Behavior and Modeling of Existing Reinforced Concrete Columns Kenneth J. Elwood University of British Columbia with contributions from Jose Pincheira, Univ of Wisconsin John 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 400 Effective Stiffness 300 Strength 200 Shear (kn) 100 0 100 200 300 Drift Capacities 400 0.06 0.04 0.02 0 0.02 0.04 0.06 Drift Ratio
Effective stiffness column tests moment curvature 1.0 EIeff / EIg 0.8 0.6 0.4 FEMA 356 0.2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 P/A g f' c
Effective stiffness Flexural Deformations: φ y L = flex 2 L φ y 6 Does not account for end rotations due to bar slip! φ y
Effective stiffness Slip Deformations: L u l bond stress u steel stress f y steel strain ε y δ C T=A s f slip = ½ ε y l y = slip Ld f b s y 8u u 6 f c φ
Effective stiffness Modeling options: Option 1 (with slip springs) Option 2 (without slip springs): Stiffness based on moment-curvature analysis (or FEMA 356 recommendations) Use effective stiffness determined from column tests. More flexible than FEMA recommendations for low axial load. Slip springs: u M kslip = d f 8 y φ b s y
Effective stiffness 1.0 0.8 column tests flexure and slip Proposed EIeff / EIg 0.6 0.4 FEMA 356 0.2 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 P/A g f' c Elwood and Eberhard, 2006
Column response 400 Effective Stiffness 300 Strength 200 Shear (kn) 100 0 100 200 300 Drift Capacities 400 0.06 0.04 0.02 0 0.02 0.04 0.06 Drift Ratio
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 Strength V = V + V n c s (f n, v c ) V = c 1 k a d 6 f ' c 1+ 6 P f ' c A g 0.8A g f t V s = k A sw s f y d vc = f t 1+ f n f t Based on principle tensile stress exceeding f t = 6 f ' c Sezen and Moehle, 2004
Shear Strength s c n V V V + = s d f A k V y sw s = Based on principle tensile stress exceeding f t = 6 c f ' Accounts for degradation due to flexural and bond cracks a d a d k c V = d a 1 g c c 0.8A g A f P f + ' ' 6 1 6 Sezen and Moehle, 2004
Shear Strength V = V + V V n V = c s = k c A sw s s 1 k a 6 d f y d f ' c 1+ 6 P f ' c A g k 0.8A g 1.2 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 Displacement Ductility Based on principle tensile stress exceeding f t = 6 Accounts for degradation due to flexural and bond cracks Degrades both V s and V c based on ductility f ' c Sezen and Moehle, 2004
Shear Strength Sezen and Moehle, 2004
Column response 400 Effective Stiffness 300 Strength 200 Shear (kn) 100 0 100 200 300 Drift Capacities 400 0.06 0.04 0.02 0 0.02 0.04 0.06 Drift Ratio
Shear Failure V Flexural capacity Shear capacity µ + σ µ - σ µ + σ µ - σ Large variation in response Drift or Ductility Elwood and Moehle, 2005a
Drift at Shear Failure Model Drift capacity depends on: amount of transverse reinforcement shear stress axial load L = 4 ρ s " 1 500 v ' f c 1 40 P A f ' g c + 3 100 1 100 Elwood and Moehle, 2005a
Drift at Axial Failure Model V P Simplifying Assumptions V d A sw f y P s N θ A sw f y d c V sf V d s V assumed to be zero since shear failure has occurred Dowel action of longitudinal bars (V d ) ignored Compression capacity of longitudinal bars (P s ) ignored P s F = θ + y P N cos Vsf sinθ Ast f yd = + c tanθ Fx Nsinθ Vsf cosθ s Classic Shear-Friction V sf = Nµ P = A st s f yd c cos θ + µ sinθ tanθ sinθ µ cosθ Elwood and Moehle, 2005b
sw Drift at Axial Failure Model Relationships combine to give a design chart for determining drift capacities. P = A st s f yd c cos θ + µ sinθ tanθ sinθ µ cosθ θ 65º µ vs. Drift at axial failure 3% Elwood and Moehle, 2005b
Drift at Axial Failure Model P/(Astfytdc/s) 35 30 25 20 15 Model Flexure-Shear Failure Shear Failure 2 o 4 1 tan 65 + = L axial 100 s tan 65 o + P A st f yt d o c tan 65 10 5 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 drift at axial failure Elwood and Moehle, 2005b
Drift models for flexural failures Flexural strength will degrade for columns with V p << V o due to spalling, bar buckling, concrete crushing, etc. Several drift models have been developed: Drift at onset of cover spalling: L spall P L = 1.6(1 )(1 + ) A f 10D Drift at bar-buckling: ρ g c vol f bb yt db P L = 3.25(1 + ke )(1 )(1 + ) L f D A f 10D c g c (Berry and Eberhard, 2004) 50 for rectangular columns, 150 for spiral-reinforced columns Drift at 20% reduction in flexural capacity: f ρ yt ρ f s P = 0.049 + 0.716 + l 0.120 0.042 0.070 L f d A f c g c (Berry and Eberhard, 2005) (Zhu, 2005)
How to apply models First classify columns based on shear strength: V p /V o > 1.0 shear failure 1.0 V p /V o 0.6 flexure-shear failure V p /V o < 0.6 flexure failure where V o 6 f c P = 1+ 0.8Ag + ad 6 f A c g A f d st s yt V p = 2M L p
How to apply models Shear failure Force-controlled Define drift at shear failure using effective stiffness and V o. May be conservative if V p V o 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 > V o V V o 12EI eff L 3 a/l drift
How to apply models Flexure-Shear failure Deformation-controlled Max shear controlled by 2M p /L Use drift at shear failure model to estimate s /L Use drift at axial failure model to estimate a /L Do not use as primary component if drift demand > s /L V V p 12EI eff L 3 FEMA 356 limit for primary component failing in shear. s /L a/l drift
How to apply models Flexure failure Deformation-controlled Max shear controlled by 2M p /L Use model for drift at 20% reduction in flexural capacity to estimate f /L Do not use as primary component if drift demand > f /L For 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. V V p 12EI eff L 3 f /L drift
Points to remember Models provide an estimate of the mean response. 50% of columns may fail at drifts less than predicted by the models. Drift Model Shear Failure Axial Failure Flexural Failure Spalling Bar Buckling Mean meas / calc 0.97 1.01 1.03 0.97 1.00 CoV meas / calc 0.34 0.39 0.27 0.43 0.26
Points to remember Shear and axial failure models based on database of columns experiencing: flexure-shear failures uni-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.
