reinforced concrete beam-column joint macroscopic super-element models

7/30/2019 Reinforced Concrete Beam-Column Joint Macroscopic Super-Element Models

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Reinforced Concrete Beam-

Column Joint: Macroscopic

Super-element models

-Nilanjan Mitra

(work performed as a PhD student while at University of Washington between 2001-2006)


2/24

Need for the study

Reinforced concrete beam column joints

subjected to earthquake loading

Experimental

Investigation

@ UW

I-280 Freeway, San Francisco, CA

following Loma Prieta Earthquake in 1989

Courtesy: NISEE, Univ. of California, Berkeley.


3/24

Loading in a joint region

Earthquake Loading of Beam-Column Joint

compression resultant(concrete and steel)

shear resultant

(concrete)

Earthquake Loading of Beam-Column Joint



shear resultant

(concrete)

shear resultant

(concrete) tension resultant (steel)


4/24

anchorage bond stress acting on

joint core concretecompression force carried by

joint core concrete

Internal load distribution in a joint


5/24

Macroscopic beam-column joint element models


6/24



7/24



8/24

shearpanel

external node

internal node

rigid externalinterface plane

shown with finite widthto facilitate discussion

beamelement

zero-width region

interface-shear spring

bar-slip spring

zero-length

zero-length

element

column

Proposed Beam-column super-element model

4-noded 12-dof element

8 bar-slip springs to simulate

anchorage failure

4 interface-shear springs to simulate

shear transfer failure at joint interface

1 shear-panel to simulate inelastic

action of shear within joint core

Note: The location of the bar-slip

springs is at the centroid of the

tension-compression couple at nominal

strength of the beams.

[Mitra & Lowes; J. Structural Eng. ASCE, 2007: 133 (1): 105-20 ]


9/24

Joint element formulation: Kinematics

External, Internal and Component deformation


10/24

Joint element formulation: Equilibrium

External, Internal and Component forces

Solution of element state achieved by an iterative procedure and requires

solving for zero reaction in the 4 internal degrees of freedom


11/24

Characterized by

Response envelope

Unload reload path

Damage rules

Hysteretic one dimensional material model

deformation

load

(ePd1,ePf1)

(ePd4,ePf4)

(ePd3,ePf3)

(ePd2,ePf2)

(eNd3,eNf3) (eNd2,eNf2)

(*,uForceP.ePf3)

(dmin,f(dmin))

(dmax,f(dmax))

(rDispP.dmax,rForceP.f(dmax))

(rDispN.dmin,rForceN.f(dmin))

(*,uForceN.eNf3)

(eNd1,eNf1)

(eNd4,eNf4)


12/24

Damage simulation in material model

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-8

-6

-4

-2

0

2

4

6

8

deformation

load

without damage

with unloading stiffness damage

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-8

-6

-4

-2

0

2

4

6

8

deformation

load

without damage

with reloading stiffness damage

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-8

-6

-4

-2

0

2

4

6

8

deformation

load

without damage

with strength damage

3 41 max 2i d

max min

max

max min

max. ,i id d

ddef def

.f Noofloadcycle

fAccumulatedEner

01 ki ik k max max 01

f

iif f

max max0

1d

ii

d d


13/24

Damage simulation in material model

loadhistoryi

monotonic

monotonicloadhistory

dEE

EgE d

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-8

-6

-4

-2

0

2

4

6

8

deformation

load

without damage

with all 3 damage rules

-0.015 -0.01 -0.005 0 0.005 0.01 0.015-5

-4

-3

-2

-1

0

1

2

3

4

5

deformation

load

with all 3 damages (Energy)

with all 3 damages (Cyclic)

max4

du

u

Energy criterion

No. of load cycle criterion:

rain-flow-counting algorithm


14/24

Shear-panel calibration

column

shear

panel

Shear panel envelope calibration

MCFT

Diagonal compression strut

Compression envelope reduction

Determination of hysteretic model

parameters

Typical response envelope

Observed Simulated

SpecimenSE

8

(Stevensetal.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

Shearstress(MPa)


15/24

Shear panel envelope calibration using proposed

Diagonal compression strut mechanism

_ coscstrut strut strstrut

jnt

f w

w

Mander et al. (1988) concrete

Column longitudinal and joint hoop

steel confine the strut.

Reduction in concrete to account for

perpendicular tensile stress to the strut

cyclic loading.

Strut force is converted to panel shear

stress as


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2

_

_

3.62 2.82 1 0.

