Behavior and Modeling of Existing Reinforced Concrete Columns

Behavior and Modeling of Existing Reinforced Concrete Columns

Kenneth J. ElwoodUniversity of British Columbia

with contributions from

Jose Pincheira, Univ of WisconsinJohn Wallace, UCLA

Questions?What is the stiffness of the column?What is the strength of the column?What failure mode is expected?What is the drift capacity…

at shear failure?at axial failure?

How can we model this behavior for the analysis of a structure?What is the influence of poor lap splices?

Column response

−0.06 −0.04 −0.02 0 0.02 0.04 0.06−400

−300

−200

−100

0

100

200

300

400

Drift Ratio

She

ar (

kN)

Effective Stiffness

Strength

Drift Capacities

Effective stiffness

FEMA 356

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

P/Agf'c

EIef

f / EI

g

column tests moment curvature

Effective stiffnessFlexural Deformations:

φy

φy

2

6flex yL φ∆ =L

Does not accountfor end rotations due to bar slip!

Effective stiffnessSlip Deformations:

L

C T=Asfyδslip

u

u

bondstress

fy

steelstress

εy

steelstrain

= ½ εyl

l

8b s y

slip

Ld fu

φ∆ =

6 cu f ′≈

Effective stiffnessModeling options:

Stiffness based on moment-curvature analysis (or FEMA 356 recommendations)

Slip springs:8 y

slipb s y

Mukd f φ

=

Option 1 (with slip springs)

Use effective stiffness determined from column tests. More flexible than FEMA recommendations for low axial load.

Option 2 (without slip springs):

Effective stiffness

FEMA 356

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

P/Agf'c

EIef

f / EI

g

column tests flexure and slip Proposed

Elwood and Eberhard, 2006

Column response

−0.06 −0.04 −0.02 0 0.02 0.04 0.06−400

−300

−200

−100

0

100

200

300

400

Drift Ratio

She

ar (

kN)

Effective Stiffness

Strength

Drift Capacities

Shear Strength

Several models available to estimate shear strength:

Aschheim and Moehle (1992)Priestley et al. (1994)Konwinski et al. (1995)FEMA 356 (Sezen and Moehle, 2004)ACI 318-05

All models (except ACI) degrade shear strength with increasing ductility demand.

Shear Strengthscn VVV +=

sdfA

kV ysws =

kcV = ⎟⎟

⎠

⎞

da⎜

⎜

⎝

⎛ 1

gcc 0.8Ag

AfPf ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛+

''

616

• Based on principle tensile stress exceeding ft = 6 cf '

ft

(fn, vc)

ft

fnvc = ft +1

Sezen and Moehle, 2004

Shear Strengthscn VVV +=

sdfA

kV ysws =


• Accounts for degradation due to flexural and bond cracks

a

d

a

d

kcV = ⎟⎟

⎠

⎞

da⎜

⎜

⎝

⎛ 1

gcc 0.8Ag

AfPf ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛+

''

616


Shear Strength

• Degrades both Vs and Vc based on ductility

scn VVV +=

sdfA

kV ysws =


• Accounts for degradation due to flexural and bond cracks

00.20.40.60.8

11.2

0 2 4 6 8 10Displacement Ductility

kkcV = ⎟

⎟

⎠

⎞

da⎜

⎜

⎝

⎛ 1

gcc 0.8Ag

AfPf ⎟

⎟

⎠

⎞

⎜⎜

⎝

⎛+

''

616


Shear Strength


Column response

−0.06 −0.04 −0.02 0 0.02 0.04 0.06−400

−300

−200

−100

0

100

200

300

400

Drift Ratio

She

ar (

kN)

Effective Stiffness

Strength

Drift Capacities

Shear Failure

V Shear capacity

Large variation in response

µ + σ

µ - σµ + σ

µ - σ

Drift or Ductility

Flexural capacity

Elwood and Moehle, 2005a

Drift capacity depends on:

Drift at Shear Failure Model

=∆L

s "ρ

amount of transverse reinforcement

'cf

v

shear stress

'cg fA

P

axial load

1003

+45001

−401

− 1100

≥

Elwood and Moehle, 2005a

Drift at Axial Failure ModelV

Ps

Ps

Vd

Vd

dc

P

s

Aswfy

Aswfy

N Vsf

θ

∑ +=→ θθ sincos sfy VNPF

∑ +=→sdcfA

VNF ystsfx

θθθ

tancossin

µNVsf =Classic Shear-Friction

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=θµθθµθθ

cossinsincostan

sdcfA

P yst

dc

P

s

Aswfy

Aswfy

N Vsf

θ

Simplifying Assumptions

• V assumed to be zero since shear failure has occurred

• Dowel action of longitudinal bars (Vd) ignored

• Compression capacity of longitudinal bars (Ps) ignored

Elwood and Moehle, 2005b

Drift at Axial Failure Model

Relationships combine to give a design chart for determining drift capacities.

⎟⎟⎠

⎞⎜⎜⎝

⎛−+

=θµθθµθθ

cossinsincostan

sdcfA

P yst

θ ≈ 65º

µ vs. Drift at axial failure

sw

≈ 3%


Drift at Axial Failure Model

24 1 tan 65100

tan 65tan 65

axial

st yt c

L sPA f d

∆ +⎛ ⎞ =⎜ ⎟ ⎛ ⎞⎝ ⎠+ ⎜ ⎟⎜ ⎟

⎝ ⎠

o

o

o


0

5

10

15

20

25

30

35

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

drift at axial failure

P/(A

stf y

tdc/s

)

ModelFlexure-Shear FailureShear Failure

Drift models for flexural failuresFlexural strength will degrade for columns with Vp << Vo due to spalling, bar buckling, concrete crushing, etc.Several drift models have been developed:

Drift at onset of cover spalling:

Drift at bar-buckling:

Drift at 20% reduction in flexural capacity:

3.25(1 )(1 )(1 )10

vol ytbb be

c g c

f d P LkL f D DA f

ρ∆= + − +

′ ′

1.6(1 )(1 )10

spall

g c

P LL DA f

∆= − +

′

0.049 0.716 0.120 0.042 0.070f ytl

c g c

f s PL f d A f

ρρ

′′∆= + + − −

′ ′

50 for rectangular columns, 150 for spiral-reinforced columns

(Berry and Eberhard, 2004)

(Berry and Eberhard, 2005)

(Zhu, 2005)

How to apply models…

First classify columns based on shear strength:

Vp/Vo > 1.0 shear failure 1.0 ≥ Vp/Vo ≥ 0.6 flexure-shear failureVp/Vo < 0.6 flexure failure

61 0.8

6

2

st ytco g

c g

pp

A f df PV Aa d sf A

MV

L

′= + +

′

=

where


Shear failureForce-controlledDefine drift at shear failure using effective stiffness and Vo.

May be conservative if Vp ≈ Vo

Use drift at axial failure model to estimate ∆a/L

Very little data available for drift at axial failure for this failure mode, but model provides conservative estimate in most cases.

Do not use as primary component if V > Vo

Vo

12EIeff

V

drift

L3

∆a/L


Flexure-Shear failureDeformation-controlledMax shear controlled by 2Mp/L Use drift at shear failure model to estimate ∆s/LUse drift at axial failure model to estimate ∆a/LDo not use as primary component if drift demand > ∆s/L

Vp

12EIeff

V

drift

L3

∆a/L∆s/L

FEMA 356 limit forprimary componentfailing in shear.


Flexure failureDeformation-controlledMax shear controlled by 2Mp/L Use model for drift at 20% reduction in flexural capacity to estimate ∆f /LDo not use as primary component if drift demand > ∆f /LFor low axial loads, axial failure not expected prior to P-delta collapse.For axial loads above the balance point and light transverse reinforcement, column may collapse after spalling of cover.

Vp

12EIeff

V

drift

L3

∆f /L

Points to rememberModels provide an estimate of the meanresponse.

50% of columns may fail at drifts less than predicted by the models.

0.261.00Bar Buckling

0.430.97Spalling

0.271.03Flexural Failure

0.391.01Axial Failure

0.340.97Shear Failure

CoV ∆meas/∆calcMean ∆meas/∆calcDrift Model

Points to rememberShear and axial failure models based on database of columns experiencing:

flexure-shear failuresuni-directional lateral loads

All models except bar buckling and spalling only based on database of rectangular columns.

