Behavior and Modeling of Existing Reinforced Concrete Columns
Transcript of 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 =
• Based on principle tensile stress exceeding ft = 6 cf '
• Accounts for degradation due to flexural and bond cracks
a
d
a
d
kcV = ⎟⎟
⎠
⎞
da⎜
⎜
⎝
⎛ 1
gcc 0.8Ag
AfPf ⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛+
''
616
Sezen and Moehle, 2004
Shear Strength
• Degrades both Vs and Vc based on ductility
scn VVV +=
sdfA
kV ysws =
• Based on principle tensile stress exceeding ft = 6 cf '
• 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
Sezen and Moehle, 2004
Shear Strength
Sezen and Moehle, 2004
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%
Elwood and Moehle, 2005b
Drift at Axial Failure Model
24 1 tan 65100
tan 65tan 65
axial
st yt c
L sPA f d
∆ +⎛ ⎞ =⎜ ⎟ ⎛ ⎞⎝ ⎠+ ⎜ ⎟⎜ ⎟
⎝ ⎠
o
o
o
Elwood and Moehle, 2005b
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
How to apply models…
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
How to apply models…
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.
How to apply models…
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
Melek and Wallace (2004)
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
Melek and Wallace (2004)
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)
(Cho and Pincheira, 2005)
0.8
FEMA 356 under-predictssteel stress.
yACId
bs f
llf =
yACId
bs f
llf
32
80
/
. ⎟⎟⎠
⎞⎜⎜⎝
⎛=
Modified Equation (Cho and Pincheira, 2005)
(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
(Cho and Pincheira, 2005)
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.