Period of a flexural-shear beam

[stealth_mode]

I have modeled a flexural-shear beam (like a column fixed at bottom and free at top) using nonlinearbeamcolumn elements and utilizing section Aggregator for combining the effect of shear and flexural deformations. When I changed the stiffnesses, EIzero and GAzero, that I defined for the uniaxial sections at the integration points, I came across with a weird situation: the fundamental period of the system did not change (By the way, I have not looked at other modes). I am providing a simpler form of this flexural-shear beam below. Please run the code and then change the stiffness values (EIzero and GAzero) re-run the code and observe the difference(?)

Am I doing smt wrong in modeling?

Koray KADAS

Code: Select all

model basic -ndm 2 -ndf 3
################################################
set GAzero 10000000
set EIzero 3000000
set GA_yield 1000
set EI_yield 1000
set GAhardratio 0.10
set EIhardratio 0.10
# Set Analysis parameters
set numintgrpts 5
set maxiters 200
set tol 1e-8
##############################
set pi 3.14159265359
##############################
node 1 0.0 0.0
node 2 0.0 1.0
node 3 0.0 2.0
node 4 0.0 3.0
node 5 0.0 4.0
mass 2 1.0 0.0 0.0
mass 3 1.0 0.0 0.0
mass 4 1.0 0.0 0.0
mass 5 1.0 0.0 0 0
fix 1 1 1 1
geomTransf Linear 1
uniaxialMaterial Steel01 1 $GA_yield $GAzero $GAhardratio
uniaxialMaterial Steel01 2 $EI_yield $EIzero $EIhardratio
section Aggregator 1 2 Mz 1 Vy
element nonlinearBeamColumn 1 1 2 $numintgrpts 1 1 -iter $maxiters $tol
element nonlinearBeamColumn 2 2 3 $numintgrpts 1 1 -iter $maxiters $tol
element nonlinearBeamColumn 3 3 4 $numintgrpts 1 1 -iter $maxiters $tol
element nonlinearBeamColumn 4 4 5 $numintgrpts 1 1 -iter $maxiters $tol
puts "-------------------------------------------------"
puts "            EIGENVALUE ANALYSIS"
puts "-------------------------------------------------"
set modes [eigen 1]
set lambda [lindex $modes 0]
set omega [expr pow($lambda,0.5)]
set pi 3.14159265359
set Tperiod [expr 2*$pi/$omega]; # period (sec.)
puts "Period 1: $Tperiod"

[silvia]

your model has no axial stiffness. so it is a bit messed up.
if you replace Vy with P in the aggregator, you do see changes.

[stealth_mode]

Although nothing to do with the axial stiffness, it solved my problem. Thank you very much, Silvia! I have started to go crazy...

[silvia]

good.
you need axial stiffness to restrain the dof.