0.45 0.

cstrut t t t

cMander cc cc cc

t

cc

f

Proposed concrete compression envelope reduction

0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

t

/ cc

f

c_obs

/fc

_Mander

Data with j

> 0

Data with j

= 0

Vecchio 1986

Stevens 1991

Hsu 1995

Noguchi 1992

Proposed eq. forj

> 0

Proposed eq. forj

= 0

2

_

_

0.36 0.60 1 0.

0.75 0.

cstrut t t t

cMander cc cc cc

t

cc

f

0j 0j Eq. for Eq. for


17/24

Comparison of MCFT and Diagonal Compression

Strut model in shear-panel envelope calibration

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

mcft_cyclic/max

0.55

JF

BYJF

BY

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

diagonal_strut

/max

JF

BYJF

BY

[J. Structural Eng. ASCE, 2005: 131 (6) ]

Transverse steel contribution to shear stress


18/24

Bar slip material model calibration

column

Bar-slip spring

Mechanistic model :- envelope

Hysteretic model calibration

Strength deterioration model

-2 0 2 4 6 8 10 12 14 16-1000

-500

0

500

1000

slip (mm)

ba

r-springforce(kN)

Typical response envelope


19/24

Bar slip mechanistic model

Assumptions for anchorage response of bond within the joint region:

Bond stress uniform for elastic reinforcement, piecewise uniform for reinforcement

loaded beyond yield

Slip is the relative movement of reinforcement bar with respect to the joint perimeter

Slip is a function of strain distribution in the joint

Bar exhibits zero slip at zero bar stress

2

0

2

fsl

fsE b Eslip s

b b

ldd xdx f

AE Ed

0

eye

e

lll

yEb Y bslip e

b bhl

fd dd xdx xlAE EAE

22

2 2yy yeE Y

s

b b

fl llf

EdEEd

Mechanistic model


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Strength deterioration

Is activated once slip exceeds the slip level corresponding to ultimate stressin the reinforcing bars.

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

0 5 10 15 200

1

2

3

4

5

specimen number

maximumslip/

slipwithanchoragelengtheq

ualtojointwidth

BYJF

BY

0 5 10 15 200

5

10

15

20

specimen number

Simulatedmaximum

bar-slip

BYJF

BY

max, lim max,f fi i ult i l d d d

Strength deterioration calibration for bar-slip spring

S f lib i h j i d l


21/24

Steps for calibrating the joint model

Calculate moment curvature of beams and columns

From moment curvature analysis determine

moment associated with first yield of the reinforcing bar

tension-compression couple distance at nominal yield strength

neutral axis depth at nominal yield strength

Define joint elements parameters using joint geometry and tension-compression

couple distance

Determine concrete compression strut response

Mander model for concrete

Concrete strength reduction eq. proposed to account for perpendicular cracks

and cyclic loading

Hysteretic parameters defined for shear panel

Determine bar-slip response

Mechanistic model for bond

Hysteretic parameters defined for bar-slip model

Interface slip-springs are defined to be stiff and elastic

M d l i l i


22/24

Concrete Stress-Strain

(Compressive only,no tensile strength)

Reinforcing Steel Stress-Strain

Beam-Column Elements:

Force based lumped plasticity element

Plastic Hinge region

Elastic region

Fiber discretisation

joint element

plastic hinge length

column axial load

applied under load control

beam-column element

lateral load applied

under displacement

control

Model simulation

Labt

est

OpenSees Model

V lid ti t d


23/24

Validation study

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

-200

-100

0

100

200

300

Drift (%)

Columnshear(kN)

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

-200

-100

0

100

200

300

Drift (%)

Columnshear(kN)

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

-200

-100

0

100

200

300

Drift (%)

Columnshear(kN)

Specimen OSJ10:

V lid ti t d di i & l i


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Validation study discussion & conclusion Failure mechanism

For joints exhibiting JF (joint failure prior to beam yielding), 82%accurate.

For joints exhibiting BYJF (beam yielding followed by joint failure),89% accurate.

For joints exhibiting BY (beam yielding), 94% accurate.

Initial and unloading stiffness

For all joints, mean of simulated to observed ranges from 1.03 to 1.06with an average C.O.V. = 0.15.

Post-yield tangent stiffness

For joints that exhibit BYJF, mean ratio of simulated to observed is 1.0with a C.O.V. = 0.22.

Maximum strength

For all joints, mean of simulated to observed is 1.03 with a C.O.V. =0.17.

Drift at maximum strength

For all joints, mean of simulated to observed is 1.12 with a C.O.V. =0.27.

Strength at final drift level

For all joints, strength for final drift cycle is 1.04 with a C.O.V = 0.2.

Pinching ratio (ratio of strength at zero drift to maximum strength)

For all joints, pinching ratio is 1.04 with a C.O.V = 0.12.

reinforced concrete beam-column joint macroscopic super-element models

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