i think there is problem in my modeling , I model 10story 3Bay MRF 2Dstructure in Opensees and Etabs and Period of stuctures in GeomTransf = Linear for 2 Software are Approximately equal ( Period in Opensees = 2.03 , Period in Etabs=2.05 )
but in PDelta mode in Etabs Period is 2.07 but in Opensees in PDelta mode it is steal 2.03 and i think it is wrong beacuse it is Not changed . Please help me.
###################################################################################################
# Set Nodes #
###################################################################################################
# Base
node 10 0. 0.
node 20 6.096 0.
node 30 12.192 0.
node 40 18.288 0.
# Floor 1
node 11 0. 4.572
node 21 6.096 4.572
node 31 12.192 4.572
node 41 18.288 4.572
# Floor 2
node 12 0. 8.2296
node 22 6.096 8.2296
node 32 12.192 8.2296
node 42 18.288 8.2296
# Middle Story 3
node 312 0. 10.0584
node 322 6.096 10.0584
node 332 12.192 10.0584
node 342 18.288 10.0584
# Floor 3
node 13 0. 11.8872
node 23 6.096 11.8872
node 33 12.192 11.8872
node 43 18.288 11.8872
# Floor 4
node 14 0. 15.5448
node 24 6.096 15.5448
node 34 12.192 15.5448
node 44 18.288 15.5448
# Middle Story 5
node 314 0. 17.3736
node 324 6.096 17.3736
node 334 12.192 17.3736
node 344 18.288 17.3736
# Floor 5
node 15 0. 19.2024
node 25 6.096 19.2024
node 35 12.192 19.2024
node 45 18.288 19.2024
# Floor 6
node 16 0. 22.86
node 26 6.096 22.86
node 36 12.192 22.86
node 46 18.288 22.86
# Middle Story 7
node 316 0. 24.6888
node 326 6.096 24.6888
node 336 12.192 24.6888
node 346 18.288 24.6888
# Floor 7
node 17 0. 26.5176
node 27 6.096 26.5176
node 37 12.192 26.5176
node 47 18.288 26.5176
# Floor 8
node 18 0. 30.1752
node 28 6.096 30.1752
node 38 12.192 30.1752
node 48 18.288 30.1752
# Middle Story 9
node 318 0. 32.004
node 328 6.096 32.004
node 338 12.192 32.004
node 348 18.288 32.004
# Floor 9
node 19 0. 33.8328
node 29 6.096 33.8328
node 39 12.192 33.8328
node 49 18.288 33.8328
# Floor 10
node 110 0 37.4904
node 210 6.096 37.4904
node 310 12.192 37.4904
node 410 18.288 37.4904
# calculate nodal masses -- lump floor masses at frame nodes
set g 10.0; # acceleration due to gravity
set FloorMass0 [expr (1936) ]; # weight of Floor 0 in kg
set FloorMass1 [expr (65317.2 +4889.6) ]; # weight of Floor 1 in kg
set FloorMass2 [expr (65317.2 +4502.3) ]; # weight of Floor 2 in kg
set FloorMass3 [expr (65317.2 +3597.
]; # weight of Floor 3 in kgset FloorMass4 [expr (65317.2 +3597.
