Simple Cantilever model

[astrella]

I have two cantilevered column models with one difference, one uses a beamWithhinges, and the other uses a nonlinearBeamColumn. The loading is a simple point load at the free end. The resulting stiffness should be 3EI/L3, which is close to what the beamWithHinges provides but not exact, and different from what the NBC provides. Has anyone done a simple exercise like this and/or have any advice?

[lish hit]

My experience (in analyze cantilevered column).......

when use ele load "Beam With Hinges Element" give more rigorous results;

when use simple node load "Nonlinear Beam Column Element" give more rigorous results;

I check it use resulting displacment,and I think if disp is rigorous ,stiffness is rigorous also,only my experience..........

[fmk]

for elastic analysis with an 'Elastic' section they will all give the same results .. for
a Fiber discretization using Elastic materials they will differ .. its due to the fiber
discretization and the different integration that is performed .. the displacement based and forced based elements will give the same results, the beamWithHinges will be be better
as an Elastic section is used internally for the elastic portion and given a larger weight
.. as increase the number of fibers they all converge.



THIS DOES NOT MEAN THAT EVERYONE IS TO GO THROWING LOTS & LOTS OF FIBERS IN A SECTION .. IF ANYONE USES MORE THAN 50-100 IN A NONLINEAR PROBLEM, DON'T BOTHER COMPLAINING ABOUT THE SPEED OF THE PROGRAM OR ANY CONVERGENCE PROBLEMS .. REMEMBER YOU ARE MODELLING BUILDINGS CONTAINING MATERIALS YOU DO NOT KNOW THE EXACT PROPERTIES OFF USING MATERIAL MODELS THAT ATTEMPT TO CAPTURE THEIR BEHAVIOUR!


anyway here is an example script to show what i am talking about:


set height 144
set P 10.0
set b 15
set d 24
set E 1e3
set A [expr $b * $d]
set Iz [expr $b * $d * $d * $d / 12.0]

puts "Expected Tip Deflection: [expr $P * $height * $height * $height / (3.0 * $E * $Iz)]"

foreach eleType {"force" "disp" "hinges" "elastic"} {

wipe
model basic -ndm 2 -ndf 3

node 1 0.0 0.0
node 2 0.0 $height

fix 1 1 1 1

section Elastic 1 $E $A $Iz

geomTransf Linear 1

set np 5

if {$eleType == "force"} {
element forceBeamColumn 1 1 2 $np 1 1
}
if {$eleType == "disp"} {
element dispBeamColumn 1 1 2 $np 1 1
}
if {$eleType == "elastic"} {
element elasticBeamColumn 1 1 2 $A $E $Iz 1
}
if {$eleType == "hinges"} {
element beamWithHinges 1 1 2 1 1.0 1 1.0 $E $A $Iz 1
}

pattern Plain 1 "Linear" {
load 2 $P 0.0 0.0
}

system BandGeneral
constraints Transformation
numberer RCM
test NormDispIncr 1.0e-12 10 3
algorithm Newton
integrator LoadControl 0.1
analysis Static

recorder Node -file node$eleType.out -time -node 2 -dof 1 2 3 disp

analyze 10

puts "RESULTS for Element Type: $eleType";
print node 2
}



foreach numFiber {10 100 1000} {
foreach eleType {"force" "disp" "hinges"} {

wipe
model basic -ndm 2 -ndf 3

node 1 0.0 0.0
node 2 0.0 $height

fix 1 1 1 1

uniaxialMaterial Elastic 1 $E
set z1 [expr $b/2.0]
set y1 [expr $d/2.0]

section Fiber 2 {
patch rect 1 $numFiber 1 [expr -$y1] [expr -$z1] [expr $y1] [expr $z1]
}

geomTransf Linear 1

set np 5

if {$eleType == "force"} {
element forceBeamColumn 1 1 2 $np 2 1
}
if {$eleType == "disp"} {
element dispBeamColumn 1 1 2 $np 2 1
}
if {$eleType == "hinges"} {
element beamWithHinges 1 1 2 2 1.0 2 1.0 $E $A $Iz 1
}

pattern Plain 1 "Linear" {
load 2 $P 0.0 0.0
}

system BandGeneral
constraints Transformation
numberer RCM
test NormDispIncr 1.0e-12 10 3
algorithm Newton
integrator LoadControl 0.1
analysis Static

recorder Node -file node$eleType.out -time -node 2 -dof 1 2 3 disp

analyze 10

puts "RESULTS for Element Type: $eleType with $numFiber fibers";
print node 2
}
}

[fmk]

before anyone asks .. forceBeamColumn is the same as nonlinearBeamColumn