OpenSees Development and Validation Efforts at...

OpenSees Development and Validation Efforts at UW

Laura N. LowesUniversity of Washington

OpenSees Developers Symposium, August 2005

OpenSees Research Activities

� Modeling RC Beam-Column Joints

� Element Development

� Material Model Development

� Pinching4 Material Model

� Bar-Slip Material Model

� Validation Study

� Modeling RC Bridge Columns for PBEE

� Concrete Material Model

� Variable Plastic-Hinge Length Model

� Plastic-Hinge Length Calibration Study


Acknowledgements

�Beam-Column Joint Modeling

� Nilanjan Mitra, Graduate Student

�Column Modeling

� Michael Berry, Graduate Student

� Dawn Lehman, Assistant Professor

� Nilanjan Mitra, Graduate Student


Modeling RC Beam-Column Joints

�Modeling Needs

�Element Development

�Material Model Development

�Material Model Calibration

�Validation


Joint Behavior

-80

-60

-40

-20

0

20

40

60

80

-6 -4 -2 0 2 4 6

Drift

Co

lum

n S

he

ar

(K)

5% Drift

Images and data from Lehman,

Stanton & Walker (2002)


Joint Element Development

� The objective was to develop a joint model that is

� Compatible with existing component models, i.e. beam-column line elements

� Computationally efficient

� Robust and accurate in predicting response

� Objective and transparent for user calibration

� This objective was achieved through development of a joint super-element


Joint Element Formulation

column

column

beam

beamshear

panel

bar-slip

springs

interface-shear

springs

� 4-node, 12-dof, 2D joint element.

� Super element comprising� 1 shear panel

� 8 bar-slip springs

� 4 Interface-shear springs

� Solution for element state is achieved using an iterative procedure and requires solving for zero reactions at internal dof.


Joint Element Formulation

4f

5f

6f 4F5F

6F

7f 8f9f

7F8F

9F

1f 2f3f

1F2F

3F

10f

11f

12f10F11F

12F

5f

4f

6f132

f

wΦ −

5 4

ˆ ˆ

2 2

h h h hf f

h h

− ++

1 2

ˆ ˆ

2 2

w w w wf f

w w

− + +

5 4

ˆ ˆ

2 2

h h h hf f

h h

+ −+

7 8

ˆ ˆ

2 2

w w w wf f

w w

− + +

13f

Component

Deformations

Component Forces


Material Model Development

�Pinching4 Uniaxial Material Model

� Multi-linear response envelope

� Tri-linear unload-reload path

� Strength, unloading stiffness, and reloading stiffness deterioration under cyclic loading

�Bar-Slip Uniaxial Material Model

� Pinching4 Material with strength degradation upon reloading


Pinching4 Material

(eNd4,eNf4)


Pinching4 Material – damage simulation

Strength Unloading Stiffness Reloading Stiffness

Strength and Stiffness Deterioration

( )ii

kkk δ−⋅= 10

( )ii

ddd δ+⋅= 10maxmax( ) ( ) ( )

iifff δ−⋅= 1

0maxmax

( ) ( )3 4

max max1 2

id

α α

δ α α χ= +%

( )

max

max

OR

i

m

E

E

number of load cycles

χβ

χ

=

=

( ) ( )max min

max

max min

max ,i id d

ddef def

=

%

i

history

E dE= ∫

m

monotonic history

E dE= ∫


Material Model Calibration – Shear Panel

� MCFT-based model (Lowes and Altoontash, 2003)� Assumes uniform shear stress is joint core.

� Envelope to panel stress-strain response is defined using MCFT (Vecchio and Collins 1986).

� Not appropriate for joints with low transverse steel ratios and/or high shear stress demands.

� Ratio of observed to predicted strength shows undesirable dependence on transverse steel ratio

� Compression-strut model (Mitra and Lowes, submitted)� Assumes shear stress transferred by a concrete strut.

� Envelope to panel stress-strain response is defined using confined concrete model (Mander et al. 1988).

� Appropriate for joints with variable transverse steel ratios andshear stress demands.

� Ratio of observed to predicted strength shows no dependence on transverse steel ratio.


