geometric properties"
#--------------------------------------------------------------------------

#Column properties
set Agcol [expr $pi*pow($Dcol,2)/4]
set Izcol [expr $pi*pow($Dcol,4)/64]; #Circular column Iz=Iy
set Jcol [expr $pi*pow($Dcol,4)/32]
set Jefcol [expr 0.2*$Jcol]
set Iefcol [expr 0.6089*$Izcol]

#Beam cap cross section properties
set C 1.0
set CapD [expr 2.0*$meter]; #Depth of beam cap
set CapW [expr 2.0*$meter]; #Width of beam cap
set Abc [expr $CapD*$CapW]
set Izb [expr $CapW*pow($CapD,3)/12]
set Iyb [expr $CapD*pow($CapW,3)/12]
set Jbcef [expr 5413612*pow($inch,4)*$C]
set GJ [expr $G*$Jbcef]

#Deck properties
set Ad [expr 12.0*pow($meter, 2)]
set Avy [expr 3.4*pow($meter, 2)]
set Avz [expr 8.71*pow($meter,2)]
set Jd [expr 24.22*pow($meter,4)]
set Iy [expr 7.282*pow($meter,4)]
set Iyd [expr 0.75*$Iy]
set Iz [expr 420.4821*pow($meter,4)]
set Izd [expr 0.75*$Iz]

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

#Define nodal coordinates
set X0 0.0
set X1 [expr $X0 + $Sp]
set X2 [expr $X0 - $Sp]

#Left span points x-coordinates
set X3 [expr -5*$Sp/6]
set X4 [expr -4*$Sp/6]
set X5 [expr -3*$Sp/6]
set X6 [expr -2*$Sp/6]
set X7 [expr -$Sp/6]

#Right span points x-coordinates
set X8 [expr $Sp/6]
set X9 [expr 2*$Sp/6]
set X10 [expr 3*$Sp/6]
set X11 [expr 4*$Sp/6]
set X12 [expr 5*$Sp/6]

set Y0 0.0
set Y1 [expr $Y0 + $Hcol + $Dcg]
set Y2 [expr $Y0 + $Hcol]
set Y3 [expr $Y1/5.0]
set Y4 [expr 2*$Y3]
set Y5 [expr 3*$Y3]
set Y6 [expr 4*$Y3]

set Z0 0.0
set Z1 [expr -$Lcap]
set Z2 [expr -$Lcap/2.0]
set Z3 [expr $Lcap/2.0]
set Z4 $Lcap

set fLmc [expr $w*$Agcol]; #linear weight of the column
set mLc [expr $fLmc/$g]; #Column linear mass
set mc [expr $mLc*$Y1/10.0]; #Five points along each column line, and only half is attributed to the base
set mcint [expr 2*$mc]; #Mass applied to intermediate points along the columns

set fLmGird [expr $w*$Ad]; #linear weight of the column
set mLs [expr $fLmGird/$g]; #Linear Mass at abutment support
set mInt [expr $mLs*$Sp/6.0]; # Interior nodal mass span. There six points in each span of the bridge

set m5 [expr $mLs*$Sp/12.0]; #Mass at roller abutments

set fLmBC [expr $w*$Abc]; #linear weight of the column
set mLbc [expr $fLmBC/$g]; #Beam cap linear mass
set mbc [expr $mLbc*$Lcap/4.0]; #There are four points along the beam cap
set m3 [expr $mbc + $mc]; #This is a contribution of the column and the beam
set m31 [expr 2.0*$mbc]; #Beam cap intermediate point

set m6 [expr $ms5 + $ms7 + 2*$mbc]; #Intersection between girder and beam cap

#Mass Moment of inertia
#These rotational masses are only applied to the girder nodes in the X direction
set Ms [expr ($mIntL*pow($Dw,2))/12]; #Apllied to intermediate nodes in the spans
set M50 [expr $Ms/2.0]; #Abutment supports
set M60 [expr (($ms5+$ms7)*pow($Dw,2))/12]; #Intersection point between girder and beam cap