]; # weight of Floor 4 in kgset FloorMass5 [expr (65317.2 +3266.0) ]; # weight of Floor 5 in kg
set FloorMass6 [expr (65317.2 +3101.4) ]; # weight of Floor 6 in kg
set FloorMass7 [expr (65317.2 +2946.0) ]; # weight of Floor 7 in kg
set FloorMass8 [expr (65317.2 +2946.0) ]; # weight of Floor 8 in kg
set FloorMass9 [expr (65317.2 +2288.0) ]; # weight of Floor 9 in kg
set FloorMass10 [expr (54431.04+1657.6) ]; # weight of Floor 10 in kg
set NodalMass0 [expr $FloorMass0 / (3.0)]; # mass at each node on Floor 0 in kg
set NodalMass1 [expr $FloorMass1 / (3.0)]; # mass at each node on Floor 1 in kg
set NodalMass2 [expr $FloorMass2 / (3.0)]; # mass at each node on Floor 2 in kg
set NodalMass3 [expr $FloorMass3 / (3.0)]; # mass at each node on Floor 3 in kg
set NodalMass4 [expr $FloorMass4 / (3.0)]; # mass at each node on Floor 4 in kg
set NodalMass5 [expr $FloorMass5 / (3.0)]; # mass at each node on Floor 5 in kg
set NodalMass6 [expr $FloorMass6 / (3.0)]; # mass at each node on Floor 6 in kg
set NodalMass7 [expr $FloorMass7 / (3.0)]; # mass at each node on Floor 7 in kg
set NodalMass8 [expr $FloorMass8 / (3.0)]; # mass at each node on Floor 8 in kg
set NodalMass9 [expr $FloorMass9 / (3.0)]; # mass at each node on Floor 9 in kg
set NodalMass10 [expr $FloorMass10 / (3.0)]; # mass at each node on Floor 10 in kg
set Negligible 1e-9; # a very small number to avoid problems with zero
# define nodal masses: lump at beam-column joints in frame
mass 10 [expr $NodalMass0/2.0] $Negligible $Negligible; # Pier 1, Floor 0
mass 20 $NodalMass0 $Negligible $Negligible; # Pier 2, Floor 0
mass 30 $NodalMass0 $Negligible $Negligible; # Pier 3, Floor 0
mass 40 [expr $NodalMass0/2.0] $Negligible $Negligible; # Pier 4, Floor 0
mass 11 [expr $NodalMass1/2.0] $Negligible $Negligible; # Pier 1, Floor 1
mass 21 $NodalMass1 $Negligible $Negligible; # Pier 2, Floor 1
mass 31 $NodalMass1 $Negligible $Negligible; # Pier 3, Floor 1
mass 41 [expr $NodalMass1/2.0] $Negligible $Negligible; # Pier 4, Floor 1
mass 12 [expr $NodalMass2/2.0] $Negligible $Negligible; # Pier 1, Floor 2
mass 22 $NodalMass2 $Negligible $Negligible; # Pier 2, Floor 2
mass 32 $NodalMass2 $Negligible $Negligible; # Pier 3, Floor 2
mass 42 [expr $NodalMass2/2.0] $Negligible $Negligible; # Pier 4, Floor 2
mass 13 [expr $NodalMass3/2.0] $Negligible $Negligible; # Pier 1, Floor 3
mass 23 $NodalMass3 $Negligible $Negligible; # Pier 2, Floor 3
mass 33 $NodalMass3 $Negligible $Negligible; # Pier 3, Floor 3
mass 43 [expr $NodalMass3/2.0] $Negligible $Negligible; # Pier 4, Floor 3
mass 14 [expr $NodalMass4/2.0] $Negligible $Negligible; # Pier 1, Floor 4
mass 24 $NodalMass4 $Negligible $Negligible; # Pier 2, Floor 4
mass 34 $NodalMass4 $Negligible $Negligible; # Pier 3, Floor 4
mass 44 [expr $NodalMass4/2.0] $Negligible $Negligible; # Pier 4, Floor 4
mass 15 [expr $NodalMass5/2.0] $Negligible $Negligible; # Pier 1, Floor 5
mass 25 $NodalMass5 $Negligible $Negligible; # Pier 2, Floor 5
mass 35 $NodalMass5 $Negligible $Negligible; # Pier 3, Floor 5
mass 45 [expr $NodalMass5/2.0] $Negligible $Negligible; # Pier 4, Floor 5
mass 16 [expr $NodalMass6/2.0] $Negligible $Negligible; # Pier 1, Floor 6
mass 26 $NodalMass6 $Negligible $Negligible; # Pier 2, Floor 6
mass 36 $NodalMass6 $Negligible $Negligible; # Pier 3, Floor 6