Use caution when applying outside the range of test data used to develop the models!

Shear and axial failure models are not coupled.If calculated drift at axial failure is less than the calculated drift at shear failure, assume axial failure occurs immediately after shear failure.

CharacteristicsHalf-scale, three column planar frameSpecimen 1:

Low axial load (P = 0.10f’cAg)

Specimen 2:Moderate axial load (P = 0.24f’cAg)

ObjectiveTo observe the process of dynamic shear and axial load failures when an alternative load path is provided for load redistribution

4’-10”

6’

Application of Drift Models –Shake Table Tests

Top of Column - Total Displ.

Center Column - Relative Displ. Full Frame - Total Displ.

Center Column Hysteresis

Specimen #1 – Low Axial Load

Top of Column - Total Displ.

Center Column - Relative Displ. Full Frame - Total Displ.

Center Column Hysteresis

Specimen #2 – Moderate Axial Load

-0.08 -0.04 0 0.04 0.08

-20

-10

0

10

20

Drift Ratio

Center Column Shear (kips)

-0.08 -0.04 0 0.04 0.08

-20

-10

0

10

20

Drift Ratio

Center Column Shear (kips)

Application of Drift Models –Shake Table Tests

P = 0.24f’cAgP = 0.10f’cAg

FEMA backbone

Backbonefrom driftmodels

Elwood and Moehle, 2003

Analytical Modelfor Shear-Critical Columns

sw

Beam-Column Element(including

flexural and slip deformations)

Zero-length Shear Spring

Zero-length Axial Spring

Axial-failure model

Shear-failure model

drift

V

P

VP

δs

δa

Elwood, 2004

Analytical Modelfor Shear-Critical Columns

sw

Test dataStatic analysislimit state surface

Elwood, 2004

Benchmark Shake Table Tests

E-Defence, Japan, 2006

NCREE, Taiwan, 2005

PEER, 2006

NCREE Shake Table Test 1

NCREE Shake Table Test 2

OpenSees Analysis – Test 1

OpenSees Analysis – Test 2

Lap Splice Failures

18"

18"

18"

18"

Section A-A

Section B-B

20"

6'-0"

B

A

B

A

Melek and Wallace (2004) Six FullSix Full--Scale SpecimensScale Specimens•• 18 in. square column18 in. square column•• 8 8 –– #8 longitudinal bars#8 longitudinal bars•• #3 ties with 90#3 ties with 90°° hookshooks•• 20d20dbb lap splicelap splice

Tested with Lateral and Axial Tested with Lateral and Axial LoadLoad•• Lateral LoadLateral Load

Standard Loading HistoryStandard Loading HistoryNear Field Loading HistoryNear Field Loading History

•• Axial LoadAxial LoadConstantConstant

Melek and Wallace (2004)

-12 -8 -4 0 4 8 12Lateral Drift (%)

-1.2

-0.8

-0.4

0

0.4

0.8

1.2

Bas

e M

omen

t / Y

ield

Mom

ent

2S10M2S20M2S30M2S20M (FEMA 356)

S10MI – S20MI – S30MI


S20HIN S20HIN –– Axial Load Capacity Axial Load Capacity MaintainedMaintainedNear Fault Displacement History (Less Near Fault Displacement History (Less cycles)cycles)

Concrete cover intactConcrete cover intact

S20MI, S20HI, S30MI, S30XIS20MI, S20HI, S30MI, S30XIAxial load capacityAxial load capacity llost due to buckling of ost due to buckling of longitudinal barslongitudinal bars

9090°° ties at 4” and 16” above pedestal ties at 4” and 16” above pedestal opened up opened up

Concrete cover lostConcrete cover lost

Axial Load Capacity


FEMA 356 lap splice provisions

Adjust yield stress based on lap splice length:

Cho and Pinchiera (2005) evaluated provisions using detailed bar analysis calibrated to test data.

yACId

bs f

llf =

fs

lb

Slip

Bond Stress

Strain

Stre

ss

εy

f y

Esh

Spring model for anchored bar

(Cho and Pincheira, 2005)

Harajli (2002)

FEMA 356 lap splice provisions

0 0.5 1 1.5lb / ldACI

0

0.5

1

1.5f s

/ fy

Calculated (S10MI)Calculated (FC4)FEMA 356

lb / ldACI = 0.65(lb = ls = 20 in. for S10MI)

lb / ldACI = 0.60(lb = ls = 24 in. for FC4)