#Column base node
node 10 $X0 $Y0 $Z1 -mass $mc $mc $mc 0.0 0.0 0.0
node 101 $X0 $Y3 $Z1 -mass $mcint $mcint $mcint 0.0 0.0 0.0
node 102 $X0 $Y4 $Z1 -mass $mcint $mcint $mcint 0.0 0.0 0.0
node 103 $X0 $Y5 $Z1 -mass $mcint $mcint $mcint 0.0 0.0 0.0
node 104 $X0 $Y6 $Z1 -mass $mcint $mcint $mcint 0.0 0.0 0.0

node 20 $X0 $Y0 $Z4 -mass $mc $mc $mc 0.0 0.0 0.0
node 201 $X0 $Y3 $Z4 -mass $mcint $mcint $mcint 0.0 0.0 0.0
node 202 $X0 $Y4 $Z4 -mass $mcint $mcint $mcint 0.0 0.0 0.0
node 203 $X0 $Y5 $Z4 -mass $mcint $mcint $mcint 0.0 0.0 0.0
node 204 $X0 $Y6 $Z4 -mass $mcint $mcint $mcint 0.0 0.0 0.0

#Beam cap nodes which correspond to the Column top nodes
node 30 $X0 $Y1 $Z1 -mass $m3 $m3 $m3 0.0 0.0 0.0
node 31 $X0 $Y1 $Z2 -mass $m31 $m31 $m31 0.0 0.0 0.0
node 32 $X0 $Y1 $Z3 -mass $m31 $m31 $m31 0.0 0.0 0.0
node 40 $X0 $Y1 $Z4 -mass $m3 $m3 $m3 0.0 0.0 0.0

#Girder box nodes
node 50 $X2 $Y1 $Z0 -mass $ms5 $ms5 $ms5 $M50 0.0 0.0

node 510 $X3 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 511 $X4 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 512 $X5 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 513 $X6 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 514 $X7 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0

node 60 $X0 $Y1 $Z0 -mass $m6 $m6 $m6 $M60 0.0 0.0

node 610 $X8 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 611 $X9 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 612 $X10 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 613 $X11 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0
node 614 $X12 $Y1 $Z0 -mass $mInt $mInt $mInt $Ms 0.0 0.0

node 70 $X1 $Y1 $Z0 -mass $ms7 $ms7 $ms7 $M50 0.0 0.0

puts "Done defining nodes and masses"
#-----------------------------------------------------------------

#Define support conditions
fix 10 1 1 1 0 0 0; #column base fixity
fix 20 1 1 1 0 0 0

fix 50 0 1 0 0 0 0; #Abutment nodes
fix 70 0 1 0 0 0 0

puts "Done with constraints"
#------------------------------------------------------------------

#Define elements
#Geometry transformation
set ColTrans 1
set CapTrans 2
set GirdTrans 3
set RigColTrans 4

geomTransf PDelta $ColTrans 0 0 -1; #For columns
geomTransf Linear $CapTrans 1 0 0; #For beam cap
geomTransf Linear $GirdTrans 0 0 1; #For girder box (deck)
geomTransf PDelta $RigColTrans 0 0 -1 -jntOffset 0.0 0.0 0.0 0.0 -$Dcg 0.0; #This is assigned to of the column to simulate the embedded portion into beam cap and girder

set ite 3

element elasticBeamColumn 1 10 101 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 2 101 102 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 3 102 103 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 4 103 104 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 5 104 30 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $RigColTrans

element elasticBeamColumn 6 20 201 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 7 201 202 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 8 202 203 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 9 203 204 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 10 204 40 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $RigColTrans

#Beam cap elements
element elasticBeamColumn 11 40 32 $Abc $Ec $G $Jbcef $Iyb $Izb $CapTrans
element elasticBeamColumn 12 32 60 $Abc $Ec $G $Jbcef $Iyb $Izb $CapTrans
element elasticBeamColumn 13 60 31 $Abc $Ec $G $Jbcef $Iyb $Izb $CapTrans
element elasticBeamColumn 14 31 30 $Abc $Ec $G $Jbcef $Iyb $Izb $CapTrans