mass 46 [expr $NodalMass6/2.0] $Negligible $Negligible; # Pier 4, Floor 6
mass 17 [expr $NodalMass7/2.0] $Negligible $Negligible; # Pier 1, Floor 7
mass 27 $NodalMass7 $Negligible $Negligible; # Pier 2, Floor 7
mass 37 $NodalMass7 $Negligible $Negligible; # Pier 3, Floor 7
mass 47 [expr $NodalMass7/2.0] $Negligible $Negligible; # Pier 4, Floor 7
mass 18 [expr $NodalMass8/2.0] $Negligible $Negligible; # Pier 1, Floor 8
mass 28 $NodalMass8 $Negligible $Negligible; # Pier 2, Floor 8
mass 38 $NodalMass8 $Negligible $Negligible; # Pier 3, Floor 8
mass 48 [expr $NodalMass8/2.0] $Negligible $Negligible; # Pier 4, Floor 8
mass 19 [expr $NodalMass9/2.0] $Negligible $Negligible; # Pier 1, Floor 9
mass 29 $NodalMass9 $Negligible $Negligible; # Pier 2, Floor 9
mass 39 $NodalMass9 $Negligible $Negligible; # Pier 3, Floor 9
mass 49 [expr $NodalMass9/2.0] $Negligible $Negligible; # Pier 4, Floor 9
mass 110 [expr $NodalMass10/2.0] $Negligible $Negligible; # Pier 1, Floor 10
mass 210 $NodalMass10 $Negligible $Negligible; # Pier 2, Floor 10
mass 310 $NodalMass10 $Negligible $Negligible; # Pier 3, Floor 10
mass 410 [expr $NodalMass10/2.0] $Negligible $Negligible; # Pier 4, Floor 10
# constrain beam-column joints in a floor to have the same lateral displacement using the "equalDOF" command
set dof1 1; # constrain movement in dof 1 (x-direction)
equalDOF 11 21 $dof1; # Floor 1: Pier 1 to Pier 2
equalDOF 11 31 $dof1; # Floor 1: Pier 1 to Pier 3
equalDOF 11 41 $dof1; # Floor 1: Pier 1 to Pier 4
equalDOF 12 22 $dof1; # Floor 2: Pier 1 to Pier 2
equalDOF 12 32 $dof1; # Floor 2: Pier 1 to Pier 3
equalDOF 12 42 $dof1; # Floor 2: Pier 1 to Pier 4
equalDOF 13 23 $dof1; # Floor 3: Pier 1 to Pier 2
equalDOF 13 33 $dof1; # Floor 3: Pier 1 to Pier 3
equalDOF 13 43 $dof1; # Floor 3: Pier 1 to Pier 4
equalDOF 14 24 $dof1; # Floor 4: Pier 1 to Pier 2
equalDOF 14 34 $dof1; # Floor 4: Pier 1 to Pier 3
equalDOF 14 44 $dof1; # Floor 4: Pier 1 to Pier 4
equalDOF 15 25 $dof1; # Floor 5: Pier 1 to Pier 2
equalDOF 15 35 $dof1; # Floor 5: Pier 1 to Pier 3
equalDOF 15 45 $dof1; # Floor 5: Pier 1 to Pier 4
equalDOF 16 26 $dof1; # Floor 6: Pier 1 to Pier 2
equalDOF 16 36 $dof1; # Floor 6: Pier 1 to Pier 3
equalDOF 16 46 $dof1; # Floor 6: Pier 1 to Pier 4
equalDOF 17 27 $dof1; # Floor 7: Pier 1 to Pier 2
equalDOF 17 37 $dof1; # Floor 7: Pier 1 to Pier 3
equalDOF 17 47 $dof1; # Floor 7: Pier 1 to Pier 4
equalDOF 18 28 $dof1; # Floor 8: Pier 1 to Pier 2
equalDOF 18 38 $dof1; # Floor 8: Pier 1 to Pier 3
equalDOF 18 48 $dof1; # Floor 8: Pier 1 to Pier 4
equalDOF 19 29 $dof1; # Floor 9: Pier 1 to Pier 2
equalDOF 19 39 $dof1; # Floor 9: Pier 1 to Pier 3
equalDOF 19 49 $dof1; # Floor 9: Pier 1 to Pier 4
equalDOF 110 210 $dof1; # Floor 10: Pier 1 to Pier 2
equalDOF 110 310 $dof1; # Floor 10: Pier 1 to Pier 3
equalDOF 110 410 $dof1; # Floor 10: Pier 1 to Pier 4
# assign boundary condidtions
fix 10 1 1 1;
fix 20 1 1 1;
fix 30 1 1 1;
fix 40 1 1 1;
# Set Beam Of Strucure
set transfTag 1
geomTransf PDelta $transfTag
set Es 2e11
# Beams For Floor 1
element elasticBeamColumn 111 11 21 $Abeam_W24X55 $Es $Ibeam_W24X55 $transfTag
element elasticBeamColumn 121 21 31 $Abeam_W24X55 $Es $Ibeam_W24X55 $transfTag
element elasticBeamColumn 131 31 41 $Abeam_W24X55 $Es $Ibeam_W24X55 $transfTag