Evaluation of Shear Panel Calibration

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

JF

BYJF

BY

`

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 0.5 1.0 1.5 2.0 2.5

JF

BYJF

BY

`

ϕ

τ MC

FT

_m

ono

/ τ m

ax

ρj

0.0

0.5

1.0

1.5

2.0

0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035 0.040

JF

BYJF

BY

`

τ str

ut/

τ max

transverse reinforcement ratio, ρj

0.0

0.5

1.0

1.5

2.0

0.0 0.5 1.0 1.5 2.0 2.5

JF

BYJF

BY

`

trans. reinforcement contribution to

max. shear demand, ϕ

str

ut-

based m

od

el

MC

FT

-based m

odel


� Experimental data used to calibrate unload-reload response and strength / stiffness deterioration.

� Cyclic response parameters calibrated using experimental data� rDisp = Displacement at reload / max. displacement = 0.09� rForce = Force at reload / max. force = 0.21� uForce = Force developed upon unloading = 0.0

� Strength / stiffness deterioration� Strength deterioration under cyclic loading included in bond strength values

� Stiffness deterioration:

� Comparison of simulated and observed response

( )0.22

max0.64k

idδ = % ( )

0.51

max0.20d

idδ = %

observed simulated

Specim

en S

E8

(Ste

vens e

t al. 1

987)

-0.012 -0.008 -0.004 0 0.004 0.008 0.012-10

-8

-6

-4

-2

0

2

4

6

8

10

Shear strain

Sh

ear

stre

ss (

MP

a)

Shear Panel - Cyclic Response


Bar-Slip Material Model

�Uses Pinching4 material model

�Strength loss is initiated once a specific force-deformation limit is exceeded


Material Model Calibration – Bar Slip Springs

Compression, - fs > fy

Compression, - fs < fy

Tension, fs > fy

Tension, fs< fy

Average bond strength, psi (fc in psi)Bar stress, fs (fy = tensile yield strength)

4.8 0.6YT c cf to fτ =

43YC cfτ =

MechanisticModel

Bond stress capacities from Lowes & Altoontash (2003)

26EC cfτ =

21ET cfτ =


0

5

10

15

20

0 10 20 30 40 50 60 70

BYJF

BY

Material Model Calibration – Bar Slip Springsmaximum slip (mm)

specimen number

0

1

2

3

4

5

0 10 20 30 40 50 60 70

specimen number

BYJF

BY

`

Max. slip / slip at activation

of full anchorage length


Material Model Calibration – Bar Slip Springs

� Envelope calibration is accomplished (within the model) using� Bond strength values� Reinforcing steel material properties� Anchorage length within the joint

� Cyclic response parameters calibrated using experimental data� rDisp = Displacement at reload / max. displacement = 0.25� rForce = Force at reload / max. force = 0.25� uForce = Force developed upon unloading = 0.0

� Stiffness deterioration is determined primarily by maximum deformation demand.

( )0.1

max0.3ki dδ = %( )

0.2

max0.6di dδ = %

� Strength deterioration� Is activated once slip exceeds the

slip level corresponding to ultimate stress in the reinforcing bars.

� Is observed upon reloading, with the result that bar-slip springs always exhibit positive tangent stiffness.

0 5 10 15-1000

-500

0

500

1000

slip (mm)

bar

-sp

rin

g f

orc

e (k

N)


Joint Element Validation

� Experimental Data Set

� 64 beam-column joint sub-assemblage tests from 13 investigations conducted in U.S., Japan, New Zealand

� Range of critical parameters

� Joint shear stress (MPa):

� Joint transverse steel ratio:

� Transverse steel contribution:

(to max shear load)

� Beam bar anchorage length:

� Average bond stress demand (MPa):

� Column axial load:

� Concrete compression strength (MPa):

0.34 ,0.8 ,1.46 c c c

f f f

[ ]0.000,0.007,0.038

[ ]14 ,23.5 ,32b b b

d d d

[ ]0.92,1.88,4.28

0.0 ,0.12 ,0.48 g c g c g cA f A f A f

[ ]24,43,107

[ ]0.00,0.56,2.54


Joint Element Validation – OpenSees Model

Lab Test

OpenSees Model


Validation Study Results

observed responsesimulated response

-6 -4 -2 0 2 4 6-300

-200

-100

0

100

200

300

Drift (%)

Colu

mn s

hea

r (k

N)