0.8

FEMA 356 under-predictssteel stress.

yACId

bs f

llf =

yACId

bs f

llf

32

80

/

. ⎟⎟⎠

⎞⎜⎜⎝

⎛=

Modified Equation (Cho and Pincheira, 2005)


Modified Equation (Cho and Pincheira, 2005)

0 0.5 1 1.5lb /(0.8* ldACI)

0

0.5

1

1.5f s

/ fy

Calculated (S10MI)Calculated (FC4)FEMA 356Proposed


Modified Steel Stress Equation (Cho and Pincheira, 2005)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.40 0.60 0.80 1.00 1.20 1.40 1.60

Calculated Moment / Measured Moment @ Splice Failure

Cum

ulat

ive

Pro

babi

lity

FEMA 356 steel stress Proposed steel stress

ReferencesBerry, M., Parrish, M., and Eberhard, M., (2004) “PEER Structural Performance Database User’s Manual,”(www.ce.washington.edu/~peera1), Pacific Earthquake Engineering Research Center, University of California, Berkeley.Berry, M., and Eberhard, M., (2004) “Performance Models for Flexural Damage in Reinforced Concrete Columns,” PEER report 2003/18, Berkeley: Pacific Earthquake Engineering Research Center, University of California.Berry, M., and Eberhard, M., (2005) “Practical Performance Model for Bar Buckling”, Journal of Structural Engineering, ASCE, Vol. 131, No. 7, pp. 1060-1070.Cho, J.-Y., and Pincheira, J.A. (2006) “Inelastic Analysis of Reinforced Concrete Columns with Short Lap Splices Subjected to Reversed Cyclic Loads” ACI Structural Journal, Vol 103, No 2.Elwood, K.J., and Eberhard, M.O. (2006) “Effective Stiffness of Reinforced Concrete Columns”, PEER Research Digest, PEER 2006/01.Elwood, K.J., and Moehle, J.P., (2005a) “Drift Capacity of Reinforced Concrete Columns with Light Transverse Reinforcement”, Earthquake Spectra, Earthquake Engineering Research Institute, vol. 21, no. 1, pp. 71-89.Elwood, K.J., and Moehle, J.P., (2005b) “Axial Capacity Model for Shear-Damaged Columns”, ACI Structural Journal, American Concrete Institute, vol. 102, no. 4, pp. 578-587.Elwood, K.J., (2004) “Modelling failures in existing reinforced concrete columns”, Canadian Journal of Civil Engineering, vol. 31, no. 5, pp. 846-859.Elwood, K.J., and Moehle, J.P., (2004) “Evaluation of Existing Reinforced Concrete Columns”, Proceedings of the Thirteenth World Conference on Earthquake Engineering, Vancouver, BC, Canada, August 2004, 15 pages.Elwood, K. J. and Moehle, J.P., (2003) “Shake Table Tests and Analytical Studies on the Gravity Load Collapse of Reinforced Concrete Frames”, PEER report 2003/01, Berkeley: Pacific Earthquake Engineering Research Center, University of California, 346 pages.Fardis, M.N. and D.E. Biskinis (2003) “Deformation Capacity of RC Members, as Controlled by Flexure or Shear,” OtaniSymposium, 2003, pp. 511-530.Melek, M., and Wallace, J. W., (2004) "Cyclic Behavior of Columns with Short Lap Splices,“ ACI Structural Journal, V. 101, No. 6, pp. 802-811.Panagiotakos, T.B., and Fardis, M.N. (2001) “Deformation of Reinforced Concrete Members at Yielding and Ultimate”, ACI Structural Journal, Vol 98, No 2.Sezen, H., and Moehle, J.P., (2004) “Shear Strength Model for Lightly Reinforced Concrete Columns,” Journal of Structural Engineering, Vol. 130, No. 11, pp. 1692-1703.Syntzirma, D.V., and Pantazopoulou, S.J. (2006) “Deformation Capacity of R.C. Members with Brittle Details under Cyclic Loads”, American Concrete Institute, ACI – SP 236.

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Behavior and Modeling of Existing Reinforced Concrete Columns