# Beams For Floor 2
element elasticBeamColumn 112 12 22 $Abeam_W24X55 $Es $Ibeam_W24X55 $transfTag
element elasticBeamColumn 122 22 32 $Abeam_W24X55 $Es $Ibeam_W24X55 $transfTag
element elasticBeamColumn 132 32 42 $Abeam_W24X55 $Es $Ibeam_W24X55 $transfTag
# Beams For Floor 3
element elasticBeamColumn 113 13 23 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 123 23 33 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 133 33 43 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
# Beams For Floor 4
element elasticBeamColumn 114 14 24 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 124 24 34 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 134 34 44 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
# Beams For Floor 5
element elasticBeamColumn 115 15 25 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 125 25 35 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 135 35 45 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
# Beams For Floor 6
element elasticBeamColumn 116 16 26 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 126 26 36 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
element elasticBeamColumn 136 36 46 $Abeam_W21X50 $Es $Ibeam_W21X50 $transfTag
# Beams For Floor 7
element elasticBeamColumn 117 17 27 $Abeam_W21X44 $Es $Ibeam_W21X44 $transfTag
element elasticBeamColumn 127 27 37 $Abeam_W21X44 $Es $Ibeam_W21X44 $transfTag
element elasticBeamColumn 137 37 47 $Abeam_W21X44 $Es $Ibeam_W21X44 $transfTag
# Beams For Floor 8
element elasticBeamColumn 118 18 28 $Abeam_W21X44 $Es $Ibeam_W21X44 $transfTag
element elasticBeamColumn 128 28 38 $Abeam_W21X44 $Es $Ibeam_W21X44 $transfTag
element elasticBeamColumn 138 38 48 $Abeam_W21X44 $Es $Ibeam_W21X44 $transfTag
# Beams For Floor 9
element elasticBeamColumn 119 19 29 $Abeam_W16X40 $Es $Ibeam_W16X40 $transfTag
element elasticBeamColumn 129 29 39 $Abeam_W16X40 $Es $Ibeam_W16X40 $transfTag
element elasticBeamColumn 139 39 49 $Abeam_W16X40 $Es $Ibeam_W16X40 $transfTag
# Beams For Floor 10
element elasticBeamColumn 1110 110 210 $Abeam_W16X40 $Es $Ibeam_W16X40 $transfTag
element elasticBeamColumn 1210 210 310 $Abeam_W16X40 $Es $Ibeam_W16X40 $transfTag
element elasticBeamColumn 1310 310 410 $Abeam_W16X40 $Es $Ibeam_W16X40 $transfTag
# Columns For Story 1
element elasticBeamColumn 211 10 11 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 221 20 21 $Acol_W14X176 $Es $Icol_W14X176 $transfTag
element elasticBeamColumn 231 30 31 $Acol_W14X176 $Es $Icol_W14X176 $transfTag
element elasticBeamColumn 241 40 41 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
# Columns For Story 2
element elasticBeamColumn 212 11 12 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 222 21 22 $Acol_W14X176 $Es $Icol_W14X176 $transfTag
element elasticBeamColumn 232 31 32 $Acol_W14X176 $Es $Icol_W14X176 $transfTag
element elasticBeamColumn 242 41 42 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
# Columns For Story 3
element elasticBeamColumn 213 12 312 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 223 22 322 $Acol_W14X176 $Es $Icol_W14X176 $transfTag
element elasticBeamColumn 233 32 332 $Acol_W14X176 $Es $Icol_W14X176 $transfTag
element elasticBeamColumn 243 42 342 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 2130 312 13 $Acol_W14X82 $Es $Icol_W14X82 $transfTag