#Superstructure (deck) elements
element elasticBeamColumn 15 50 510 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 16 510 511 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 17 511 512 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 18 512 513 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 19 513 514 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 20 514 60 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans

element elasticBeamColumn 21 60 610 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 22 610 611 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 23 611 612 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 24 612 613 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 25 613 614 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 26 614 70 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans

puts "Elements have been defined"
#Eigen analysis
file mkdir modal

set numModes 5

set eigenvalues [eigen $numModes]
set omega { }
set T { }
foreach lam $eigenvalues {
lappend omega [expr sqrt ($lam)]
lappend T [expr 2.0*$pi/sqrt($lam)]
}
set period "modal/Periods.txt"
set Periods [open $period "w"]
foreach t $T {
puts $Periods "$t"
}
close $Periods
record
#------------------------------------------------------------------------------------

#Define load
#Load pattern
timeSeries Constant 1

pattern Plain 1 1 {eleLoad -ele 15 16 17 18 19 20 21 22 23 24 25 26 -type -beamUniform -$fLmGird 0.0 0.0
}
pattern Plain 2 1 {eleLoad -ele 11 12 13 14 -type -beamUniform -$fLmBC 0.0 0.0
}
pattern Plain 3 1 {eleLoad -ele 1 2 3 4 5 6 7 8 9 10 -type -beamUniform 0.0 0.0 -$fLmc
}
puts "Loads have been applied"

recorder Node -file ReactionsNode.out -node 10 20 50 70 -dof 2 reaction

system UmfPack -lvalueFact 10
numberer RCM
constraints Transformation
integrator LoadControl 1
test NormDispIncr 1.0e-12 100
algorithm Newton
analysis Static

analyze 1
print -node 10 20 50 70
Thank you

[vesna]

Can you further simplify your code to include only 6 elastic elements? To check reactions you do not need more than that. When posting your code include only the lines of your code that are used within the code so it is readable.

[Fame]

model BasicBuilder -ndm 3 -ndf 6

set meter 1.0
set KPa 1.0
set KN 1.0
set Kip [expr 4.448*$KN]
set inch [expr 0.0254*$meter]
set ft [expr 12.0*$inch]
set Ksi [expr 6896.6*$KPa]

set pi 3.1416
set g 9.81
set fy [expr 60.0*$Ksi];
set fye [expr 68.0*$Ksi]
set Es [expr 29000.0*$Ksi]

set w [expr 0.14396*$Kip/pow($ft,3)];
set pois_ratio 0.2
set fc [expr 4.0*$Ksi]
set Ec [expr 4700.0*sqrt($fc/1000.0)*1000.0]
set G [expr $Ec/(2*(1+$pois_ratio))]
#---------------------------------------------

#Bridge parameters
set Hcol 7.50;
set Dcol 1.3;
set Sp 15.0;
set Total_Span 30.0;
set Dcg 1.0;
set Lcap 5.5;
set Dw 23.0;
#--------------------------------------------------------------------------

#Column properties
set Agcol [expr $pi*pow($Dcol,2)/4]
set Izcol [expr $pi*pow($Dcol,4)/64];
set Jcol [expr $pi*pow($Dcol,4)/32]
set Jefcol [expr 0.2*$Jcol]
set Iefcol [expr 0.6089*$Izcol]

#Beam cap cross section properties
set C 1.0
set CapD 2.0;
set CapW 2.0;
set Abc [expr $CapD*$CapW]
set Izb [expr $CapW*pow($CapD,3)/12]
set Iyb [expr $CapD*pow($CapW,3)/12]
set Jbcef [expr 5413612*pow($inch,4)*$C]
set GJ [expr $G*$Jbcef]

#Deck properties
set Ad 12.0
set Jd 24.22
set Iy 7.282
set Iyd [expr 0.75*$Iy]
set Iz 420.4821
set Izd [expr 0.75*$Iz]
#-----------------------------------------------------------------------------

