Nonlinear analysis vs linear analysis results

[xavio]

Hi,
I am modelling a bridge structure and I am performing linear and nonlinear analyses on it. I tried to do a pushover of my model containing only linear elements (elasticBeamColumn elements). After it, I did a pushover with the very same model, but I replaced the columns of the bridge by nonlinear elements (forceBeamColumn elements) with fiber section. The pushover is displacement-based. In both cases, I recorded the "base shear-top displacement" curve. Normally, I should obtain similar results in the elastic portion of the curve but I don't, so I suppose something is wrong in the model or in the analyses...

It is as if the initial stiffness of the linear model was really higher than the nonlinear one... Like 10 times higher. My model returns no errors and I checked the materials and everything carefully... I tried other convergence tests, number of integration points, element types, integrators, geometric transformations, but nothing works. I'm running out of ideas... Does somebody have an idea please? Also, I noted that when I use Concrete02 for my nonlinear column elements, the model doesn't converge, but when I use Concrete01, it does.

Thank you very much!

Here are the materials and sections I use for the columns (units in Pa, m):

Linear:

set Acol 1.80
set Icrycol 0.086
set Icrzcol 0.157
set Etrentecinq 2.642e10
set Gtrentecinq 1.157e10
set Jcol 0.4434

element elasticBeamColumn $eleTag 441 442 $Acol $Etrentecinq $Gtrentecinq $Jcol $Icrycol $Icrzcol $transfvert -mass [expr $ro*$HSec1*$BSec1]


Nonlinear:

uniaxialMaterial Concrete01 1 -35000000.0 -0.002 -25000000 -0.004
uniaxialMaterial Concrete01 2 -38140000 -0.0021 -33000000 -0.004
uniaxialMaterial ReinforcingSteel 4 425.00e6 670.00e6 200000.00e6 6000.0e6 0.008 0.135

set Col 1
set HSec1 1.500
set BSec1 1.200
set coverH1 [expr 0.075+0.020+(0.030/2.000)]
set coverB1 [expr 0.075+0.020+(0.030/2.000)]
set coreID1 2
set coverID1 1
set steelID1 4
set numBarsTop1 7
set barAreaTop1 7.07e-4
set numBarsBot1 7
set barAreaBot1 7.07e-4
set numBarsIntTot1 14
set barAreaInt1 7.07e-4
set nfCoreY1 50
set nfCoreZ1 50
set nfCoverY1 20
set nfCoverZ1 20

#This is a procedure to build a rectangular fiber RC section
BuildRCrectSection $Col $HSec1 $BSec1 $coverH1 $coverB1 $coreID1 $coverID1 $steelID1 $numBarsTop1 $barAreaTop1 $numBarsBot1 $barAreaBot1 $numBarsIntTot1 $barAreaInt1 $nfCoreY1 $nfCoreZ1 $nfCoverY1 $nfCoverZ1

uniaxialMaterial Elastic 201 1000.0e20
section Aggregator 5 201 T -section 1

element forceBeamColumn $eleTag 441 442 3 5 $transfvert -mass [expr $ro*$HSec1*$BSec1]

[tazarv]

The method I want you to try is not really necessary but in your case that you are not sure about your linear/nonlinear analysis, that may be help. Do this, for the linear analysis, instead of using Elastic element, use the same nonlinear element which you uses in the fiber model but increase the concrete and steel fibers' strength 1000 times. Now, the structure won't experience any nonlinearity with the same displacement you had in the nonlinear case even though the element is nonlinear. By this method, at least you will have same material, fiber and element to compare. Briefly, do the both linear and nonlinear analyses with your fiber model however increase the strength in the linear case.

You can also check the period of your two models and see the initial stiffness are same for both.

Bests,

[xavio]

Thank you for your help! I tried it by multiplying yield stress and yield strain by 1000 for each of my materials. I obtain a very stiff response. The stiffness is even higher than the one of the elastic response. I'm not sure this is working and if it is, I'm not sure what it means...

The first period is not the same for the 2 models (linear and nonlinear). I don't know what to change to obtain the same initial stiffness (or at least something close)... All parameters seem good to me...

[tazarv]

As you mentioned, we don't want to have different initial stiffness for linear and nonlinear analyses. Please make sure that for the Concrete01 you used, both f'c and strain at maximum stress (epsc0) have been increased by the same scale factor since the modulus of elasticity is 2*$fpc/$epsc0 (see http://opensees.berkeley.edu/wiki/index ... e_Strength) for this material. And also for ReinforcingSteel, please keep the $Es same. Hopefully you will have same initial stiffness now.

[xavio]

I tried it and it worked. Thank you very much for your reply!