element elasticBeamColumn 2230 322 23 $Acol_W14X132 $Es $Icol_W14X132 $transfTag
element elasticBeamColumn 2330 332 33 $Acol_W14X132 $Es $Icol_W14X132 $transfTag
element elasticBeamColumn 2430 342 43 $Acol_W14X82 $Es $Icol_W14X82 $transfTag
# Columns For Story 4
element elasticBeamColumn 214 13 14 $Acol_W14X82 $Es $Icol_W14X82 $transfTag
element elasticBeamColumn 224 23 24 $Acol_W14X132 $Es $Icol_W14X132 $transfTag
element elasticBeamColumn 234 33 34 $Acol_W14X132 $Es $Icol_W14X132 $transfTag
element elasticBeamColumn 244 43 44 $Acol_W14X82 $Es $Icol_W14X82 $transfTag
# Columns For Story 5
element elasticBeamColumn 215 14 314 $Acol_W14X82 $Es $Icol_W14X82 $transfTag
element elasticBeamColumn 225 24 324 $Acol_W14X132 $Es $Icol_W14X132 $transfTag
element elasticBeamColumn 235 34 334 $Acol_W14X132 $Es $Icol_W14X132 $transfTag
element elasticBeamColumn 245 44 344 $Acol_W14X82 $Es $Icol_W14X82 $transfTag
element elasticBeamColumn 2150 314 15 $Acol_W14X74 $Es $Icol_W14X74 $transfTag
element elasticBeamColumn 2250 324 25 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 2350 334 35 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 2450 344 45 $Acol_W14X74 $Es $Icol_W14X74 $transfTag
# Columns For Story 6
element elasticBeamColumn 216 15 16 $Acol_W14X74 $Es $Icol_W14X74 $transfTag
element elasticBeamColumn 226 25 26 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 236 35 36 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 246 45 46 $Acol_W14X74 $Es $Icol_W14X74 $transfTag
# Columns For Story 7
element elasticBeamColumn 217 16 316 $Acol_W14X74 $Es $Icol_W14X74 $transfTag
element elasticBeamColumn 227 26 326 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 237 36 336 $Acol_W14X109 $Es $Icol_W14X109 $transfTag
element elasticBeamColumn 247 46 346 $Acol_W14X74 $Es $Icol_W14X74 $transfTag
element elasticBeamColumn 2170 316 17 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 2270 326 27 $Acol_W14X99 $Es $Icol_W14X99 $transfTag
element elasticBeamColumn 2370 336 37 $Acol_W14X99 $Es $Icol_W14X99 $transfTag
element elasticBeamColumn 2470 346 47 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
# Columns For Story 8
element elasticBeamColumn 218 17 18 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 228 27 28 $Acol_W14X99 $Es $Icol_W14X99 $transfTag
element elasticBeamColumn 238 37 38 $Acol_W14X99 $Es $Icol_W14X99 $transfTag
element elasticBeamColumn 248 47 48 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
# Columns For Story 9
element elasticBeamColumn 219 18 318 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 229 28 328 $Acol_W14X99 $Es $Icol_W14X99 $transfTag
element elasticBeamColumn 239 38 338 $Acol_W14X99 $Es $Icol_W14X99 $transfTag
element elasticBeamColumn 249 48 348 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 2190 318 19 $Acol_W14X48 $Es $Icol_W14X48 $transfTag
element elasticBeamColumn 2290 328 29 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 2390 338 39 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 2490 348 49 $Acol_W14X48 $Es $Icol_W14X48 $transfTag
# Columns For Story 10
element elasticBeamColumn 2110 19 110 $Acol_W14X48 $Es $Icol_W14X48 $transfTag
element elasticBeamColumn 2210 29 210 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 2310 39 310 $Acol_W14X68 $Es $Icol_W14X68 $transfTag