Application of Drift Models Shake Table Tests 4-10 6 Characteristics Half-scale, three column planar frame Specimen 1: Low axial load (P = 0.10f c A g ) Specimen 2: Moderate axial load (P = 0.24f c A g ) Objective To observe the process of dynamic shear and axial load failures when an alternative load path is provided for load redistribution
Specimen #1 Low Axial Load Top of Column - Total Displ. Center Column Hysteresis Center Column - Relative Displ. Full Frame - Total Displ.
Specimen #2 Moderate Axial Load Top of Column - Total Displ. Center Column Hysteresis Center Column - Relative Displ. Full Frame - Total Displ.
Application of Drift Models Shake Table Tests p s) k i a r( e h m ns C ol u r C ente 20 10 0-10 -20 P = 0.10f c A g -0.08-0.04 0 0.04 0.08 Drift Ratio p s) k i a r( e h m ns C ol u r C ente 20 10 0-10 -20 P = 0.24f c A g FEMA backbone Backbone from drift models -0.08-0.04 0 0.04 0.08 Drift Ratio Elwood and Moehle, 2003
sw Analytical Model for Shear-Critical Columns P V Shear-failure model V Zero-length Axial Spring Zero-length Shear Spring δ s δ a drift Beam- Column Element (including flexural and slip deformations) P Axial-failure model Elwood, 2004
sw Analytical Model for Shear-Critical Columns Test data Static analysis limit state surface Elwood, 2004
Benchmark Shake Table Tests NCREE, Taiwan, 2005 E-Defence, Japan, 2006 PEER, 2006
NCREE Shake Table Test 1
NCREE Shake Table Test 2
OpenSees Analysis Test 1
OpenSees Analysis Test 2
Lap Splice Failures
Melek and Wallace (2004) Six Full-Scale Specimens 18 in. square column 8 #8 longitudinal bars #3 ties with 90 hooks 20d b lap splice Tested with Lateral and Axial Load Lateral Load Standard Loading History Near Field Loading History Axial Load 6'-0" B A B A 20" 18" 18" 18" Section B-B 18" Section A-A Constant Melek and Wallace (2004)
S10MI S20MI S30MI 1.2 Base Moment / Yield Moment 0.8 0.4 0-0.4-0.8 2S10M 2S20M 2S30M 2S20M (FEMA 356) -1.2-12 -8-4 0 4 8 12 Lateral Drift (%) Melek and Wallace (2004)
Axial Load Capacity S20MI, S20HI, S30MI, S30XI Axial load capacity lost ost due to buckling of longitudinal bars 90 ties at 4 and 16 above pedestal opened up Concrete cover lost S20HIN Axial Load Capacity Maintained Near Fault Displacement History (Less cycles) Concrete cover intact Melek and Wallace (2004)
FEMA 356 lap splice provisions Adjust yield stress based on lap splice length: f = s b ACI d Cho and Pinchiera (2005) evaluated provisions using detailed bar analysis calibrated to test data. l l f y
Spring model for anchored bar l b f s Stress f y E sh Bond Stress Harajli (2002) ε y Strain Slip (Cho and Pincheira, 2005)
FEMA 356 lap splice provisions f s / f y 1.5 1 0.5 Calculated (S10MI) Calculated (FC4) FEMA 356 l b / l d ACI = 0.60 (l b = l s = 24 in. for FC4) FEMA 356 under-predicts steel stress. 0 l b / l d ACI = 0.65 (l b = l s = 20 in. for S10MI) 0.8 0 0.5 1 1.5 ACI l b / l d (Cho and Pincheira, 2005)
Modified Equation (Cho and Pincheira, 2005) f = s l l b ACI d f y f s = l b l ACI d 0. 8 2/ 3 f y (Cho and Pincheira, 2005)
Modified Equation (Cho and Pincheira, 2005) 1.5 1 Calculated (S10MI) Calculated (FC4) FEMA 356 Proposed f s / f y 0.5 0 0 0.5 1 1.5 l b /(0.8* l ACI d ) (Cho and Pincheira, 2005)
Modified Steel Stress Equation (Cho and Pincheira, 2005) FEMA 356 steel stress Proposed steel stress 1 0.9 0.8 Cumulative Probability 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0.40 0.60 0.80 1.00 1.20 1.40 1.60 Calculated Moment / Measured Moment @ Splice Failure
References Berry, 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, Otani Symposium, 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.