#Define nodal coordinates
set X0 0.0
set X1 [expr $X0 + $Sp]
set X2 [expr $X0 - $Sp]

set Y0 0.0
set Y1 [expr $Y0 + $Hcol + $Dcg]

set Z0 0.0
set Z1 [expr -$Lcap]
set Z2 $Lcap

set fLmc [expr $w*$Agcol];
set mLc [expr $fLmc/$g];
set mc [expr $mLc*$Y1/2.0];

set fLmGird [expr $w*$Ad];
set mLs [expr $fLmGird/$g];
set m50 [expr $mLs*$Sp/4.0];
set m70 $m50

set fLmBC [expr $w*$Abc];
set mLbc [expr $fLmBC/$g];
set mbc [expr $mLbc*$Lcap/4.0];
set m30 [expr $mbc + $mc];

set m60 [expr $m50 + $m70 + 2*$mbc];

node 10 $X0 $Y0 $Z1 -mass $mc $mc $mc 0.0 0.0 0.0
node 20 $X0 $Y0 $Z2 -mass $mc $mc $mc 0.0 0.0 0.0

node 30 $X0 $Y1 $Z1 -mass $m30 $m30 $m30 0.0 0.0 0.0
node 40 $X0 $Y1 $Z2 -mass $m30 $m30 $m30 0.0 0.0 0.0

node 50 $X2 $Y1 $Z0 -mass $m50 $m50 $m50 0.0 0.0 0.0
node 60 $X0 $Y1 $Z0 -mass $m60 $m60 $m60 0.0 0.0 0.0
node 70 $X1 $Y1 $Z0 -mass $m70 $m70 $m70 0.0 0.0 0.0
#-----------------------------------------------------------------
fix 10 1 1 1 0 0 0;
fix 20 1 1 1 0 0 0

fix 50 0 1 0 0 0 0;
fix 70 0 1 0 0 0 0
#------------------------------------------------------------------

#Define elements
set ColTrans 1
set CapTrans 2
set GirdTrans 3
set RigColTrans 4

geomTransf PDelta $ColTrans 0 0 -1;
geomTransf Linear $CapTrans 1 0 0;
geomTransf Linear $GirdTrans 0 0 1;
geomTransf PDelta $RigColTrans 0 0 -1 -jntOffset 0.0 0.0 0.0 0.0 -$Dcg 0.0;

set ite 3

element elasticBeamColumn 1 10 30 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans
element elasticBeamColumn 2 20 40 $Agcol $Ec $G $Jefcol $Iefcol $Iefcol $ColTrans

element elasticBeamColumn 3 40 60 $Abc $Ec $G $Jbcef $Iyb $Izb $CapTrans
element elasticBeamColumn 4 60 30 $Abc $Ec $G $Jbcef $Iyb $Izb $CapTrans

element elasticBeamColumn 5 50 60 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
element elasticBeamColumn 6 60 70 $Ad $Ec $G $Jd $Iyd $Izd $GirdTrans
#------------------------------------------------------------------------------------

timeSeries Constant 1

pattern Plain 1 1 {eleLoad -ele 5 6 -type -beamUniform -$fLmGird 0.0 0.0
eleLoad -ele 3 4 -type -beamUniform -$fLmBC 0.0 0.0
eleLoad -ele 1 2 -type -beamUniform 0.0 0.0 -$fLmc
}

recorder Node -file ReactionsNode.out -node 10 50 -dof 2 reaction

system UmfPack -lvalueFact 10
numberer RCM
constraints Transformation
integrator LoadControl 1
test NormDispIncr 1.0e-12 100
algorithm Newton
analysis Static

analyze 1
print -node 10 50

Thank you.

[vesna]

I carefully checked your model (geometry, boundary conditions, transformation, elements, load, analysis) and all is representative of the model you described in your earlier post. Check for errors in input values and for errors in your hand calculation.

[parasismique]

Hi Fame and all;

I'm trying to anlyze 3D, 6DOF bridge with two spans. I did a modal analysis that gave me a priod of 1.83 s. When i tried the static analysis, i have the problem.
I tried changing all types of algorithm command, my last program was almost identical to yours. But algorithm still failed and error occured as:

" ForceBeamColumn 3d:update- could not invert flexibility
WARNING: ForceBeamColumn 3d:update-failed to get compatible element forces deeformations for element
Domain update- domain failed in update .....

I have tried many times for a month and I can't find the solution.
I will be very grateful if you can help me! I leave you my email if you want to contact me. ' hayatb2011@yahoo.fr '

[selimgunay]

You can try to increase the steel strain hardening. If you cannot overcome the issue, you can use multiple displacement based elements to model one column.