-4 -2 0 2 4

-200

-100

0

100

200

300

Drift (%)

Colu

mn s

hea

r (k

N)

-6 6-300

-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6-60

-40

-20

0

20

40

60

Drift (%)

Colu

mn S

hea

r (k

ips)

-5 -4 -3 -2 -1 0 1 2 3 4 5-60

-40

-20

0

20

Drift (%)

Colu

mn S

hea

r (k

ips)

40

60

-6 6

Specimen OSJ10

(Okaand Shiohara 1992)

Specimen PEER0850

(Alire2002)



Obs. Sim. Obs.Sim. /

Obs.Obs. Sim.

Sim. /

Obs.Obs.

Sim. /

Obs.Obs.

Sim. /

Obs.Obs.

Sim. /

Obs.Obs.

Sim. /

Obs.Obs.

Sim. /

Obs.

DWX1 BYJF BYJF 5.02 0.77 0.00 0.00 1.00 191 0.84 2.54 1.18 6.54 1.14 0.76 1.18 0.23 1.19

DWX2 BY BYJF 5.44 0.77 0.17 0.20 1.20 200 0.85 3.62 1.00 6.56 1.45 0.81 1.16 0.22 1.18

DWX3 BY BY 4.71 0.75 0.00 0.50 > 10 160 0.87 3.67 1.60 5.25 0.87 0.86 1.22 0.28 1.20

OKAJ1 BY BYJF 5.31 1.09 0.45 0.63 1.40 115 1.13 5.00 1.00 7.63 1.13 0.82 1.05 0.19 1.55

OKAJ2 BY BYJF 5.98 0.97 0.31 0.50 1.61 119 1.19 5.00 1.43 8.47 0.83 0.83 1.19 0.19 1.48

OKAJ3 BY BY 5.88 0.98 0.31 0.62 2.00 132 1.13 5.00 1.50 6.58 1.03 0.84 1.31 0.17 1.72

OKAJ4 BYJF BYJF 6.14 0.95 0.30 0.35 1.17 112 1.16 2.50 1.93 13.98 0.77 0.61 1.57 0.30 1.01

Maximum

Column Load

(kN)

Strength at Final

Drift Level /

Max. Strength

Unloading

Stiffness at Max.

Load (kN/mm)

Pinching RatioDrift at Max.

Load (%)

Post Yield Stiffness

(kN/mm)Joint

Specimens

Failure

Mechanism

Initial Stiffness

(kN/mm)

LSD35Aa-2 JF BYJF NA NA NA NA NA 24 1.41 2.35 1.00 NA NA NA NA NA NA

LSD35Ab-1 JF JF NA NA NA NA NA 24 1.07 1.18 1.00 NA NA NA NA NA NA

LSD35Ab-2 JF BYJF NA NA NA NA NA 23 1.46 2.35 1.05 NA NA NA NA NA NA

B11 BY BY 7.81 0.99 0.29 0.33 1.14 200 0.97 3.81 1.00 4.18 0.97 1.00 1.00 0.25 1.44

B12 BY BY 7.81 1.08 0.27 0.28 1.04 205 0.99 3.81 1.00 4.29 0.91 1.00 1.00 0.24 2.21

O4 BYJF BY 7.50 1.50 0.00 0.10 > 10 177 1.21 1.24 4.00 8.85 1.62 0.68 1.56 0.17 3.48

O5 BYJF BY 5.25 1.90 0.00 0.08 > 10 150 1.40 2.76 2.00 7.50 1.40 0.58 1.78 0.27 1.83

ALL 1.08 (0.22) 1.20 (0.66) 1.01 (0.21) 1.32 (0.48) 1.05 (0.26) 1.17 (0.26) 1.44 (0.35)

JF 1.17 (0.22) 1.06 (0.25) 1.03 (0.27) 1.16 (0.26) 1.16 (0.19) 1.29 (0.37)

BYJF 1.13 (0.27) 0.87 (0.32) 0.97 (0.21) 1.63 (0.59) 1.06 (0.30) 1.31 (0.32) 1.54 (0.42)

BY 1.00 (0.15) 1.41 (0.66) 0.99 (0.12) 1.34 (0.32) 0.99 (0.22) 1.08 (0.19) 1.47 (0.27)