element elasticBeamColumn 2410 49 410 $Acol_W14X48 $Es $Icol_W14X48 $transfTag
############################################################################
# Gravity Loads & Gravity Analysis #
############################################################################
# apply gravity loads
#command: pattern PatternType $PatternID TimeSeriesType
pattern Plain 2 Linear {
eleLoad -ele 111 121 131 -type -beamUniform -5059.75
eleLoad -ele 112 122 132 -type -beamUniform -5059.75
eleLoad -ele 113 123 133 -type -beamUniform -5059.75
eleLoad -ele 114 124 134 -type -beamUniform -5059.75
eleLoad -ele 115 125 135 -type -beamUniform -5059.75
eleLoad -ele 116 126 136 -type -beamUniform -5059.75
eleLoad -ele 117 127 137 -type -beamUniform -5059.75
eleLoad -ele 118 128 138 -type -beamUniform -5059.75
eleLoad -ele 119 129 139 -type -beamUniform -5059.75
eleLoad -ele 1110 1210 1310 -type -beamUniform -3452.54
}
############################################################################
# Gravity Analysis #
############################################################################
# Gravity-analysis: load-controlled static analysis
set Tol 1.0e-6; # convergence tolerance for test
constraints Plain; # how it handles boundary conditions
numberer RCM; # renumber dof's to minimize band-width (optimization)
system UmfPack; # how to store and solve the system of equations in the analysis (large model: try UmfPack)
test NormDispIncr $Tol 6; # determine if convergence has been achieved at the end of an iteration step
algorithm Newton; # use Newton's solution algorithm: updates tangent stiffness at every iteration
set NstepGravity 10; # apply gravity in 10 steps
set DGravity [expr 1.0/$NstepGravity]; # load increment
integrator LoadControl $DGravity; # determine the next time step for an analysis
analysis Static; # define type of analysis: static or transient
analyze $NstepGravity; # apply gravity
# maintain constant gravity loads and reset time to zero
loadConst -time 0.0
puts "Model Built"
############################################################################
# Eigenvalue Analysis #
############################################################################
set pi [expr 2.0*asin(1.0)]; # Definition of pi
set nEigenI 1; # mode i = 1
set nEigenJ 2; # mode j = 2
set nEigenK 3; # mode j = 3
set lambdaN [eigen [expr $nEigenK]]; # eigenvalue analysis for nEigenK modes
set lambdaI [lindex $lambdaN [expr $nEigenI-1]]; # eigenvalue mode i = 1
set lambdaJ [lindex $lambdaN [expr $nEigenJ-1]]; # eigenvalue mode j = 2
set lambdaK [lindex $lambdaN [expr $nEigenK-1]]; # eigenvalue mode K = 3
set w1 [expr pow($lambdaI,0.5)]; # w1 (1st mode circular frequency)
set w2 [expr pow($lambdaJ,0.5)]; # w2 (2nd mode circular frequency)
set w3 [expr pow($lambdaK,0.5)]; # w3 (3nd mode circular frequency)
set T1 [expr 2.0*$pi/$w1]; # 1st mode period of the structure
set T2 [expr 2.0*$pi/$w2]; # 2nd mode period of the structure
set T3 [expr 2.0*$pi/$w3]; # 3nd mode period of the structure
puts "T1 = $T1 s"; # display the first mode period in the command window
puts "T2 = $T2 s"; # display the second mode period in the command window
puts "T3 = $T3 s"; # display the Third mode period in the command window