Ambiguity in using the equalDOF command

[EFearthquake]

I want to model a 2d moment frame. This frame is one bay and one storey. It's supports are fixed.
When I use simple following programe , the natural frequency is obtained 1.274:

wipe
model basic -ndm 2 -ndf 3

# file mkdir $dataDirection

set L 5. ;
set H 3. ;

node 1 0. 0.
node 2 $L 0.0
node 3 0. $H
node 4 $L $H

fix 1 1 1 1
fix 2 1 1 1

equalDOF 3 4 1


set E 2.0E10 ;
set A 43e-4
set Iz 1510.0e-8


set transfTag 1
geomTransf Linear $transfTag

element elasticBeamColumn 1 1 3 $A $E $Iz $transfTag
element elasticBeamColumn 2 2 4 $A $E $Iz $transfTag
element elasticBeamColumn 3 3 4 $A $E $Iz $transfTag

mass 3 50000.0 0.01 0.01
mass 4 50000.0 0.01 0.01

set Landa [eigen 1] ;
set w [expr pow([lindex $Landa 0],0.5)]
puts "w is $w"

Now if two new nodes 33 and 44 be added that have similar coordinate with respectively nodes 3 and 4.
One of Columns is modeled with nodes 1 and 33 and another column is modeled with nodes 2 and 44. The beam is modeled with nodes 3 and 4.
Then between nodes 3 and 33 as 4 and 44 be used total degrees of freedom constraint. For this modeling I use following commands. I beleive two
these models are identical, but eigen value analysis show natural frequency of second model is 1.226 that is not the same as first model.

Does anyone know the reason for this difference?

wipe
model basic -ndm 2 -ndf 3

# file mkdir $dataDirection

set L 5. ;
set H 3. ;

node 1 0. 0.
node 2 $L 0.0
node 3 0. $H
node 4 $L $H

node 33 0. $H
node 44 $L $H

fix 1 1 1 1
fix 2 1 1 1

equalDOF 3 4 1
equalDOF 3 33 1 2 3
equalDOF 4 44 1 2 3

set E 2.0E10 ;
set A 43e-4
set Iz 1510.0e-8


set transfTag 1
geomTransf Linear $transfTag

element elasticBeamColumn 1 1 33 $A $E $Iz $transfTag
element elasticBeamColumn 2 2 44 $A $E $Iz $transfTag
element elasticBeamColumn 3 3 4 $A $E $Iz $transfTag

mass 3 50000.0 0.01 0.01
mass 4 50000.0 0.01 0.01

set Landa [eigen 1] ;
set w [expr pow([lindex $Landa 0],0.5)]
puts "w is $w"

[fmk]

The Transformation method, the default used when you do not build up an analysis object before issuing the eigen command, cannot handle one node constrained to another that has already been constrained, i.e. constraints in series .. remove the equalDOF 3 4 1 from both scripts (or given this particular model and what the first mode is, just the second script)

if you abs need such constraints you need to use the Penalty method, so build the analysis before the eigen command, e.g. for you case add the following before eigen command

constraints Penalty 1e12 1e12
analysis Transient