ALL 1.06 (0.19) 1.29 (0.75) 0.99 (0.18) 1.25 (0.34) 1.02 (0.25) 1.17 (0.16) 1.35 (0.33)

JF 1.13 (0.23) 0.99 (0.25) 0.89 (0.19) 1.15 (0.29) 1.15 (0.22) 1.25 (0.43)

BYJF 1.07 (0.20) 0.92 (0.27) 1.00 (0.13) 1.42 (0.35) 1.06 (0.18) 1.32 (0.16) 1.35 (0.32)

BY 1.00 (0.13) 1.43 (0.77) 0.99 (0.09) 1.48 (0.26) 0.92 (0.18) 1.15 (0.10) 1.53 (0.28)

Mea

n (

C.O

.V.) All specimens

Failure

mechanism

correctly

simulated



� Failure mechanism� For joints exhibiting JF (joint failure prior to beam yielding), 76% accurate. � For joints exhibiting BY (beam yielding), 73% accurate.� Un-conservative for BYJF joints (beam yielding followed by joint failure).

� Initial and unloading stiffness� For all joints, mean of simulated to observed ranges from 0.92 to 1.17 with an

average C.O.V. = 0.3.

� Post-yield tangent stiffness� For joints that exhibit hardening, the mean ratio of simulated to observed post-yield

stiffness is 1.20 with a C.O.V. = 0.66.� For joints that exhibit BYJF, mean ratio of simulated to observed in 0.90 with a C.O.V.

= 0.30.

� Maximum strength � For all joints, mean of simulated to observed is 1.01 with a C.O.V. = 0.21.

� Drift at maximum strength� For all joints, mean of simulated to observed is 1.32 with a C.O.V. = 0.48.

� Strength at final drift level � For all joints, strength for final drift cycle is over-predicted� For joints that exhibit JF, mean of simulated to observed is 1.15 with a C.O.V = 0.22.� For joints that exhibit BYJF, mean of simulated to observed is significantly larger that

1.0, this is attributed to minimal strength deterioration in the bar-slip model.

� Pinching ratio (ratio of strength at zero drift to maximum strength)� For all joints, pinching ratio is over-predicted. � Pinching ratio is simulated best for joints that exhibit JF.


Modeling RC Bridge Columns

�Concrete Material Model

�Variable Plastic-Hinge Length Model

�Plastic-Hinge Length Calibration Study


Concrete 04 Material Model

� Comparison of simulated and observed response indicated concretematerial model did not represent well the initial compressive stiffness, especially for high-strength or well-confined concrete

� New model is revision of Concrete03 with

� Popovics (1973) model used to simulate envelope of compression response.This allows user to identify initial stiffness (default in ACI 318 model).

� Concrete develops tensile stress only under tensile strain

� Concrete04 material response:

0.000 0.002 0.004 0.006 0.0080.0

2.0

4.0

Stress (ksi)

Compression Response

Strain

0.0 0.00005 0.0001 0.000150.0

0.2

0.4Tension Response

Strain

-0.005 0.000 .005 0.010-2.0

0.0

2.0

4.0

Strain

Comp.(+) & Tension(-) Response


Variable Plastic-Hinge Length Model

� The expressions defining plastic-hinge length are calibrated to provide accurate prediction of global (e.g. drift) or local (e.g. demand measures).

� For performance-based earthquake engineering, it may be appropriate to have different hinge lengths for different demand levels or performance states.

� The variable plastic-hinge length model allows for use of the Beam-With-Hinges element with a hinge-length that is defined by

� Model parameters are calibrated as part of the validation study.

( )α β

− −= ⋅ +

s y bnp

n c

f f dM M Ll

M f2


Bridge Column Model Development

� The objective is to develop recommendations for using the BeamWithHinges element to predict bridge column damage.

� Experimental data from the PEER column database are being used.� Recommendations will include effective stiffness and re-calibration

of plastic-hinge length expressions.� Effective stiffness is calibrated to ensure accurate prediction of

yield displacement.� Hinge-length models are calibrated to enable precise prediction

of the EDPs that determine initial of damage states� EDPs include drift, plastic rotation, and concrete and steel strains.� Damage states include cracking, spalling, crushing and bar buckling.

� Several hinge-length models are considered.

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